<PAGE>   1
                                                                     EXHIBIT 4.2




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                           BRIGHAM EXPLORATION COMPANY

                                    Borrower


                                       AND

                    CHASE BANK OF TEXAS, NATIONAL ASSOCIATION

                                     Trustee


                                 ---------------


                                I N D E N T U R E

                          Dated as of August ___, 1998


                                 ---------------


                                   $50,000,000
                   Senior Subordinated Secured Notes due 2003



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<PAGE>   2

                                TABLE OF CONTENTS
<TABLE>
<S>                                                                                                              <C>
PRELIMINARY STATEMENT.............................................................................................1

ARTICLE I
         DEFINITIONS..............................................................................................1
         Section 1.01  Definitions................................................................................1
         Section 1.02  Accounting Procedures and Interpretation..................................................15

ARTICLE II
         ISSUE, DESCRIPTION, FORM, EXECUTION, REGISTRATION
         OF TRANSFER AND EXCHANGE OF NOTES.......................................................................16
         Section 2.01  Form and Dating...........................................................................16
         Section 2.02  Execution and Authentication..............................................................16
         Section 2.03  Denomination of Notes and Record Date.....................................................16
         Section 2.04  Manual Execution..........................................................................16
         Section 2.05  Transfer and Exchange.....................................................................17
         Section 2.06  Replacement Notes.........................................................................18
         Section 2.07  Cancellation of Notes.....................................................................18
         Section 2.08  No Third Party Benefit....................................................................18

ARTICLE III
         SUBORDINATION...........................................................................................19

ARTICLE IV
         SECURITY FOR THE OBLIGATIONS............................................................................19
         Section 4.01  Security..................................................................................19

ARTICLE V
         [RESERVED]..............................................................................................20

ARTICLE VI
         [RESERVED]..............................................................................................20

ARTICLE VII
         AFFIRMATIVE COVENANTS...................................................................................20
         Section 7.01  Financial Statements and Reports..........................................................20
         Section 7.02  Litigation................................................................................22
         Section 7.03  Maintenance, Etc..........................................................................22
         Section 7.04  Environmental Matters.....................................................................23
         Section 7.05  Further Assurances........................................................................23
         Section 7.06  Performance of Obligations................................................................24
         Section 7.07  Engineering Reports.......................................................................24
         Section 7.08  Intentionally Omitted.....................................................................25
         Section 7.09  Additional Collateral.....................................................................25
</TABLE>



                                       -i-

<PAGE>   3

<TABLE>
<S>              <C>                                                                                            <C>
         Section 7.10  ERISA Information and Compliance..........................................................26
         Section 7.11  Subsidiary Security.......................................................................26

ARTICLE VIII
         NEGATIVE COVENANTS......................................................................................27
         Section 8.01  Debt......................................................................................27
         Section 8.02  Liens.....................................................................................27
         Section 8.03  Investments, Loans and Advances...........................................................28
         Section 8.04  Dividends, Distributions and Redemptions..................................................29
         Section 8.05  Sales and Leasebacks......................................................................29
         Section 8.06  Nature of Business........................................................................29
         Section 8.07  Mergers, Etc..............................................................................29
         Section 8.08  Proceeds of Notes.........................................................................29
         Section 8.09  ERISA Compliance..........................................................................30
         Section 8.10  Sale of Oil and Gas Properties............................................................30
         Section 8.11  Environmental Matters.....................................................................31
         Section 8.12  Transactions with Affiliates..............................................................31
         Section 8.13  Negative Pledge Agreements................................................................31
         Section 8.14  Gas Imbalances, Take-or-Pay Prepayments...................................................31
         Section 8.15  Borrower as Operator......................................................................32
         Section 8.16  Consolidated Interest Coverage Ratio......................................................32

ARTICLE IX
         PAYMENT OF THE NOTES....................................................................................32
         Section 9.01  Repayment.................................................................................32
         Section 9.02  Interest..................................................................................32
         Section 9.03  Payments and Computations.................................................................34

ARTICLE X
         DEFAULT AND REMEDIES....................................................................................36
         Section 10.01  Events of Default........................................................................36
         Section 10.02  Remedies.................................................................................38
         Section 10.03  Production and Proceeds..................................................................38
         Section 10.04  Set-Off..................................................................................39

ARTICLE XI
         THE AGENT...............................................................................................39
         Section 11.01  Authorization and Action.................................................................39
         Section 11.02  Agent's Reliance, Etc....................................................................39
         Section 11.03  The Agent and Its Affiliates.............................................................40
         Section 11.04  Noteholders Loan Decision................................................................40
         Section 11.05  Indemnification..........................................................................40
         Section 11.06  Successor Agent..........................................................................40

ARTICLE XII
         TRUSTEE.................................................................................................41
</TABLE>



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<PAGE>   4
<TABLE>
<S>              <C>                                                                                            <C>
         Section 12.01  Duties of Trustee........................................................................41
         Section 12.02  Rights of Trustee........................................................................42
         Section 12.03  Individual Rights of Trustee.............................................................43
         Section 12.04  Trustee's Disclaimer.....................................................................43
         Section 12.05  Notice of Defaults.......................................................................43
         Section 12.06  Reports by Trustee to Noteholders........................................................43
         Section 12.07  Compensation and Indemnity...............................................................44
         Section 12.08  Replacement of Trustee...................................................................45
         Section 12.09  Successor Trustee by Merger, etc.........................................................45
         Section 12.10  Eligibility, Disqualification............................................................45
         Section 12.11  Preferential Collection of Claims Against Borrower.......................................46
         Section 12.12  Appointment of Co-Trustee................................................................46

ARTICLE XIII
         MISCELLANEOUS...........................................................................................47
         Section 13.01  Interpretation and Survival of Provisions................................................47
         Section 13.02  Costs, Expenses and Taxes................................................................47
         Section 13.03  No Waiver; Modifications in Writing......................................................49
         Section 13.04  Binding Effect; Assignment...............................................................49
         Section 13.05  Communications...........................................................................50
         Section 13.06  Governing Law............................................................................51
         Section 13.07  Arbitration..............................................................................51
         Section 13.08  Confidentiality..........................................................................52
         Section 13.09  Execution in Counterparts................................................................53
         Section 13.10  Trust Indenture Act Controls.............................................................53
         Section 13.11  Communication by Noteholders with Other Noteholders......................................53
         Section 13.12  Certificate and Opinion as to Conditions Precedent.......................................53
         Section 13.13  Statements Required in Certificate or Opinion............................................53
         Section 13.14  Rules by Trustee and Agents..............................................................54
         Section 13.15  Legal Holidays...........................................................................54
</TABLE>


EXHIBITS

         Exhibit A    Form of Note
         Exhibit B    Form of Guaranty Agreement
         Exhibit C    Form of Subordination Agreement
         Exhibit D    Form of Security Agreement
         Exhibit E    Form of Security Agreement
         Exhibit F    Form of Mortgage, Deed of Trust, Assignment of Production,
                           Security Agreement and Financing Statement
         Exhibit G    Acceptance of Appointment



                                      -iii-

<PAGE>   5

         INDENTURE, dated as of August ___, 1998, between BRIGHAM EXPLORATION
COMPANY, a corporation duly organized and existing under the laws of the State
of Delaware (hereinafter sometimes referred to as the "Borrower"), and Chase
Bank of Texas, National Association, a national banking association existing
under the laws of the United States (hereinafter sometimes referred to as the
"Trustee").

                              PRELIMINARY STATEMENT

         All covenants and agreements made by the Borrower herein are for the
benefit and security of the holders of the Borrower's Senior Subordinated
Secured Notes due 2003.


                                    ARTICLE I
                                   DEFINITIONS

         Section 1.01  Definitions.

         "Acquired Shares" means _____________ shares of Common Stock acquired
by the Noteholders on the Funding Date in accordance with Section 2.01 of the
Securities Purchase Agreement and any additional shares of Common Stock of the
Borrower issued to the Noteholders after the Funding Date in accordance with
Section 2.01(ii) of the Securities Purchase Agreement.

         "Adjusted Consolidated Net Tangible Assets" or "ACNTA" means (without
duplication), as of the date of determination, (a) the sum of (i) the discounted
future net revenue from proved crude oil and natural gas reserves of the
Borrower and its Consolidated Subsidiaries calculated in accordance with
Commission guidelines before any state or federal income taxes, as estimated in
the most current Reserve Report, as increased by, as of the date of
determination, the discounted future net revenue of (A) estimated proved crude
oil and natural gas reserves of the Borrower and its Consolidated Subsidiaries
attributable to acquisitions consummated since the date of such Reserve Report,
and (B) estimated proved crude oil and natural gas reserves of the Borrower and
its Consolidated Subsidiaries attributable to extensions, discoveries and other
additions and upward determinations of estimates of proved crude oil and natural
gas reserves due to exploration, development or exploitation, production or
other activities which reserves were not reflected in the most current Reserve
Report which would, in the case of determination made pursuant to clauses (A)
and (B), in accordance with standard industry practice, result in such
determinations, in each case calculated in accordance with Commission guidelines
(utilizing the Commission guideline prices utilized in the most current Reserve
Report), and decreased by, as of the date of determination, the discounted
future net revenue attributable to (C) estimated proved crude oil and natural
gas reserves of the Borrower and its Consolidated Subsidiaries reflected in the
most current Reserve Report produced or disposed of since the date of such
Reserve Report and (D) reductions in the estimated proved crude oil and natural
gas reserves of the Borrower and its Consolidated Subsidiaries reflected in such
Reserve Report since the date of such Reserve Report attributable to downward
determinations of estimates of proved crude oil and natural gas reserves due to
exploration, development or exploitation, production or other activities 
conducted or otherwise occurring since the date of the most current Reserve 




                                      -1-
<PAGE>   6

Report which would, in the case of determinations made pursuant to clauses (C)
and (D), in accordance with standard industry practice, result in such
determinations, in each case calculated in accordance with Commission guidelines
(utilizing the Commission guideline prices utilized in the most current Reserve
Report); provided, however, that, in the case of each of the determinations made
pursuant to clauses (A) through (D), such increases and decreases shall be as
estimated by the Borrower's engineers, except that if as a result of such
acquisitions, dispositions, discoveries, extensions or revisions, there is a net
increase in the ACNTA which exceeds $10,000,000, the Agent shall have the right
to require that such increases and decreases in the discounted future net
revenue be confirmed in writing by an independent petroleum engineer, at the
Borrower's expense, (ii) the capitalized costs that are attributable to seismic
and undeveloped oil and gas leases of the Borrower and its Consolidated
Subsidiaries to which no proved crude oil and natural gas reserves are
attributed, based on the Borrower's books and records as of a date no earlier
than the date of the Borrower's latest annual or quarterly financial statements,
(iii) the Net Working Capital on a date no earlier than the date of the
Borrower's latest annual or quarterly financial statements and (iv) the greater
of (I) the net book value on a date no earlier than the date of the Borrower's
latest annual or quarterly financial statements and (II) the appraised value, as
estimated by independent appraisers reasonably acceptable to the Agent, of other
tangible assets of the Borrower and its Consolidated Subsidiaries as of a date
no earlier than the date of the Borrower's latest audited financial statements,
minus (b) to the extent not otherwise taken into account in the immediately
preceding clause (a), the sum of (i) minority interests, (ii) any natural gas
balancing liabilities and credits of the Borrower and its Consolidated
Subsidiaries reflected in the Borrower's latest audited financial statements,
(iii) the discounted future net revenue, calculated in accordance with
Commission guidelines (utilizing the Commission guideline prices utilized in the
Borrower's most current Reserve Report), attributable to reserves subject to
participation interests, overriding royalty interests or other interests of
third parties, pursuant to participation, partnership, vendor financing or other
agreements then in effect, or which otherwise are required to be delivered to
third parties, (iv) the discounted future net revenue, calculated in accordance
with Commission guidelines (utilizing the Commission guideline prices utilized
in the Borrower's most current Reserve Report), attributable to reserves that
are required to be delivered to third parties to fully satisfy the obligations
of the Borrower and its Consolidated Subsidiaries with respect to volumetric
production payments and (v) the discounted future net revenue, calculated in
accordance with Commission guidelines, attributable to reserves subject to
dollar-denominated production payments that, based on the estimates of
production included in determining the discounted future net revenue specified
in the immediately preceding clause (a) (i) (utilizing the Commission guideline
prices utilized in the Borrower's most current Reserve Report), would be
necessary to satisfy fully the obligations of the Borrower and its Consolidated
Subsidiaries with respect to dollar-denominated production payments.

         "Affiliate" of any Person shall mean (i) any Person directly or
indirectly controlled by, controlling or under common control with such first
Person, (ii) any director or officer of such first Person or of any Person
referred to in clause (i) above and (iii) if any Person in clause (i) above is
an individual, any member of the immediate family (including parents, spouse and
children) of such individual and any trust whose principal beneficiary is such
individual or one or more members of such immediate family and any Person who is
controlled by any such member or trust. For purposes of this definition, any
Person which owns directly or indirectly



                                      -2-
<PAGE>   7

20% or more of the securities having ordinary voting power for the election of
directors or other governing body of a corporation or 20% or more of the
partnership or other ownership interests of any other Person (other than as a
limited partner of such other Person) will be deemed to "control" (including,
with its correlative meanings, "controlled by" and "under common control with")
such corporation or other Person.

         "Agent" means JEDI-II in its capacity as agent pursuant to Article XI
and includes any successor agent pursuant to Section 11.06.

         "Agent's Account" shall have the meaning specified in Section 9.03.

         "Average Share Price" means $__________.

         "Basic Documents" means, collectively, this Indenture, the Securities
Purchase Agreement and the other Loan Documents.

         "Board of Directors" means the Board of Directors of the Borrower.

         "BOG" means Brigham Oil & Gas, L.P., a Delaware limited partnership.

         "Business Day" means any day other than a Saturday, Sunday, or a legal
holiday for commercial banks in Houston, Texas, or New York, New York.

         "Business Opportunities Agreement" means the Corporate Shareholders'
Agreement dated as of even date herewith between the Purchasers and the
Borrower.

         "Capital Stock" of any Person means any and all shares, interests,
participations, or other equivalents (however designated) of, or rights,
warrants, or options to purchase, corporate stock, partnership interests, or any
other equity interest (however designated) of or in such Person.

         "Change in Control" means (i) a transaction, including any merger or
consolidation of Borrower with any other Person, in which the shareholders of
the Borrower immediately prior to such transaction (treating the holders of the
Warrants as holders of voting shares) do not own at least fifty-one percent
(51.0%) of the voting shares of stock of the Borrower (or the surviving entity
in the case of a merger or consolidation) immediately following the consummation
of such transaction, or (ii) a transaction, including any merger or
consolidation of Borrower with any other Person, in which the members of the
Board of Directors immediately prior to such transaction do not comprise at
least a majority of the board of directors of the Borrower (or the surviving
entity in the case of a merger or consolidation) for a period of twelve (12)
months immediately following the consummation of such transaction, or (iii) an
event, including any merger or consolidation of Borrower with any other Person,
such that Mr. Ben Brigham no longer manages the Borrower (or the surviving
entity in the case of a merger or consolidation), other than as a result of his
death or disability.

         "Closing" has the meaning provided therefor in Section 2.02 of the
Securities Purchase Agreement.



                                      -3-
<PAGE>   8


         "Closing Date" means the date upon which the Closing occurs as provided
in Section 2.02 of the Securities Purchase Agreement.

         "Code" means the Internal Revenue Code of 1986, as amended from time to
time, and any successor statute.

         "Collateral" means the properties, property interests and rights
described in Section 4.01 hereof, or otherwise covered by the Collateral
Documents, as security for the Obligations.

         "Collateral Documents" means collectively the documents required by the
Agent or the Noteholders to obtain the security interests in the Collateral, as
described in Section 4.01 hereof, and all other agreements, documents and
instruments required in Section 4.01, as the same may from time to time be
amended or supplemented.

         "Commission" means the United States Securities and Exchange 
Commission.

         "Common Stock" means the common stock, par value $0.01 per share, of
the Borrower or such other class of securities as shall, after the date of this
Indenture, constitute the common equity of the Borrower.

         "Consolidated Indebtedness" means all Debt of the Borrower and its
Consolidated Subsidiaries.

         "Consolidated Interest Coverage Ratio" means, as of the date of
determination, the ratio of (i) EBITDA for the preceding four calendar quarters
to (ii) Interest Expense for the same four calendar quarters.

         "Consolidated Net Income" means with respect to the Borrower and its
Consolidated Subsidiaries, for any period, the aggregate of the net income (or
loss) of the Borrower and its Consolidated Subsidiaries after allowance for
taxes for such period, determined on a consolidated basis in accordance with
GAAP; provided that there shall be excluded from the calculation of such net
income (to the extent otherwise included therein) the following: (i) the net
income of any Person in which Borrower or any Consolidated Subsidiary has an
interest (which interest does not cause the net income of such other Person to
be consolidated with the net income of Borrower and its Consolidated
Subsidiaries in accordance with GAAP), except to the extent of the amount of
dividends or distributions actually paid in such period by such other Person to
the Borrower or to a Consolidated Subsidiary, as the case may be; (ii) the net
income (but not loss) of any Consolidated Subsidiary to the extent that the
declaration or payment of dividends or similar distributions or transfers or
loans by that Consolidated Subsidiary is not at the time permitted by operation
of the terms of its charter or any agreement, instrument or Governmental
Requirement applicable to such Consolidated Subsidiary, or is otherwise
restricted or prohibited, in each case determined in accordance with GAAP; (iii)
the net income (or loss) of any Person acquired in a pooling-of-interests
transaction for any period prior to the date of such transaction; (iv) any
extraordinary gains or losses, including gains or losses attributable to
Property sales not in the ordinary course of business; and (v) the



                                      -4-
<PAGE>   9

cumulative effect of a change in accounting principles and any gains or losses
attributable to writeups or writedowns of assets.

         "Consolidated Subsidiaries" shall mean each Subsidiary of the Borrower
(whether now existing or hereafter created or acquired) the financial statements
of which shall be (or should have been) consolidated with the financial
statements of the Borrower in accordance with GAAP.

         "corporate trust office" of the Trustee means the office of the Trustee
at the address set out in Section 13.05 or at any other office or agency so
designated by the Trustee.

         "Debt" means, for any Person the sum of the following (without
duplication): (i) all obligations of such Person for borrowed money or evidenced
by bonds, debentures, notes or other similar instruments (including principal
and earned but unpaid issuance fees); (ii) all obligations of such Person
(whether contingent or otherwise) in respect of bankers' acceptances, letters of
credit, surety or other bonds and similar instruments; (iii) all obligations of
such Person to pay the deferred purchase price of Property or services (other
than for borrowed money) excluding Trade Payables but including Schedule 8.02
Payables; (iv) all obligations under leases which shall have been, or should
have been, in accordance with GAAP, recorded as capital leases in respect of
which such Person is liable (whether contingent or otherwise); (v) all
obligations under leases (other than capital leases and oil and gas leases)
which require such Person or its Affiliate to make payments exceeding $100,000
(or $500,000 in the aggregate) over the term of such lease, including payments
at termination, which are substantially equal to at least eighty percent (80%)
of the purchase price of the Property subject to such lease plus interest at an
imputed rate of interest; (vi) all Debt (as described in the other clauses of
this definition) of others secured by a Lien on any asset of such Person,
whether or not such Debt is assumed by such Person; (vii) all Debt (as described
in the other clauses of this definition) of others guaranteed by such Person or
in which such Person otherwise assures a creditor against loss of the Debt of
others; (viii) all obligations or undertakings of such Person to maintain or
cause to be maintained the financial position or covenants of others including
without limitation agreements expressed as an agreement to purchase the Debt or
Property of others or otherwise; (ix) obligations to deliver Hydrocarbons in
consideration of advance payments; (x) obligations to pay for goods or services
whether or not such goods or services are actually received or utilized by such
Person; (xi) any capital stock of such Person in which such Person has a
mandatory obligation to redeem such stock; (xii) any Debt of a Special Entity
for which such Person is liable either by agreement or because of a Governmental
Requirement; (xiii) the undischarged balance of any production payment created
by such Person or for the creation of which such Person directly or indirectly
received payment; and (xiv) all obligations of such Person under Hedging
Agreements, provided that "Debt" shall not include (a) interest or fees (other
than earned but unpaid issuance fees) on any of the foregoing, (b) obligations
associated with bid, performance, surety or appeal bonds (including those
required by Governmental Requirements in connection with Oil and Gas
Properties), (c) gas balancing obligations (whether volumetric or dollar
denominated), (d) intercompany obligations among the Borrower and its
Consolidated Subsidiaries, (e) indemnity obligations which have not matured into
fixed liabilities, and (f) purchase price adjustments and similar post-closing
obligations (but excluding the deferred payment of any purchase price) incurred
in connection with the permitted



                                      -5-
<PAGE>   10

purchase and sale of Property or stock, and which is to be determined and
payable no later than 180 days following the closing of such purchase and sale.

         "Default" shall mean an Event of Default or an event which with notice
or lapse of time, or both, would become, an Event of Default.

         "Default Rate" means, for any applicable period, an interest rate equal
to the then applicable rate of interest on the Notes (for cash payments of
interest) plus 4.00% per annum, but in no event shall the Default Rate exceed
the Maximum Rate.

         "EBITDA" shall mean, for any period, the sum of Consolidated Net Income
for such period plus the following expenses or charges to the extent deducted
from Consolidated Net Income in such period: interest, taxes, depreciation,
depletion and amortization, and other non-cash charges, minus all non-cash
income added to Consolidated Net Income in such period.

         "Effective Date" means the date this Indenture is executed by all the
parties hereto.

         "Employee Plan" means any employee benefit plan, program or policy with
respect to which the Borrower or any ERISA Affiliate may have any liability or
any obligation to contribute, other than a Plan or a Multiemployer Plan.

         "Environmental Laws" means any and all Governmental Requirements
pertaining to the environment in effect in any and all jurisdictions in which
the Borrower or any Subsidiary is conducting or at any time has conducted
business, or where any Property of the Borrower or any Subsidiary is located,
including, without limitation, the Oil Pollution Act of 1990 ("OPA"), as
amended, the Clean Air Act, as amended, the Comprehensive Environmental,
Response, Compensation, and Liability Act of 1980 ("CERCLA"), as amended, the
Federal Water Pollution Control Act, as amended, the Occupational Safety and
Health Act of 1970, as amended, the Resource Conservation and Recovery Act of
1976 ("RCRA"), as amended, the Safe Drinking Water Act, as amended, the Toxic
Substances Control Act, as amended, the Superfund Amendments and Reauthorization
Act of 1986, as amended, the Hazardous Materials Transportation Act, as amended,
and other environmental conservation or protection laws. As used in the
provisions hereof relating to Environmental Laws, the term "oil" has the meaning
specified in OPA; the terms "hazardous substance" and "release" (or "threatened
release") have the meanings specified in CERCLA, and the terms "solid waste" and
"disposal" (or "disposed") have the meanings specified in RCRA; provided,
however, that (i) in the event either OPA, CERCLA or RCRA is amended so as to
broaden the meaning of any term defined thereby, such broader meaning shall
apply subsequent to the effective date of such amendment, and (ii) to the extent
the laws of the state in which any Property of the Borrower or any Subsidiary is
located establish a meaning for "oil," "hazardous substance," "release," "solid
waste" or "disposal" which is broader than that specified in either OPA, CERCLA
or RCRA, such broader meaning shall apply.



                                      -6-
<PAGE>   11

         "Equity Documents" means the Warrants, the stock certificates
representing the Acquired Shares, the Registration Rights Agreement and the
Business Opportunities Agreement.

         "ERISA" means the Employee Retirement Income Security Act of 1974, as
amended from time to time and any successor statute.

         "ERISA Affiliate" shall mean each trade or business (whether or not
incorporated) which together with the Borrower or any Subsidiary of the Borrower
would be deemed to be a "single employer" within the meaning of Section
4001(b)(1) of ERISA or subsections (b), (c), (m) or (o) of section 414 of the
Code.

         "Event of Default" shall have the meaning assigned such term in Section
10.01.

         "Excepted Liens" means (i) Liens for taxes, assessments or other
governmental charges or levies not yet due or which are being contested in good
faith by appropriate action and for which adequate reserves have been maintained
in accordance with GAAP; (ii) Liens in connection with workman's compensation,
unemployment insurance or other social security, old age pension or public
liability obligations not yet due or which are being contested in good faith by
appropriate action and for which adequate reserves have been maintained in
accordance with GAAP; (iii) operators', vendors', carriers', warehousemen's,
repairmen's, mechanics', workmen's, materialmen's, construction or other like
Liens arising by operation of law in the ordinary course of business or incident
to the exploration, development, operation and maintenance of Oil and Gas
Properties or customary landlord's liens, each of which is in respect of
obligations that have not been outstanding more than 90 days or which are being
contested in good faith by appropriate proceedings and for which adequate
reserves have been maintained in accordance with GAAP; (iv) any Liens reserved
in leases or farmout agreements for rent or royalties and for compliance with
the terms of the farmout agreements or leases in the case of leasehold estates,
to the extent that any such Lien referred to in this clause does not materially
impair the use of the Property covered by such Lien for the purposes for which
such Property is held or materially impair the value of the Property subject
thereto; (v) encumbrances (other than to secure the payment of borrowed money or
the deferred purchase price of Property or services), easements, restrictions,
servitudes, permits, conditions, covenants, exceptions or reservations in any
rights of way or other Property for the purpose of roads, pipelines,
transmission lines, transportation lines, distribution lines for the removal of
gas, oil, coal or other minerals or timber, and other like purposes, or for the
joint or common use of real estate, rights of way, facilities and equipment, and
defects, irregularities, zoning restrictions and deficiencies in title of any
rights of way or other Property which in the aggregate do not materially impair
the use of such rights of way or other Property for the purposes for which such
rights of way and other Property are held or materially impair the value of such
Property subject thereto; (vi) deposits of cash or securities to secure the
performance of bids, trade, contracts, leases, statutory obligations and other
obligations of a like nature incurred in the ordinary course of business; and
(vii) Liens permitted by the Loan Documents.

         "Federal Funds Rate" means, for any day, a fluctuating interest rate
per annum (rounded upwards, if necessary, to the nearest 1/100 of 1%) equal to
the weighted average of the rates on overnight federal funds transactions with
members of the Federal Reserve System arranged 



                                      -7-
<PAGE>   12

by federal funds brokers on such day, as published for such day (or, if such day
is not a Business Day, for the next preceding Business Day) by the Federal
Reserve Bank of New York, or, if such rate is not so published for any day which
is a Business Day, the average of the quotations for any such day on such
transactions received by the Agent from three federal funds brokers of
recognized standing selected by it.

         "Financial Statements" means the financial statement or statements
described or referred to in Section 4.02 of the Securities Purchase Agreement.

         "First Reserve Report" shall have the meaning set out in Section
7.07(a).

         "Funding Date" means the first Business Day following the date all of
the conditions precedent to funding in Article VI of the Securities Purchase
Agreement have been satisfied.

         "GAAP" means generally accepted accounting principles in the United
States of America in effect from time to time.

         "Governmental Authority" shall include the country, the state, county,
city and political subdivisions in which any Person or such Person's Property is
located or which exercises valid jurisdiction over any such Person or such
Person's Property, and any court, agency, department, commission, board, bureau
or instrumentality of any of them including monetary authorities which exercises
valid jurisdiction over any such Person or such Person's Property. Unless
otherwise specified, all references to Governmental Authority herein shall mean
a Governmental Authority having jurisdiction over, where applicable, the
Borrower, the Subsidiaries or any of their Property or the Agent or any
Noteholder.

         "Guarantors" means Brigham, Inc., Brigham Holdings I, LLC, Brigham
Holdings II, LLC, BOG and any other Person who becomes party to a Guaranty
Agreement pursuant to the terms of Section 7.11.

         "Guaranty Agreements" means the agreements executed by the Guarantors
substantially in the form of Exhibit B guarantying, unconditionally, payment of
the Obligations, as the same may be amended, modified or supplemented from time
to time.

         "Hedging Agreements" means any commodity, interest rate or currency
swap, cap, floor, collar, forward agreement or other exchange or protection
agreements or any option with respect to any such transaction.

         "Hydrocarbon Interests" means all rights, titles, interests and estates
now or hereafter acquired in and to oil and gas leases, oil, gas and mineral
leases, or other liquid or gaseous hydrocarbon leases, mineral fee interests,
overriding royalty and royalty interests, net profit interests and production
payment interests, including any reserved or residual interests of whatever
nature.



                                      -8-
<PAGE>   13

         "Hydrocarbons" means oil, gas, casinghead gas, drip gasoline, natural
gasoline, condensate, distillate, liquid hydrocarbons, gaseous hydrocarbons and
all products refined or separated therefrom.

         "Indenture" means this instrument as originally executed, or, if
amended or supplemented as herein provided, as so amended or supplemented.

         "Initial Reserve Report" means the report of Cawley, Gillespie &
Associates with respect to the Oil and Gas Properties of BOG as of November 30,
1997, a copy of which has been delivered to Agent.

         "Interest Expense" means, for each applicable period for which EBITDA
is to be calculated, the sum of all required cash payments of interest during
such period on borrowed money. Interest on the Notes, for purposes of this
definition, shall be deemed cash payments, calculated at the cash interest rate,
whether paid in cash or in kind.

         "Interest Payment Date" means each November __, February __, May __,
and August __ following the Funding Date until and including the Maturity Date.

         "Lien" means any interest in Property securing an obligation owed to,
or a claim by, a Person other than the owner of the Property, whether such
interest is based on the common law, statute or contract, and whether such
obligation or claim is fixed or contingent, and including but not limited to (i)
the lien or security interest arising from a mortgage, encumbrance, pledge,
security agreement, conditional sale or trust receipt or a lease, consignment or
bailment for security purposes or (ii) production payments and the like payable
out of Oil and Gas Properties. The term "Lien" shall include reservations,
exceptions, encroachments, easements, rights of way, covenants, conditions,
restrictions, leases and other title exceptions and encumbrances affecting
Property. For the purpose of this Indenture, a Person shall be deemed to be the
owner of any Property which it has acquired or holds subject to a conditional
sale agreement, or leases under a financing lease or other arrangement pursuant
to which title to the Property has been retained by or vested in some other
Person in a transaction intended to create a financing.

         "Loan Documents" means this Indenture, the Notes, the Structuring Fee
Agreement, the Collateral Documents, and any and all other agreements or
instruments now or hereafter executed and delivered by the Borrower or any
Subsidiary or Affiliate of the Borrower (other than the Equity Documents and any
assignments, participation or similar agreements between any Noteholder and any
other lender or creditor with respect to any Obligations pursuant to this
Indenture) in connection with, or as security for the payment or performance of,
the Notes or this Indenture, as such agreements may be amended, supplemented or
restated from time to time.

         "Majority Noteholders" means, at any time, the Noteholders holding more
than 50% of the outstanding principal balance of the Notes.



                                      -9-
<PAGE>   14

         "Material Adverse Effect" means any material and adverse effect on (i)
the assets, liabilities, financial condition, business, operations or affairs of
the Borrower and its Subsidiaries taken as a whole, from those reflected in the
Financial Statements, or from the facts represented or warranted in any Loan
Document at the time made, or (ii) the ability of the Borrower and its
Subsidiaries taken as a whole to carry out their business as of the Closing Date
or as proposed as of the Closing Date to be conducted or to meet their
obligations under the Loan Documents on a timely basis.

         "Maturity Date" means August __, 2003, or in the event of an
acceleration of the Obligations, such earlier date as the Obligations become due
and payable in full.

         "Maximum Rate" means at any particular time in question, the maximum
nonusurious rate of interest, if any, which under applicable law may then be
charged on the Notes. If such maximum rate changes after the date hereof, the
Maximum Rate shall be automatically increased or decreased, as the case may be,
without notice to the Borrower from time to time as the effective date of each
change in such maximum rate.

         "Mortgage" means the "Mortgage" referred to in Section 4.01(c) or
4.01(f)(ii) and any other mortgages executed pursuant to Section 7.09 hereof.

         "Mortgaged Property" means the Property owned by the Borrower and its
Subsidiaries which is subject to the Liens existing and to exist under the Loan
Documents.

         "Multiemployer Plan" means a Plan defined as such in Section 3(37) or
4001(a)(3) of ERISA.

         "NASDAQ" means the National Association of Securities Dealers Automated
Quotation System.

         "Net Working Capital" means, for any Person or group of Persons and as
of any date of its determination, the difference (shown on the balance sheets of
such Person or group as of the end of the most recent fiscal quarter of such
Person or group for which internal financial statements are available) between
(i) all current assets of such Person or group and (ii) all current liabilities
of such Person or group, except the current portion of long-term Debt.

         "Notes" means the Senior Subordinated Secured Notes issued pursuant to
Section 2.03 of the Securities Purchase Agreement, in the aggregate face amount
of $50,000,000, dated as of the date hereof, made by the Borrower and payable to
the order of the Noteholders in their respective Participations.

         "Noteholders" means ___________________ and/or, to the extent then
applicable, each assignee of ______________ or their respective successors or
assigns in whose name a Note may be registered in the Note Register kept for
that purpose.

         "Noteholder's Account" means for any Noteholder, the account specified
by such Noteholder as its Noteholder's Account by notice in writing to the
Agent.



                                      -10-
<PAGE>   15

         "Note Register" and "Note Registrar" have the respective meanings
specified in Section 2.05.

         "Obligations" means any and all amounts, liabilities and obligations
owing from time to time by Borrower to the Agent or the Noteholders, pursuant to
any of the Basic Documents and all renewals, extensions and/or rearrangements
thereof, whether such amounts, liabilities or obligations be liquidated or
unliquidated, now existing or hereafter arising, absolute or contingent.

         "Officers' Certificate" means a certificate signed by the Chairman of
the Board, the President or any Vice President and by the Treasurer or any
Assistant Treasurer or the Secretary or any Assistant Secretary of the Borrower.
Each such certificate shall include the statements provided for in Section
13.13, if and to the extent required by the provisions thereof.

         "Oil and Gas Properties" means Hydrocarbon Interests; the Properties
now or hereafter pooled or unitized with Hydrocarbon Interests; all presently
existing or future unitization, pooling agreements and declarations of pooled
units and the units created thereby (including without limitation all units
created under orders, regulations and rules of any Governmental Authority) which
may affect all or any portion of the Hydrocarbon Interests; all operating
agreements, contracts and other agreements which relate to any of the
Hydrocarbon Interests or the production, sale, purchase, exchange or processing
of Hydrocarbons from or attributable to such Hydrocarbon Interests; all
Hydrocarbons in and under and which may be produced and saved or attributable to
the Hydrocarbon Interests, including all oil in tanks, the lands covered thereby
and all rents, issues, profits, proceeds, products, revenues and other incomes
from or attributable to the Hydrocarbon Interests; all tenements, hereditaments,
appurtenances and Properties in any manner appertaining, belonging, affixed or
incidental to the Hydrocarbon Interests; and all Properties, rights, titles,
interests and estates described or referred to above, including any and all
Property, real or personal, now owned or hereafter acquired and situated upon,
used, held for use or useful in connection with the operating, working or
development of any of such Hydrocarbon Interests or Property (excluding drilling
rights, automotive equipment or other personal property which may be on such
premises for the purpose of drilling a well or other similar temporary use) and
including any and all oil wells, gas wells, injection wells or other wells,
buildings, structures, fuel separators, liquid extraction plants, plant
compressors, pumps, pumping units, field gathering systems, tanks and tank
batteries, fixtures, valves, fittings, machinery and parts, engines, boilers,
meters, apparatus, appliances, tools, implements, cables, wires, towers, casing,
tubing and rods, similar equipment, surface leases, rights-of-way, easements and
servitudes together with all additions, substitutions, replacements, accessions
and attachments to any and all of the foregoing.

         "Opinion of Counsel" means an opinion in writing signed by legal
counsel who shall be reasonably satisfactory to the Trustee and may be counsel
to the Borrower. Each such opinion shall include the statements provided for in
Section 13.13, if and to the extent required by the provisions thereof.

         "outstanding", when used with reference to Notes, means, as of any
particular time, all Notes authenticated and delivered by the Trustee under this
Indenture, except



                                      -11-
<PAGE>   16

                  (a)      Notes that have been canceled by the Trustee or 
         delivered to the Trustee for cancellation;

                  (b) Notes for which monies in the necessary amount for payment
         or redemption shall have been deposited in trust with the Trustee or
         with any paying agent (other than the Borrower), provided that, if such
         Notes are to be redeemed, notice of such redemption shall have been
         given as provided in Article IV or provision satisfactory to the
         Trustee shall have been made for giving such notice; and

                  (c) Notes in lieu of or in substitution for which other Notes
         shall have been authenticated and delivered pursuant to the terms of
         Section 2.06.

         "Participation" means, for each Noteholder, such Noteholder's
proportionate share of the Obligations and the Warrants.

         "PBGC" means the Pension Benefit Guaranty Corporation or any entity
succeeding to any or all of its functions.

         "Permitted Debt" means:

                  (a)      The Senior Loan, up to the lesser of $75,000,000 or 
         the "Borrowing Base" under the Senior Credit Agreement;

                  (b) The Notes or other Obligations arising under the Loan
         Documents or any guaranty of or suretyship arrangement for the Notes or
         other Obligations arising under the Loan Documents;

                  (c) Debt of the Borrower which is existing on the Closing Date
         and is reflected in the Financial Statements or which constitutes
         Schedule 8.02 Payables, and any renewals or extensions (but not
         increases) thereof;

                  (d) Accounts payable for the deferred purchase price of
         Property or services (other than Trade Payables) from time to time
         incurred in the ordinary course of business which, if greater than 60
         days past the invoice or billing date, are being contested in good
         faith by appropriate proceedings if reserves adequate under GAAP shall
         have been established therefor;

                  (e) Debt of the Borrower under capital leases (as required to
         be reported on the financial statements of the Borrower pursuant to
         GAAP) not to exceed $2,000,000;

                  (f) Debt of the Borrower under Hedging Agreements with a
         Senior Lender or another investment grade counterparty the notional
         amounts on which do not exceed 75% of Borrower's anticipated oil and/or
         gas production to be produced during the term of such Hedging
         Agreements entered into as a part of its normal business operations as



                                      -12-
<PAGE>   17

         a risk management strategy and/or hedge against changes resulting from
         market conditions related to the Borrower's and its Subsidiaries'
         operations; and

                  (g) Debt of the Borrower not described in clauses (a) through
         (f) which, in the aggregate, does not exceed $1,000,000 at any one time
         outstanding.

         "Person" means any individual, corporation, company, voluntary
association, partnership, joint venture, trust, limited liability company,
unincorporated organization or government or any agency, instrumentality or
political subdivision thereof, or any other form of entity.

         "Plan" means any employee pension benefit plan, as defined in Section
3(2) of ERISA, which (i) is currently or hereafter sponsored, maintained or
contributed to by the Borrower, any Subsidiary or an ERISA Affiliate or (ii) was
at any time during the preceding six calendar years sponsored, maintained or
contributed to, by the Borrower, any Subsidiary or an ERISA Affiliate.

         "Property" means any interest in any kind of property or asset, whether
real, personal or mixed, or tangible or intangible.

         "Registration Rights Agreement" means the Registration Rights Agreement
dated as of the date hereof, made by the Borrower relating to the Warrants, the
Warrant Shares and the Acquired Shares.

         "Reportable Event" means an event described in Section 4043(c) of ERISA
with respect to a Plan, other than an event described in paragraphs (1) through
(8) as to which the 30 day notice requirement has been waived by the PBGC.

         "Reserve Report" means a report, in form satisfactory to the Senior
Loan Agent (or if there is no Senior Loan or requirement for a Reserve Report
under the Senior Loan, the Agent), setting forth, as of the dates set forth in
Sections 7.07(a) and (b) (or such other date in the event of an unscheduled
redetermination); (i) the proved oil and gas reserves attributable to the
Borrower's and its Subsidiaries' Hydrocarbon Interests together with a
projection of the rate of production and future net income, taxes, operating
expenses and capital expenditures with respect thereto as of such date, based
upon the pricing assumptions consistent with Commission reporting requirements
at the time and (ii) such other information as the Senior Loan Agent (or, if
there is no Senior Loan, or requirement for a Reserve Report under the Senior
Loan, the Agent) may reasonably request. The term "Reserve Report" shall also
include the Initial Reserve Report, the First Reserve Report, the supplemental
Reserve Reports described in Section 7.07(b), and the information to be provided
by the Borrower each year pursuant to Section 7.07(d).

         "Responsible Officer" means, as to any Person, the Chief Executive
Officer, the President, any Vice President or the Chief Financial Officer of
such Person. Unless otherwise specified, all references to a Responsible Officer
herein shall mean a Responsible Officer of the Borrower. "Responsible Officer"
when used with respect to the Trustee means the chairman or the vice-chairman of
the board of directors, the chairman of the executive committee of the board of
directors, the president, any vice president, any second or assistant vice
president, the 



                                      -13-
<PAGE>   18

cashier, any assistant cashier, the secretary, any assistant secretary, the
treasurer, any assistant treasurer, any senior trust officer or trust officer,
or any other officer or assistant officer of the Trustee customarily performing
functions similar to those performed by the persons who at the time shall be
such officers, respectively, or to whom any corporate trust matter is referred
because of his knowledge of and familiarity with the particular subject.

         "Schedule 8.02 Payables" means payables owing under the agreements
listed on Schedule 8.02 which are outstanding more than 75 days after they
become fixed and owing, provided that the aggregate amounts of such payables
under each such agreement do not exceed the amount set forth for each such
agreement on such schedule.

         "Scheduled Redetermination Date" means the last Business Day of each
September and March during the term of the Notes, commencing September 1999.

         "Securities" means the Notes, the Warrants and the Acquired Shares.

         "Securities Act" means the Securities Act of 1933, as amended from time
to time, and the rules and regulations of the Commission promulgated thereunder.

         "Securities Purchase Agreement" means the Securities Purchase Agreement
dated of even date herewith between the Noteholders and the Borrower.

         "Senior Credit Agreement" means the Credit Agreement dated as of
January 26, 1998, among BOG, the Senior Loan Agent, and the Senior Lenders, as
it may from time to time be amended, modified or supplemented from time to time,
and any Credit Agreement or similar agreement executed with banks or other
financial institutions in connection with any refinancing of the Senior Loan
permitted hereunder and under the Subordination Agreement.

         "Senior Loan Agent" means the agent or agents designated under the
Senior Credit Agreement. Bank of Montreal is the Senior Loan Agent as of the
date hereof.

         "Senior Lenders" means each of the lenders from time to time under the
Senior Credit Agreement.

         "Senior Loan" shall mean, collectively, any advance or advances of
principal made by the Senior Lenders to BOG or the Borrower under the Senior
Credit Agreement and the other Senior Loan Documents.

         "Senior Loan Documents" means the Senior Credit Agreement and all
promissory notes, collateral documents and other agreements, documents and
instruments executed or delivered in connection therewith, as such agreements
may be amended, modified or supplemented from time to time.

         "Special Entity" means any joint venture, limited liability company or
partnership, general or limited partnership or any other type of partnership or
company other than a corporation, in which a Person or one or more of its other
Subsidiaries is a member, owner, partner or joint 



                                      -14-
<PAGE>   19

venturer and owns, directly or indirectly, at least a majority of the equity of
such entity or controls such entity, but excluding any tax partnerships that are
not classified as partnerships under state law. For purposes of this definition,
any Person which owns directly or indirectly an equity investment in another
Person which allows the first Person to manage or elect managers who manage the
normal activities of such second Person will be deemed to "control" such second
Person (e.g.,a sole general partner controls a limited partnership).

         "Structuring Fee Agreement" means the agreement between the Borrower
and ___________________ dated as of the date hereof.

         "Subordination Agreement" means the Intercreditor and Subordination
Agreement dated as of even date herewith, by and among the Trustee, the Senior
Loan Agent, the Senior Lenders, the Agent, the Noteholders, the Borrower and
certain Subsidiaries, substantially in the form of Exhibit C as the same may be
supplemented or amended from time to time.

         "Subsidiary" means (i) any corporation of which at least a majority of
the outstanding shares of stock having by the terms thereof ordinary voting
power to elect a majority of the board of directors of such corporation
(irrespective of whether or not at the time stock of any other class or classes
of such corporation shall have or might have voting power by reason of the
happening of any contingency) is at the time directly or indirectly owned or
controlled by a Person or one or more of its Subsidiaries or by a Person and one
or more of its Subsidiaries and (ii) any Special Entity. Unless otherwise
indicated herein, each reference to the term "Subsidiary" shall mean a
Subsidiary of the Borrower. Quest Resources L.L.C. and Venture Acquisitions L.P.
shall not be considered Subsidiaries of Borrower.

         "TIA" (except as herein otherwise expressly provided or unless the
context otherwise requires) means the Trust Indenture Act of 1939, as amended,
as in force at the date of this Indenture as originally executed.

         "Trade Payables" means customary trade payables incurred in the
ordinary course of business.

         "Trustee" means Chase Bank of Texas, National Association, and, subject
to the provisions of Article XII, shall also include its successors and assigns.

         "Warrants" means the Warrants issued by the Borrower to ECT and JEDI-II
in their respective Participations pursuant to Section 2.03 of the Securities
Purchase Agreement, for the purchase of an aggregate of 1,000,000 shares of
Common Stock, and any Warrants issued upon the transfer thereof or in
substitution therefore, pursuant to the Warrant Certificate to be issued to ECT
and JEDI-II, forms of which are attached to the Securities Purchase Agreement as
Exhibit A.

         "Warrant Shares" means the shares of Common Stock and other securities
receivable upon exercise of the Warrants.



                                      -15-
<PAGE>   20

         Section 1.02 Accounting Procedures and Interpretation. Unless otherwise
specified herein, all accounting terms used herein shall be interpreted, all
determinations with respect to accounting matters hereunder shall be made, and
all financial statements and certificates and reports as to financial matters
required to be furnished to the Agent or the Noteholders (including ACNTA
calculations) hereunder shall be prepared, in accordance with GAAP, applied on a
basis consistent with the Financial Statements (except for changes concurred
with by the Borrower's independent public accountants).


                                   ARTICLE II
                ISSUE, DESCRIPTION, FORM, EXECUTION, REGISTRATION
                        OF TRANSFER AND EXCHANGE OF NOTES

         Section 2.01 Form and Dating. The Notes and the Trustee's certificate
of authentication are to be substantially in the form of Exhibit A with such
appropriate insertions, omissions, substitutions, amendments, changes and other
variations as are required or permitted by this Indenture, and may have such
letters, numbers or other marks of identification and such legends or
endorsements placed thereon as may be required to comply with the rules of any
securities exchange on which the Notes may be listed or as may, consistently
herewith, be determined by the officers executing such Notes as evidenced by
their execution of the Notes.

         The terms and provisions contained in the Notes and each Guaranty
Agreement shall constitute, and are hereby expressly made, a part of this
Indenture and, to the extent applicable, the Borrower and the Guarantors, by
their execution and delivery of this Indenture and each Guaranty Agreement,
expressly agree to such terms and provisions and to be bound thereby.

         The definitive Notes shall be printed or produced in any manner as may
be determined by the officers executing such Notes, as evidenced by their
execution of such Notes.

         Section 2.02 Execution and Authentication. The Notes and each Guaranty
Agreement shall be executed by the Borrower and Guarantors, respectively, and be
delivered to the Trustee for authentication, and the Trustee shall thereupon, or
from time to time thereafter, authenticate and deliver said Notes and each
Guaranty Agreement to and upon the written order of the Borrower, signed by its
President or a Vice President and by its Treasurer, Assistant Treasurer,
Secretary or Assistant Secretary, without any further action by the Borrower.

         Section 2.03 Denomination of Notes and Record Date. The Notes shall be
issuable as registered Notes without coupons in denominations of $1,000 and any
integral multiple thereof. Each Note shall be dated the date of its 
authentication.

         The person in whose name any Note is registered at the close of
business on any record date (as hereinafter defined) with respect to any
interest payment date shall be entitled to receive the interest payable on such
interest payment date. The term "record date" as used with respect to any
Interest Payment Date shall mean the day of the calendar month preceding the day
on which such Interest Payment Date falls. The principal of, and premium, if
any, and interest on, 



                                      -16-
<PAGE>   21

the Notes shall be payable at the principal office of the Borrower and any other
office or agency of the Borrower designated for that purpose; provided, however,
that principal and interest may be payable at the option of the Noteholders to
the Agent's Account.

         Section 2.04 Manual Execution. The Notes and Guaranty Agreements shall
be signed manually or by facsimile signature on behalf of the Borrower by its
President or a Vice President attested by the manual or facsimile signature of
its Secretary or an Assistant Secretary.

         Only such Notes as shall bear thereon a certificate of authentication
substantially in the form recited in Exhibit A, manually executed by the
Trustee, shall be entitled to the benefits of this Indenture or be valid or
obligatory for any purpose. Such certificate by the Trustee upon any Note
executed by the Borrower shall be conclusive evidence that the Note so
authenticated has been duly authenticated and delivered hereunder.

         In case any officer of the Borrower who shall have signed any of the
Notes shall cease to be such officer before the Notes so signed shall have been
authenticated and delivered by the Trustee, or disposed of by the Borrower, such
Notes nevertheless may be authenticated and delivered or disposed of as though
the person who signed such Notes had not ceased to be such officer of the
Borrower; and any Note may be signed on behalf of the Borrower by such persons
as, at the actual date of the execution of such Note, shall be the proper
officers of the Borrower, although at the date of the execution of this
Indenture any such person was not an officer.

         Section 2.05 Transfer and Exchange. The Notes may be exchanged for a
like aggregate principal amount of Notes of other authorized denominations.
Notes to be exchanged shall be surrendered at the Borrower's principal office,
and the Borrower shall execute and the Trustee shall authenticate and deliver in
exchange therefor the Note or Notes which the Noteholder making the exchange
shall be entitled to receive.

         The Borrower shall keep or cause to be maintained at said office or
agency a register (herein sometimes referred to as the "Note Register") in
which, subject to such reasonable regulations as it may prescribe, the Borrower
shall register Notes and shall register the transfer of Notes as in this Article
II provided. For the purposes of registration, exchange, registration of
transfer, redemption or conversion of Notes, the Trustee is hereby appointed
Note Registrar. Upon surrender for registration of transfer of any Note at said
office or agency, the Borrower shall execute and the Trustee shall authenticate
and deliver in the name of the transferee or transferees a new Note or Notes in
a like aggregate principal amount. At all reasonable times the Note Register
shall be open for inspection by the Trustee. No transfer of any Note shall be
valid unless made at said office or agency.

         All Notes presented or surrendered for registration of transfer,
exchange, conversion or payment shall (if so required by the Borrower or the
Trustee) be accompanied by a written instrument or instruments of transfer, in
form satisfactory to the Borrower and the Trustee, duly executed by the
registered Noteholder or his attorney duly authorized in writing.

         No service charge shall be made for any exchange or registration of
transfer of Notes, or issue of new Notes in case of partial prepayment or
conversion, but the Borrower may 



                                      -17-
<PAGE>   22


require payment of a sum sufficient to cover any tax or other governmental
charge that may be imposed in relation thereto.

         The Borrower shall not be required (i) to issue, register the transfer
of, or exchange any Note during a period beginning at the opening of business 15
days before the mailing of a notice of redemption of the Notes selected for
redemption and ending on the day of such mailing, or (ii) to register the
transfer of or exchange any Note so selected for redemption in whole or in part,
except the unredeemed portions of Notes being redeemed in part.

         Section 2.06 Replacement Notes. In case any Note shall become mutilated
or be destroyed, lost or stolen, the Borrower shall execute, and the Trustee
shall authenticate and deliver, a new Note, in exchange and substitution for the
mutilated Note or in lieu of and substitution for the Note destroyed, lost or
stolen. In every case, the applicant for a substituted Note shall furnish to the
Borrower and the Trustee such security or indemnity as may be required by them
to hold each of them harmless, and, in every case of destruction, loss or theft,
the applicant shall also furnish to the Borrower and to the Trustee evidence to
their satisfaction of the destruction, loss or theft of such Note and of the
ownership thereof. The Trustee may authenticate any such substituted Note and
deliver the same upon the request or authorization of the Borrower. Upon the
issuance of any substituted Note, the Borrower may require the payment of a sum
sufficient to cover any tax or other governmental charge that may be imposed in
relation thereto and any other expenses connected therewith, including fees and
expenses of the Trustee. In case any Note which has matured or is about to
mature or has been called for prepayment or has been presented for conversion
shall become mutilated or be destroyed, lost or stolen, the Borrower may,
instead of issuing a substitute Note, pay or authorize the payment of the same
(without surrender thereof except in the case of a mutilated Note) if the
applicant for such payment shall furnish the Borrower and the Trustee with such
security or indemnity as may be required by them to hold each of them harmless,
and, in case of destruction, loss or theft, evidence to the satisfaction of the
Borrower and the Trustee of the destruction, loss or theft of such Note and of
the ownership thereof.

         If, after the delivery of such replacement Note, a bona fide purchaser
of the original Note in lieu of which such replacement Note was issued presents
for payment or registration such original Note, the Trustee shall be entitled to
recover such replacement Note from the person to whom it was delivered or any
person taking therefrom, except a bona fide purchaser, and shall be entitled to
recover upon the security or indemnity provided therefor to the extent of any
loss, damage, cost or expense incurred by the borrower or Trustee in connection
therewith.

         Every substituted Note issued pursuant to the provisions of this
Section 2.06 upon evidence that any Note is destroyed, lost or stolen shall,
with respect to such Note, constitute an additional contractual obligation of
the Borrower, whether or not the destroyed, lost or stolen Note shall be found
at any time, and shall be entitled to all the benefits of this Indenture equally
and proportionately with any and all other Notes duly issued hereunder. All
Notes shall be held and owned upon the express condition that the foregoing
provisions are exclusive with respect to the replacement or payment of
mutilated, destroyed, lost or stolen Notes, and shall preclude any and all other
rights or remedies, notwithstanding any law or statute existing or hereafter



                                      -18-
<PAGE>   23

enacted to the contrary with respect to the replacement or payment of negotiable
instruments or other securities without their surrender.

         Section 2.07 Cancellation of Notes. All Notes surrendered for payment,
conversion, registration of transfer or exchange shall, if surrendered to the
Borrower or any paying agent, be delivered to the Trustee for cancellation, or,
if surrendered to the Trustee, shall be canceled by it, and no Notes shall be
issued in lieu thereof except as expressly permitted by any of the provisions of
this Indenture. On request of the Borrower, the Trustee shall deliver to the
Borrower canceled Notes held by the Trustee; provided, however, that the Trustee
may at any time destroy any canceled Notes and deliver to the Borrower a
certificate of such destruction. If the Borrower shall acquire any of the Notes,
however, such acquisition shall not operate as a redemption or satisfaction of
the indebtedness represented by such Notes unless and until the same are
delivered to the Trustee or surrendered to the Trustee for cancellation.

         Section 2.08 No Third Party Benefit. Subject to the terms of the
Subordination Agreement, nothing in this Indenture or in the Notes, expressed or
implied, shall give or be construed to give to any person, firm or corporation,
other than the parties hereto and the Noteholders, any legal or equitable right,
remedy or claim under or in respect of this Indenture, or under any covenant,
condition or provision herein contained; all its covenants, conditions and
provisions being for the sole benefit of the parties hereto and of the
Noteholders.

                                   ARTICLE III
                                  SUBORDINATION

         The Notes shall be subject to the Subordination Agreement.

                                   ARTICLE IV
                          SECURITY FOR THE OBLIGATIONS

         Section 4.01 Security. The Obligations shall be secured by the
following which, in each case shall be subordinate in priority only to those
liens, security interests or rights granted in the same collateral to secure the
performance of Borrower under the Senior Loan Documents, in accordance with, but
subject to, the terms of the Subordination Agreement:

                  (a) (i) A Security Agreement substantially in the form of
Exhibit D duly executed by the Borrower in favor of the Trustee for the ratable
benefit of the Noteholders granting a security interest in all of the Borrower's
right, title and interest in and to the Capital Stock of Brigham, Inc. and
Brigham Holdings I, LLC, together with proper UCC-1 Financing Statements duly
filed in Texas, (ii) a Security Agreement substantially in the form of Exhibit D
duly executed by Brigham, Inc. in favor of the Trustee for the ratable benefit
of the Noteholders granting a security interest in all of Brigham, Inc.'s right,
title and interest in and to the Capital Stock of Brigham Holdings II, LLC and
BOG, together with proper UCC-1 Financing Statements duly filed in Texas, (iii)
a Security Agreement substantially in the form of Exhibit D duly executed by
Brigham Holdings II, LLC in favor of the Trustee for the ratable



                                      -19-
<PAGE>   24

benefit of the Noteholders granting a security interest in all of Brigham
Holdings II, LLC's, right, title and interest in and to the Capital Stock of
BOG, together with proper UCC-1 Financing Statements duly filed in Texas and
(iv) a Security Agreement substantially in the form of Exhibit D duly executed
by Brigham Holdings I, LLC in favor of the Trustee for the ratable benefit of
the Noteholders granting a security interest in all of Brigham Holdings I, LLC's
right, title and interest in and to the Capital Stock of BOG, together with
proper UCC-1 Financing Statements duly filed in Texas.

                  (b) A Security Agreement, substantially in the form of Exhibit
E duly executed by BOG in favor of the Trustee, as collateral agent for the
ratable benefit of the Noteholders granting a security interest in all of BOG's
right, title and interest in and to all accounts, general intangibles, equipment
and inventory of BOG subject to Liens under the Senior Loan Documents.

                  (c) A Mortgage, Deed of Trust, Assignment of Production,
Security Agreement and Financing Statement substantially in the form of Exhibit
F executed by BOG in favor of the Trustee, as collateral agent for the ratable
benefit of the Noteholders covering all of the Property of BOG subject to Liens
under the Senior Loan Documents.

                  (d) A Guaranty Agreement duly executed by each of BOG,
Brigham, Inc., Brigham Holdings I, LLC and Brigham Holdings II, LLC in favor of
the Trustee for the ratable benefit of the Noteholders guarantying the payment
and performance of the Obligations.

                  (e) Stock Powers executed by the Borrower and related stock
certificates of Brigham, Inc.

                  (f) (i) Guaranty Agreements from each and every Person now or
hereafter guaranteeing all or any portion of the Senior Loan, (ii) Mortgages
covering any and all real property (including Oil and Gas Property) now or
hereafter pledged as collateral for all or any portion of the Senior Loan, (iii)
security agreements covering any and all Property (other than real property
subject to a Mortgage) now or hereafter pledged as collateral for all or any
portion of the Senior Loan, and (iv) financing statements, stock pledges or
other agreements necessary or appropriate to perfect the liens and/or security
interests granted pursuant to any of the foregoing. Each of the foregoing
instruments shall be in substantially the same form and substance as those
executed of even date herewith or otherwise.


                                    ARTICLE V
                                   [RESERVED]


                                   ARTICLE VI
                                   [RESERVED]


                                      -20-
<PAGE>   25

                                   ARTICLE VII
                              AFFIRMATIVE COVENANTS

         Unless the Agent's prior written consent to the contrary is obtained,
the Borrower will, for the benefit of each of the Noteholders, at all times
comply with the covenants contained in this Article VII (or cause each
Subsidiary's compliance with the applicable covenants), from the date hereof and
for so long as any part of the Obligations is outstanding.

         Section 7.01 Financial Statements and Reports. The Borrower shall
deliver, or shall cause to be delivered, to the Agent with sufficient copies for
each of the Noteholders:

                  (a) Annual Financial Statements. As soon as available and in
any event within 90 days after the end of each fiscal year of the Borrower, the
audited consolidated statements of income, stockholders' equity, changes in
financial position and cash flow of the Borrower and its Consolidated
Subsidiaries for such fiscal year, and the related consolidated and unaudited
consolidating balance sheets of the Borrower and its Consolidated Subsidiaries
as at the end of such fiscal year, and setting forth in each case in comparative
form the corresponding figures for the preceding fiscal year, and accompanied by
the related opinion of independent public accountants of recognized national
standing acceptable to the Senior Loan Agent (or in the absence of a Senior
Loan, the Agent) which opinion shall state that said financial statements fairly
present the consolidated financial condition and results of operations of the
Borrower and its Consolidated Subsidiaries as at the end of, and for, such
fiscal year and that such financial statements have been prepared in accordance
with GAAP except for such changes in such principles with which the independent
public accountants shall have concurred and such opinion shall not contain a
"going concern" or like qualification or exception.

                  (b) Quarterly Financial Statements. As soon as available and
in any event within 60 days after the end of each of the first three fiscal
quarterly periods of each fiscal year of the Borrower, consolidated statements
of income, stockholders' equity, changes in financial position and cash flow of
the Borrower and its Consolidated Subsidiaries for such period and for the
period from the beginning of the respective fiscal year to the end of such
period, and the related consolidated and consolidating balance sheets as at the
end of such period, setting forth in each case in comparative form the
corresponding figures for the corresponding period in the preceding fiscal year,
accompanied by the certificate of a Responsible Officer, which certificate shall
state that said financial statements fairly present the consolidated financial
condition and results of operations of the Borrower and its Consolidated
Subsidiaries in accordance with GAAP, as at the end of, and for, such period
(subject to normal year-end audit adjustments).

                  (c) Notice of Default. Promptly after the Borrower knows that
any Default or any Material Adverse Effect has occurred, a notice of such
Default or Material Adverse Effect, describing the same in reasonable detail and
the action the Borrower proposes to take with respect thereto.

                  (d) Other Accounting Reports. Promptly upon receipt thereof, a
copy of each other report or letter (excluding routine correspondence and audit
request letters) submitted to 



                                      -21-
<PAGE>   26

the Borrower by independent accountants in connection with any annual, interim
or special audit made by them of the books of the Borrower, and a copy of any
response by the Borrower to such letter or report (including responses to any
audit request letters).

                  (e) SEC Filings, Etc. Promptly upon its becoming available,
each financial statement, report, notice or proxy statement sent by the Borrower
to stockholders generally and each regular or periodic report and any
registration statement, prospectus or written communication (other than
transmittal letters) in respect thereof filed by the Borrower with or received
by the Borrower in connection therewith from any securities exchange or the
Commission or any successor agency.

                  (f) Notices Under Other Loan Agreements. Promptly after the
furnishing thereof, copies of any statement, report or notice furnished to any
Person pursuant to the terms of any indenture, loan or credit or other similar
agreement, other than this Indenture and not otherwise required to be furnished
to the Agent or the Trustee pursuant to any other provision of this Section
7.01.

                  (g) Other Matters. Subject to any applicable restrictions on
disclosure, from time to time such other information regarding the business,
affairs or financial condition of the Borrower (including, without limitation,
any Plan or Multiemployer Plan and any reports or other information required to
be filed under ERISA) as may be requested by and provided to the Senior Lender
or Senior Loan Agent.

                  (h) Annual Budgets. Concurrent with the First Reserve Report
and each January 1 Reserve Report thereafter, a one-year financial projection
for the Borrower and its Subsidiaries in form acceptable to the Senior Loan
Agent (or in the absence of a Senior Loan or Senior Loan Agent, the Agent),
which projection shall include revenues, expenses and capital expenditures.

                  (i) Monthly Operating Statements. As soon as available and in
any event within 30 days after the end of each month, monthly operating
statements of BOG including, without limitation, production reports and general
and administrative cost summaries by lease for its Oil and Gas Properties, which
reports shall include quantities or volume of production, revenue, realized
product prices, taxes, capital expenditures by category and lease operating
costs which have accrued to BOG's accounts in such period, and such other
information with respect thereto as the Senior Loan Agent (or in the absence of
a Senior Loan or Senior Loan Agent, the Agent) may require.

The Borrower will furnish to the Agent, at the time it furnishes each set of
financial statements pursuant to paragraph (a) or (b) above, a certificate
substantially in the form of Exhibit C-2 to the Senior Credit Agreement executed
by a Responsible Officer (i) certifying as to the matters set forth therein and
stating that no Default has occurred and is continuing (or, if any Default has
occurred and is continuing, describing the same in reasonable detail), (ii)
setting forth in reasonable detail the computations necessary to determine
whether the Borrower is in compliance with Sections 8.01 and 8.16 as of the end
of the respective fiscal quarter or fiscal year, and (iii) certifying that said
financial statements fairly present the consolidated and 



                                      -22-
<PAGE>   27

consolidating financial condition and consolidated results of operations in
accordance with GAAP, as at the end of, and for, such period (subject to normal
year-end audit adjustments).

         Section 7.02 Litigation. The Borrower shall promptly give to the Agent
notice of: (i) all legal or arbitral proceedings, and of all proceedings before
any Governmental Authority involving the Borrower or any Guarantor, except
proceedings which, if adversely determined within any reasonable range of loss,
would not have a Material Adverse Effect, and (ii) of any material litigation or
material proceeding against the Borrower or any Guarantor in which the amount
involved is not covered in full by insurance (subject to normal and customary
deductibles), or in which injunctive or similar relief is sought. The Borrower
will, and will cause each of the Guarantors to, promptly notify the Agent of any
claim, judgment, Lien or other encumbrance affecting any Property of the
Borrower or any Guarantor if the value of the claim, judgment, Lien, or other
encumbrance affecting such Property shall exceed $1,000,000.

         Section 7.03  Maintenance, Etc.

                  (a) The Borrower shall and shall cause each Subsidiary to:
upon reasonable notice, permit representatives of the Agent, during normal
business hours, to examine, copy and make extracts from its financial books and
records, to inspect its Properties, and to discuss its business and affairs with
its officers, all to the extent reasonably required by the Agent; keep, or cause
to be kept, insured by financially sound and reputable insurers all Property of
a character usually insured by Persons engaged in the same or similar business
similarly situated against loss or damage of the kinds and in the amounts
customarily insured against by such Persons and carry such other insurance as is
usually carried by such Persons including, without limitation, environmental
risk insurance to the extent reasonably available; and, where failure to do so
would have a Material Adverse Effect: preserve and maintain its corporate
existence and all of its material attendant rights, privileges and franchises,
keep appropriate books of record and account in relation to its business and
activities, comply with all Governmental Requirements, pay and discharge all
taxes, assessments and governmental charges or levies imposed on it or on its
income or profits or on any of its Property, except for any such tax,
assessment, charge or levy the payment of which is being contested in good faith
and by proper proceedings and against which adequate reserves are being
maintained.

                  (b) Contemporaneously with the delivery of the financial
statements required by Section 7.01(a) to be delivered for each year, the
Borrower will furnish or cause to be furnished to the Agent a certificate of
insurance coverage from the insurer in form and scope reasonably satisfactory to
the Agent and, if required by the Agent, will furnish the Agent copies of the
applicable policies.

                  (c) The Borrower will and will cause each Subsidiary to
maintain and operate its Oil and Gas Properties and other material Properties or
cause or make reasonable and customary efforts to cause such Oil and Gas
Properties and other material Properties to be maintained and operated in all
material respects in a good and workmanlike manner in accordance with the
practices of the industry and in compliance with all applicable contracts and
agreements and in compliance in all material respects with all Governmental
Requirements. The 



                                      -23-
<PAGE>   28

covenants contained in this Section 7.03(c) shall not apply to insignificant
Properties unless a failure of such covenant could have a Material Adverse
Effect.

         Section 7.04  Environmental Matters.

                  (a) To the extent that a reasonably prudent owner or operator
would do so under the same or similar circumstances, the Borrower will and will
cause each Subsidiary to establish and implement such procedures as may be
reasonably necessary to periodically determine and assure that all Oil and Gas
Properties of the Borrower and the Subsidiaries and the operations conducted
thereon and other activities of the Borrower and the Subsidiaries are in
compliance with and do not violate the requirements of any Environmental Laws,
where failure of the foregoing would have a Material Adverse Effect.

                  (b) The Borrower will promptly notify the Agent in writing of
any threatened action, investigation or inquiry by any Governmental Authority of
which the Borrower has knowledge in connection with any Environmental Laws with
respect to the Property of the Borrower or any Subsidiary, excluding routine
testing, compliance and correction action.

         Section 7.05 Further Assurances. The Borrower will and will cause each
Guarantor to cure promptly any defects in the creation and issuance of the Notes
and the execution and delivery of the Basic Documents. The Borrower at its
expense will and will cause each Guarantor to promptly execute and deliver to
the Agent upon request all such other documents, agreements and instruments to
further evidence and more fully describe the collateral intended as security for
the Notes, or to correct any omissions in the Basic Documents, or to state more
fully the security obligations set out herein or in any of the Basic Documents,
or to perfect, protect or preserve any Liens created pursuant to any of the
Basic Documents, or to make any recordings, to file any notices or obtain any
consents, all as may be necessary or appropriate in connection therewith.

         Section 7.06 Performance of Obligations. The Borrower will pay the
Notes according to the reading, tenor and effect thereof; and the Borrower will
and will cause each Guarantor to do and perform every act and discharge all of
the obligations to be performed and discharged by them under the Basic
Documents, at the time and times and in the manner specified.

         Section 7.07  Engineering Reports.

                  (a) Not less than 30 days prior to the First Borrowing Base
Determination Date, the Borrower shall furnish to the Agent a Reserve Report
prepared as of December 1, 1998 or later (the "First Reserve Report") and as
provided in clause 7.07(b) below.

                  (b) On January 31, 1999 and not less than 30 days prior to
each Scheduled Redetermination Date thereafter, commencing with the Scheduled
Redetermination Date to occur on September 30, 1999, the Borrower shall furnish
to the Agent a Reserve Report. The Reserve Report furnished for the September 30
Scheduled Redetermination Date shall be prepared as of the preceding July 1 and
the Reserve Report furnished for the March Scheduled Redetermination Date (as
well as the Reserve Report furnished on January 31, 1999) shall be prepared as
of the 



                                      -24-
<PAGE>   29

preceding January 1. The Reserve Report furnished on January 31, 1999 and the
January 1 Reserve Report of each year beginning January 1, 2000 shall be
prepared by certified independent petroleum engineers or other independent
petroleum consultant(s) acceptable to the Agent and the First Reserve Report and
the July 1 Reserve Report of each year shall be prepared by or under the
supervision of the chief engineer or Vice President of Operations of the
Borrower who shall certify such Reserve Report to have been prepared in
accordance with the procedures used in the immediately preceding First Reserve
Report or January 1 Reserve Report, as appropriate. At Borrower's option, the
July 1 Reserve Report of each year may instead consist of a report from the
independent petroleum engineers referred to above on any new wells and a
roll-forward by Borrower on any wells previously reported on.

                  (c) In addition, the Borrower shall furnish to the Agent
copies of any additional Reserve Reports (other than those specified in Sections
7.07(a) and (b) above) that Borrower or any of its Subsidiaries deliver to the
Senior Loan Agent or Senior Lenders pursuant to the Senior Loan Documents.

                  (d) With the delivery of each Reserve Report, the Borrower
shall provide to the Agent:

                           (i) a certificate from a Responsible Officer
         certifying that, to the best of his knowledge and in all material
         respects: (i) the most recently delivered Reserve Report does not in
         the belief of such officer and based upon information in the Borrower's
         possession, materially overstate the oil and gas reserves of the
         Borrower and the Subsidiaries as a whole bearing in mind that reserves
         are evaluated based upon estimates and assumptions with respect to
         which reasonable minds of competent engineers may differ, (ii) except
         as set forth in such Reserve Report or on an exhibit to the
         certificate, on a net basis there are no gas imbalances, take or pay or
         other prepayments with respect to its Oil and Gas Properties evaluated
         in such Reserve Report which would violate Section 8.14, (iii) none of
         its proved Hydrocarbon Interests have been sold since the date of the
         last Borrowing Base determination except as set forth on an exhibit to
         the certificate, which certificate shall list all of its proved
         Hydrocarbon Interests sold and in such detail as reasonably required by
         the Agent, (iv) attached to the certificate is a list of its proved
         Hydrocarbon Interests added to and deleted from the immediately prior
         Reserve Report and a list showing any change in working interest or net
         revenue interest in its Hydrocarbon Interests occurring, (v) at the
         Agent's request, attached to the certificate is a list of all Persons
         disbursing proceeds to the Borrower from its Oil and Gas Properties and
         (vi) except as set forth on a schedule attached to the certificate all
         of the proved Hydrocarbon Interests evaluated by such Reserve Report
         are Mortgaged Property; and

                           (ii) a certificate from a Responsible Officer
         certifying that, to the best of his knowledge and in all material
         respects (i) the representations of the Borrower in Section 4.10 are
         true and correct and apply to the Hydrocarbon Interests evaluated in
         the Reserve Report that are described in the Mortgage and (ii) the
         Borrower has, with respect to those material Hydrocarbon Interests that
         are evaluated in the most recently delivered Reserve Report, but that
         are not covered by a Mortgage, conducted overall title due diligence
         that, in all material respects, equals or exceeds industry standards
         given the applicable facts and circumstances.



                                      -25-
<PAGE>   30

                  (e) In addition to the foregoing, on August 30, 1998, the
Borrower shall furnish to the Agent a Reserve Report prepared as of July 1,
1998, by or under the supervision of the chief engineer or Vice President of
Operations of the Borrower who shall certify such Reserve Report to have been
prepared in accordance with the procedures used in the immediately preceding
Initial Reserve Report.

                  (f) Notwithstanding the foregoing, so long as there is a
Senior Credit Agreement in effect which requires the semi-annual delivery to the
Senior Lenders of reserve reports evaluating the Borrower's and its
Subsidiaries' Oil and Gas Properties, delivering the Agent and Noteholders with
a copy of each such reserve report and any accompanying officer's certificate
(certified to Agent and the Noteholders) required thereunder shall satisfy the
Borrower's obligations under this Section 7.07, so long as such reserve report
includes a calculation of reserve value based upon pricing assumptions
consistent with Commission reporting requirements at the time.

         Section 7.08  Intentionally Omitted.

         Section 7.09  Additional Collateral.

                  (a) Should any of the Borrower's or any Subsidiary's
Properties which are not Mortgaged Property be pledged as collateral for the
payment of all or any portion of the Senior Loan Obligations, the Borrower will
simultaneously with such pledge in favor of the Senior Lenders (or Senior Loan
Agent) grant or cause such Subsidiary to grant to the Trustee as security for
the Obligations a second-priority Lien interest (subject only to Excepted Liens,
the matters set out on Schedule 4.10 hereto, and any additional qualifications
and exceptions accepted by the Senior Lenders under any mortgage of such
Property to the Senior Agent) in the Borrower's or the Subsidiary's interest in
such Properties not already subject to a Lien of the Basic Documents, which Lien
will be created and perfected by and in accordance with the provisions of deeds
of trust, security agreements and financing statements, or other Basic
Documents, all in form substantially the same as the previous Collateral
Documents and in sufficient executed (and acknowledged where necessary or
appropriate) counterparts for recording purposes.

                  (b) Concurrently with the granting of the Lien or other action
referred to in Section 7.09(a) above, the Borrower will provide to the Agent all
title information provided to the Senior Lenders or Senior Loan Agent in
connection therewith and any legal opinion (addressed to the Agent as well)
provided to the Seniors Lenders or Senior Loan Agent in connection therewith.

         Section 7.10 ERISA Information and Compliance. Immediately after any
Responsible Officer of the Borrower knows or has reason to know any of the
following items are true, the Borrower will deliver to the Agent a certificate
of a Responsible Officer of the Borrower setting forth details as to such
occurrence and such action, if any, the Borrower or any ERISA Affiliate 



                                      -26-
<PAGE>   31
is required or proposes to take, together with any notices required or proposed
to be given to or filed with or by the Borrower or its ERISA Affiliate with
respect thereto: that a Reportable Event has occurred or that an application may
be or has been made to the Secretary of the Treasury for a waiver or
modification of the minimum funding standard; that a Multiemployer Plan has been
or may be terminated, reorganized, partitioned or declared insolvent under Title
IV of ERISA; that any required contribution which is material to a Plan,
Multiemployer Plan or Employee Plan has not been or may not be timely made; that
proceedings may be or have been instituted under Section 4069(a) of ERISA to
impose liability on the Borrower or an ERISA Affiliate or under Section 4042 of
ERISA to terminate a Plan or appoint a trustee to administer a Plan; that the
Borrower or any ERISA Affiliate has incurred or may incur any liability
(including any contingent or secondary liability) on account of the termination
of or withdrawal from a Plan or a Multiemployer Plan; and that the Borrower or
any ERISA Affiliate may be required to provide security to a Plan under Section
401(a)(29) of the Code; or any other condition(s) exist(s) or may occur with
respect to one or more Plans, Employee Plans and/or Multiemployer Plans which
would reasonably be expected to result, individually or in the aggregate, in a
Material Adverse Effect.

         Section 7.11 Subsidiary Security. Should the Borrower grant to the
Senior Loan Agent for the benefit of the Senior Lenders, or to the Senior
Lenders, a security interest and pledge of the Capital Stock of any Subsidiary
(whether existing as of the Closing Date or created or acquired thereafter), the
Borrower will, simultaneously with such pledge in favor of the Senior Loan Agent
or Senior Lenders, grant to the Trustee for the benefit of the Noteholders, a
second in priority security interest and pledge of such Capital Stock in form
and substance satisfactory to the Agent and if any Subsidiary should guaranty
all or any portion of the Senior Loan, the Borrower will cause such Subsidiary
to enter into a Guaranty Agreement of the Obligations in substantially the same
form as the Guaranty Agreement given by Brigham, Inc. on the Closing Date or
otherwise in form and substance satisfactory to the Agent. The delivery of such
security and guaranty shall be accompanied by such back up corporate authority
and opinions of counsel (addressed to the Agent as well as the Senior Loan
Agent) as are provided to the Senior Loan Agent.


                                  ARTICLE VIII
                               NEGATIVE COVENANTS

         Unless the Agent's prior written consent to the contrary is obtained,
for the benefit of each of the Noteholders, the Borrower will at all times
comply with the covenants contained in this Article VIII (or cause each
Subsidiary's compliance with the applicable covenants), from the date hereof and
for so long as any part of the Obligations is outstanding.

         Section 8.01  Debt.  Neither the Borrower nor any Subsidiary will:

                  (a) Incur, create or assume any Debt, other than Permitted
Debt, such that the ratio of the Borrower's Adjusted Consolidated Net Tangible
Assets (as at the end of the immediately preceding calendar quarter) to the sum
of (i) Borrower's Consolidated Indebtedness (after such incurrence, creation or
assumption of additional Debt other than Permitted Debt) plus 



                                      -27-
<PAGE>   32


(ii) past due interest on Debt, is less than 1.5 to 1.0. This covenant shall
also apply to any such Debt incurred or assumed as a result of a merger or
consolidation with any other Person. Any such Debt so incurred, created or
assumed (without violation of this Section 8.01) must be fully subordinated to
the Obligations unless the Agent agrees otherwise, provided that, so long as ECT
has been given a first look and right to make a proposal for any future
subordinated indebtedness, up to $25,000,000 (less the maximum potential balance
at the time in question of the Schedule 8.02 Payables) in the aggregate of such
Debt may be incurred that is pari passu in right of payment with the Notes.
Notwithstanding the foregoing, in the event of any refinancing of the Senior
Loan, which refinancing does not violate, on a proforma basis for the four
fiscal quarters of the Borrower after the refinancing, the interest coverage
test of Section 8.16, the current ratio test of Section 8.17, or, provided the
amount of such refinanced Senior Loan is more than $75,000,000, the covenant in
the first sentence of this subsection (a), the refinanced Senior Loan shall
remain senior to (and shall not be subordinate to) the Obligations; or

                  (b) Incur, create, suffer or assume any accounts payable for
the deferred purchase price of Property or services or any Trade Payables which
are more than 75 days past the invoice or billing date, unless such accounts
payable are either (i) being contested in good faith by appropriate proceedings
and reserves as required under GAAP shall have been established therefor, or
(ii) Schedule 8.02 Payables which are not past due.

Notwithstanding the foregoing, if at any time the ratio of the Borrower's
Adjusted Consolidated Net Tangible Assets to the sum of (a) Borrower's
Consolidated Indebtedness plus (b) past due interest on Debt, is less than 1.5
to 1.0, the Agent shall have the right to require, and the Borrower covenants
and agrees to convey (or cause to be conveyed) to the Trustee or the Agent for
the benefit of the Agent and the Noteholders, such additional Potential
Collateral as the Agent shall require (subject to the Senior Lenders' rights to
a first and prior lien in such Potential Collateral). Such conveyance shall be
made within 30 days following receipt of written notice from the Agent and shall
be deemed a pledge of additional Collateral in accordance with Section 7.09. As
used in this paragraph, "Potential Collateral" means any of Borrower's or any
Subsidiary's Oil and Gas Properties (which are not already Collateral) which are
identified as containing proved Hydrocarbon reserves, whether currently existing
or hereafter acquired.

         Section 8.02 Liens. Neither the Borrower nor any Subsidiary will
create, incur, assume or permit to exist any Lien on any of its Properties (now
owned or hereafter acquired), except:

                  (a) Liens securing the Senior Loan; provided the Trustee or
the Agent is granted a second Lien in such Property securing the payment of the
Obligations;

                  (b) Liens securing the payment of the Obligations;

                  (c) Excepted Liens;

                  (d) Liens securing leases allowed under clause (e) of the
definition of Excepted Liens but only on the Property under lease;



                                      -28-
<PAGE>   33

                  (e) Liens disclosed on Schedule 8.02; and

                  (f) Any Permitted Encumbrances as described in the Mortgage.

         Section 8.03 Investments, Loans and Advances. Neither the Borrower nor
any Subsidiary will make or permit to remain outstanding any loans or advances
to or investments in any Person, except that the foregoing restriction shall not
apply to:

                  (a) investments, loans or advances reflected in the 
Financial Statements or which are disclosed to the Noteholders in Schedule 8.03;

                  (b) accounts receivable arising in the ordinary course Of
business;

                  (c) direct obligations of the United States or any agency
thereof, or obligations guaranteed by the United States or any agency thereof,
in each case maturing within one year from the date of creation thereof;

                  (d) commercial paper maturing within one year from the date of
creation thereof rated in the highest grade by Standard & Poors Corporation or
Moody's Investors Service, Inc.;

                  (e) deposits maturing within one year from the date of
creation thereof with, including certificates of deposit issued by any office
located in the United States, Canada, or England of, any bank or trust company
which is organized under the laws of the United States, Canada, England or any
state or province thereof, which has capital, surplus and undivided profits
aggregating at least $100,000,000.00 (as of the date of such bank or trust
company's most recent financial reports) and has a short term deposit rating of
no lower than A2 or P2, as such rating is set forth from time to time, by
Standard & Poors Corporation or Moody's Investors Service, Inc. (or their
successors), respectively;

                  (f) deposits in money market funds investing exclusively in
investments described in Section 8.03(c), 8.03(d) or 8.03(e);

                  (g) Investments of up to $400,000 in the aggregate in Quest
Resources L.L.C.;

                  (h) (i) investments, distributions, loans and advances by the
Borrower in or to any Subsidiary of the Borrower which is a Guarantor, (ii)
investments, distributions, loans and advances by the Borrower in or to any
Subsidiary of the Borrower which is not a Guarantor, provided that such
Subsidiary has direct or indirect ownership interests in Oil and Gas Properties
or gas gathering systems, gas plants, and similar assets related thereto and the
aggregate outstanding amount of such investments, distributions, loans and
advances under this clause (ii) shall not exceed $1,000,000 at any time, or
(iii) investments in equity interests in any Person (other than a Subsidiary as
provided in clauses (i) or (ii)) whose business is the acquisition, exploration
and development of Oil and Gas Properties, gas gathering systems, gas plants, or
any line of business which is closely related thereto, provided that the
aggregate outstanding amount of any such investments under this clause (iii)
shall not exceed $1,000,000 at any time;



                                      -29-
<PAGE>   34

                  (i) investments, distributions, loans and advances by a
Subsidiary to the Borrower;

                  (j) extensions of credit to purchasers, working interest
owners, employees and other persons in the ordinary course of business, up to an
aggregate of $1,000,000 at any one time.

         Section 8.04 Dividends, Distributions and Redemptions. Neither the
Borrower or any Subsidiary will declare or pay any dividend, purchase, redeem or
otherwise acquire for value any of its stock now or hereafter outstanding,
return any capital to its stockholders or make any distribution of its assets to
its partners, except to the Borrower or any Subsidiary.

         Section 8.05 Sales and Leasebacks. Neither the Borrower nor any
Subsidiary will enter into any arrangement, directly or indirectly, with any
Person whereby the Borrower or any Subsidiary shall sell or transfer any of its
Property, whether now owned or hereafter acquired, and whereby the Borrower or
any Subsidiary shall then or thereafter rent or lease as lessee such Property or
any part thereof or other Property which the Borrower or any Subsidiary intends
to use for substantially the same purpose or purposes as the Property sold or
transferred.

         Section 8.06 Nature of Business. Neither the Borrower nor any
Subsidiary will allow any material change to be made in the character of its
business as an independent oil and gas exploration and production company.

         Section 8.07 Mergers, Etc. The Borrower will not and will not permit
any Subsidiary to merge into or with or consolidate with any other Person (other
than the Borrower or a Subsidiary) or sell, lease or otherwise dispose of
(whether in one transaction or in a series of transactions) all or substantially
all of its Property or assets to any other Person (other than the Borrower or a
Subsidiary) unless (i) no Default or Event of Default exists and after giving
effect to such merger, no Default or Event of Default shall exist, (ii) after
giving effect to such merger or consolidation, the surviving entity (as the
Borrower hereunder), or in the event of a merger or consolidation of a
Subsidiary, the Borrower, would be able to incur at least $1 in additional Debt
(other than Permitted Indebtedness), and (iii) the surviving entity ratifies and
confirms its Obligations under the Basic Documents and the Notes to the
reasonable satisfaction of the Agent and each Guarantor whose Guaranty Agreement
is in full force and effect ratifies and confirms its Guaranty Agreement to the
reasonable satisfaction of the Agent.

         Section 8.08 Proceeds of Notes. The Borrower will not permit proceeds
of the Notes to be used for any purpose other than the partial payment of the
Senior Loan. Neither the Borrower nor any Person acting on behalf of the
Borrower has taken or will take any action which might cause any of the Basic
Documents to violate Regulation G, U or X or any other regulation of the Board
of Governors of the Federal Reserve System or to violate Section 7 of the
Securities Exchange Act of 1934 or any rule or regulation thereunder, in each
case as now in effect or as the same may hereinafter be in effect.



                                      -30-
<PAGE>   35

         Section 8.09 ERISA Compliance. The Borrower will not at any time:

                  (a) Engage in, or permit any ERISA Affiliate to engage in, any
transaction in connection with which the Borrower or any ERISA Affiliate could
be subjected to either a civil penalty assessed pursuant to section 502(c), (i),
or (l) of ERISA or a tax imposed by Chapter 43 of Subtitle D of the Code, which
could reasonably be expected to have a Material Adverse Effect;

                  (b) Terminate, or permit any ERISA Affiliate to terminate, any
Plan in a manner, or take any other action with respect to any Plan, which could
reasonably be expected to result in any liability of the Borrower or any ERISA
Affiliate to the PBGC, which could have a Material Adverse Effect;

                  (c) Permit to exist, or allow any ERISA Affiliate to permit to
exist, any accumulated funding deficiency within the meaning of Section 302 of
ERISA or section 412 of the Code, whether or not waived, with respect to any
Plan which, if funded, could reasonably be expected to have a Material Adverse
Effect;

                  (d) Permit, or allow any ERISA Affiliate to permit, the
actuarial present value of the benefit liabilities under any Plan maintained by
the Borrower or any ERISA Affiliate which is regulated under Title IV of ERISA
to exceed the current value of the assets (computed on a plan termination basis
in accordance with Title IV of ERISA) of such Plan allocable to such benefit
liabilities by an amount which could, if such benefits become payable,
reasonably be expected to have a Material Adverse Effect. The term "actuarial
present value of the benefit liabilities" shall have the meaning specified in
section 4041 of ERISA;

                  (e) Contribute to or assume an obligation to contribute to, or
permit any ERISA Affiliate to contribute to or assume an obligation to
contribute to, any Multiemployer Plan;

                  (f) Incur, or permit any ERISA Affiliate to incur, a liability
to or on account of a Plan under sections 515, 4062, 4063, 4064, 4201 or 4204 of
ERISA which, in the aggregate for all such liabilities, could reasonably be
expected to have a Material Adverse Effect;

                  (g) Contribute to or assume an obligation to contribute to, or
permit any ERISA Affiliate to contribute to or assume an obligation to
contribute to, any employee welfare benefit plan, as defined in section 3(1) of
ERISA, including, without limitation, any such plan maintained to provide
benefits to former employees of such entities, that may not be terminated by
such entities in their sole discretion at any time without any material
liability; or

                  (h) Amend or permit any ERISA Affiliate to amend, a Plan
resulting in an increase in current liability such that Borrower or any ERISA
Affiliate is required to provide security to such Plan under section 401(a)(29)
of the Code.



                                      -31-
<PAGE>   36

         Section 8.10 Sale of Oil and Gas Properties. The Borrower will not, and
will not permit any Subsidiary to, sell, assign, farm-out, convey or otherwise
transfer any Hydrocarbon Interests except for (i) the sale of Hydrocarbons in
the ordinary course of business; (ii) assignments, farmouts, and other
disposition of Hydrocarbon Interests which do not contain identified proved
Hydrocarbon reserves, provided such assignments, farmouts, and other
dispositions are in the normal course of business (e.g., in bringing in
participants or disposing of unattractive prospects); (iii) the sale or transfer
of equipment that is no longer necessary for the business of the Borrower or
such Subsidiary or is replaced by equipment of at least comparable value and use
and (iv) during any consecutive four fiscal quarters, sales of Hydrocarbon
Interests containing identified proved Hydrocarbon reserves which, when taken
together with the proceeds of any permitted sales of Subsidiaries during such
four quarters under the next sentence of this Section 8.10, shall not exceed
$3,000,000 in the aggregate. The Borrower will not sell, and will not permit the
sale of, any interest in any Subsidiary unless all or substantially all of the
Borrower's interest in such Subsidiary is sold and, during any consecutive four
fiscal quarters, the proceeds of any such sale taken together with the proceeds
of any sale of Hydrocarbon Interests permitted under clause (iv) of this Section
8.10 does not exceed $3,000,000.

         Section 8.11 Environmental Matters. Neither the Borrower nor any
Subsidiary will knowingly cause or permit any of its Property to be in violation
of, or knowingly do anything or permit anything to be done which will subject
any such Property to any remedial obligations under any Environmental Laws,
assuming disclosure to the applicable Governmental Authority of all relevant
facts, conditions and circumstances, if any, pertaining to such Property, where
such violations or remedial obligations would have a Material Adverse Effect.

         Section 8.12 Transactions with Affiliates. Neither the Borrower nor any
Subsidiary will enter into any transaction, including, without limitation, any
purchase, sale, lease or exchange of Property or the rendering of any service,
with any Affiliate (other than the Borrower or a Subsidiary) unless such
transaction (a) is otherwise not in violation of this Indenture, and (b) unless
approved by a majority of the disinterested members of the Board of Directors,
is in the ordinary course of its business and is upon fair and reasonable terms
no less favorable to it than it would obtain in a comparable arm's length
transaction with a Person not an Affiliate.

         Section 8.13 Negative Pledge Agreements. The Borrower will not and will
not permit any Subsidiary to create, incur, assume or suffer to exist any
contract, agreement or understanding (other than the Basic Documents) which in
any way prohibits or restricts any Subsidiary from paying dividends or making
any other distribution to the Borrower or which requires the consent of a notice
to other Persons in connection with any of the foregoing, other than the Senior
Loan Documents so long as the Senior Loan Documents permit the payment of
dividends and making of other distributions by the Subsidiaries to the Borrower
to the extent needed for the Borrower to meet its scheduled debt service
obligations to the Noteholders.

         Section 8.14 Gas Imbalances, Take-or-Pay Prepayments. The Borrower will
not allow gas imbalances, take-or-pay or other prepayments with respect to the
Hydrocarbon Interests of the Borrower and its Subsidiaries which would require
the Borrower or its Subsidiaries to deliver five percent (5%) or more of the
Borrower's and its Subsidiaries' Hydrocarbons 



                                      -32-
<PAGE>   37

produced on a monthly basis from the Hydrocarbon Interests at some future time
without then or thereafter receiving full payment therefor.

         Section 8.15 Borrower as Operator. The Borrower will not and will not
allow any of its Subsidiaries to voluntarily resign as operator of more than
twenty-five percent (25%) of their currently operated Oil and Gas Properties,
unless a substitute operator is appointed that is another Subsidiary of the
Borrower or is otherwise acceptable to the Majority Noteholders, approval of
such substitute operator not to be unreasonably withheld.

         Section 8.16 Consolidated Interest Coverage Ratio. As of the last day
of each fiscal quarter, the Borrower will not permit the Consolidated Interest
Coverage Ratio to be less than (i) 1.5 to 1.0 as of the end of the first four
(4) fiscal quarters following the Closing Date and (ii) 2.0 to 1.0 as of the end
of each fiscal quarter thereafter.

         Section 8.17 Current Ratio. The Borrower will not permit its ratio of
(i) consolidated current assets of the Borrower and its Consolidated
Subsidiaries (including, without limitation, any unused and available
commitments under the Senior Credit Agreement) to (ii) their consolidated
current liabilities (excluding any principal or interest payments due on the
Senior Loan or the Notes), to be less than .8 to 1.0 at any time.

                                   ARTICLE IX
                              PAYMENT OF THE NOTES

         Section 9.01 Repayment. The Borrower shall pay to the Noteholders on
the Maturity Date an amount equal to the outstanding principal amount of the
Notes plus the accrued and unpaid interest on the outstanding principal amount
of the Notes. The Borrower may prepay the Obligations at any time in whole or in
part without penalty or premium.

         Section 9.02  Interest.

                  (a) Subject to the provisions of Section 9.02(b), the
outstanding principal amount of the Notes shall bear interest at the following
rates per annum:

                    Period                                            Rate
                    ------                                            ----

                  Funding Date through August __, 2001                 12%

                  August __, 2001 through August __, 2002              13%

                  August __, 2002 through Maturity Date                14%

The foregoing rates shall apply only to interest which is paid in cash. In the
event the Borrower should elect to make any interest payments in kind as
permitted by Section 9.02(b), the rates applicable to such payments shall be as
set forth in Section 9.02(b).

                  (b) So long as there exists no Event of Default, if on any
Interest Payment Date either (i) there exists a "Borrowing Base Deficiency"
under the Senior Credit Agreement or (ii) the payment in cash of interest
accrued on the Notes would cause the Borrower to be in violation of any covenant
or other restriction set forth in the Senior Loan Documents or any Basic
Document, the Borrower may pay such interest in kind, as provided in this
Section 9.02(b). In such event the accrued interest due on such Interest Payment
Date shall be calculated at the rates set forth in this Section 9.02(b) and the
interest due (calculated at the 



                                      -33-
<PAGE>   38

rates set forth in this Section 9.02(b)) shall be deemed an advance of principal
under the Notes and, as of the Interest Payment Date, shall be added to the
outstanding principal balance of the Notes (notwithstanding that the outstanding
principal balance may exceed, in the aggregate, the face amount of the Notes).
In order to exercise its option to pay interest in kind under this Section
9.02(b), the Borrower shall, on or before the applicable Interest Payment Date,
deliver written notice to the Agent executed by a Responsible Officer specifying
the applicable covenant or restriction of the Senior Loan Documents or the Basic
Documents that will be violated by payment of accrued interest in cash and
notifying Agent of its election to pay interest in kind. Any such election must
be made as to all Notes. Should Borrower fail to deliver such written notice in
a timely fashion Borrower shall be deemed to have irrevocably elected to make
payment of accrued interest in cash and any subsequent failure to do so in a
timely fashion (subject to the thirty (30) day grace period provided in Section
10.01(a)) shall constitute an Event of Default hereunder. Notwithstanding
anything contained herein to the contrary, the Borrower may not pay interest in
kind over the term of the Notes for more than six (6) calendar quarters. In the
event the Borrower elects to pay interest in kind, such interest to be paid
shall be calculated at the following rates commencing on the immediately
preceding Interest Payment Date:

                           Period                                 Rate
                           ------                                 ----

                  Funding Date through August __, 2001             13%

                  August __, 2001 through August __, 2002          14%

                  August __, 2002 through Maturity Date            15%

                  (c) In the event any sum due and payable hereunder is not paid
when due such past due amount shall accrue interest at the Default Rate from the
date due until paid. Should an Event of Default occur hereunder, interest on the
Obligations shall accrue at the Default Rate from the date of occurrence of the
Default to which such Event of Default is attributable, until such Event of
Default is cured or waived.

                  (d) Interest shall be computed based on a year of 360 days and
twelve 30-day months (pro-rated appropriately for the period from the Funding
Date until the first Interest Payment Date and for any period of less than three
months for which interest may be due as a result of the prepayment or
acceleration of the Notes). The rates of interest applicable to the Notes
provided in Sections 9.02(a) and (b) shall commence on the first day immediately
following the Funding Date or the applicable anniversary of the Funding Date and
remain in effect through the next succeeding anniversary of the Funding Date, or
the Maturity Date, as applicable.

                  (e) Accrued interest on the Notes shall be due and payable in
cash or, if permitted by Section 9.02(b), in kind, quarterly on each Interest
Payment Date (including the Maturity Date) or, in the event the maturity of the
Notes is accelerated pursuant to the terms of the Basic Documents, such earlier
date as the Notes become due and payable, or the date the Notes are paid in
full, whichever first occurs. If any Interest Payment Date is not a Business



                                      -34-
<PAGE>   39

Day, the interest payment that would be due thereon shall instead be due on the
next following Business Day.

                  (f) Notwithstanding anything herein or in the other Basic
Documents to the contrary, it is the intention of the parties hereto to conform
strictly to usury laws applicable to this transaction. Accordingly, if the
transactions contemplated hereby would be usurious under applicable law, then,
in that event, notwithstanding anything to the contrary in the Notes, this
Indenture or in any other Basic Document or agreement entered into in connection
with or as security for the Notes, it is agreed as follows: (a) the aggregate of
all consideration which constitutes interest under law applicable to the
Noteholders that is contracted for, taken, reserved, charged or received under
the Notes, this Indenture or under any of the other Basic Documents or
agreements or otherwise in connection with this transaction shall under no
circumstances exceed the maximum amount allowed by such applicable law, and any
excess shall be canceled automatically and, if already paid, shall be credited
by the Noteholders on the principal amount of the Obligations (or, to the extent
that the principal amount of the Obligations shall have been or would thereby be
paid in full, refunded to the Borrower); and (b) in the event that the maturity
of the Notes is accelerated by reason of any Event of Default under this
Indenture or otherwise, or in the event of any required or permitted prepayment,
then such consideration that constitutes interest under law applicable to this
transaction may never include more than the maximum amount allowed by such
applicable law, and (c) excess interest, if any, provided for in this Indenture
or otherwise in connection with the Notes shall be canceled automatically and,
if already paid, shall be credited by the Noteholders on the principal amount of
the Obligations (or, to the extent that the principal amount of the Obligations
shall have been or would thereby be paid in full, refunded by the Noteholders to
the Borrower). All sums paid or agreed to be paid to the Noteholders for the
use, forbearance or detention of sums included in the Obligations shall, to the
extent permitted by applicable law, be amortized, prorated, allocated and spread
throughout the full term of the Notes until payment in full so that the rate or
amount of interest on account of the Obligations does not exceed the applicable
usury ceiling, if any. As used in this Section 9.02(f), the term "applicable
law" shall mean the laws which govern this Indenture as described in Section
12.07 (or the law of any other jurisdiction whose laws may be mandatorily
applicable notwithstanding other provisions of this Indenture), or law of the
United States of America applicable to the Noteholders and the Notes which would
permit the Noteholders to contract for, charge, take, reserve or receive a
greater amount of interest than under any other applicable law. If the stated
rate of interest under this Indenture ever exceeds the Maximum Rate, then the
outstanding principal amount of the Notes made hereunder shall bear interest at
the Maximum Rate until the difference between the interest which would have been
due at the stated rates of interest and the amount due at the Maximum Rate (the
"Lost Interest") has been recaptured by the Noteholders. If the Notes are repaid
in full and the Lost Interest has not been fully recaptured by the Noteholders
pursuant to the preceding sentence, then the Notes shall be deemed to have
accrued interest at the Maximum Rate since the date the initial advance under
the Notes was made to the extent necessary to recapture the Lost Interest not
recaptured pursuant to the preceding sentence and, to the extent allowed by law,
the Borrower shall pay to the Noteholders the amount of the Lost Interest
remaining to be recaptured by the Noteholders.


                                      -35-
<PAGE>   40


         Section 9.03  Payments and Computations.

                  (a) All payments and obligations by Borrower under the Notes
or any other Basic Document shall be made to the Agent, without any presentment
and without any notation of such payment being made on the Notes (i) by wire
transfer in immediately available funds to such account as the Agent may
designate from time to time by written notice to the Borrower (the "Agent's
Account") or (ii) in such other manner as may be designated in writing to the
Borrower by the Agent.

                  (b) The Borrower shall make each payment under this Indenture
and under the Notes not later than 2:00 p.m. (Houston, Texas time) on the day
when due in U.S. Dollars to the Agent at the location specified in paragraph (a)
above in immediately available funds. All payments by the Borrower hereunder
shall be made without any offset, abatement, withholding, or reduction.

                  (c) Whenever any payment under the Basic Documents shall be
stated to be due on a day other than a Business Day, such payment shall be made
on the next succeeding Business Day, and (other than an interest payment subject
to Section 9.02(e) above) such extension of time shall in such case be included
in the computation of payment of interest. If the time for payment for an amount
payable is not specified in the Basic Documents, or in any other document, the
payment shall be due and payable ten days after the date on which the Agent or
any Noteholder demands payment therefor.

                  (d) Following receipt of payment in cash of any obligations
due under the Notes or any other Basic Document the Agent will promptly
thereafter cause to be distributed like funds relating to the payment of
principal, interest or fees ratably to the Noteholders at their respective
Noteholder's Account. If and to the extent that the Agent receives any payment
or prepayment from the Borrower and fails to distribute such payment or
prepayment to the Noteholders ratably on the basis of their respective
Participations on the day the Agent receives such payment or prepayment (if
received prior to 1:00 P.M. (Houston, Texas time) on such day) or the next
Business Day (if received after 1:00 P.M. (Houston, Texas time) on such day),
then the Agent shall pay to each Noteholder such Noteholder's Participation of
such payment or prepayment together with interest thereon at the Federal Funds
Rate for each day from the date such amount should have been distributed by the
Agent until such payment or prepayment is actually distributed to the
Noteholders. All payments and prepayments received shall be applied first to
accrued interest and second to the reduction of principal.

                  (e) Unless the Agent shall have received written notice from
the Borrower prior to the date on which any payment is due to the Noteholders
that the Borrower will not make such payment in full or will make such payment
in kind pursuant to Section 9.02(b), the Agent may assume that the Borrower has
made such payment in full, in cash, to the Agent on such date and the Agent may,
in reliance upon such assumption, cause to be distributed to each Noteholder on
such date an amount equal to the amount then due such Noteholder. If and to the
extent the Borrower shall not have so made such payment in full, in cash, to the
Agent, each Noteholder shall repay to the Agent forthwith on demand such amount
distributed to such Noteholder, together with interest, for each day from the
date such amount is distributed to such



                                      -36-
<PAGE>   41

Noteholder until the date such Noteholder repays such amount to the Agent, at
the Federal Funds Rate for such day.


                                    ARTICLE X
                              DEFAULT AND REMEDIES

         Section 10.01 Events of Default. The occurrence of any of the following
shall be an "Event of Default" for the purposes of this Indenture and the Notes:

                  (a) the Borrower shall default in the payment or prepayment
when due of any Obligations, and such default, other than a default of a payment
or prepayment of principal (which shall have no cure period), shall continue
unremedied for a period of thirty (30) days after such Obligations become due,
in the case of interest, or thirty (30) days after the Borrower receives notice
from the Agent that such Obligations are due, in the case of Obligations other
than principal or interest; or

                  (b) (i) The Borrower or any Guarantor shall, as to any Debt
(other than the Obligations and the Senior Loan) aggregating more than
$2,000,000 default in the payment when due of any principal of or interest
thereon, or any event specified in any note, agreement, indenture or other
document evidencing or relating to any such Debt shall occur if the effect of
such event is to cause, or (with the giving of any notice or the lapse of time
or both) to permit the holder or holders of such Debt (or a trustee or agent on
behalf of such holder or holders) to cause, such Debt to become due prior to its
stated maturity, or (ii) as to the Senior Loan, there shall have occurred a
default thereunder and the holders of the Senior Loan shall have elected to
accelerate the payment of the Senior Loan (or it shall be accelerated
automatically or otherwise be due and payable in full); or

                  (c) any representation, warranty or certification made or
deemed made herein or in any other Basic Document by the Borrower or any
Guarantor, or any certificate furnished by the Borrower or any Guarantor to the
Trustee, any Noteholder or the Agent pursuant to the provisions hereof or any
other Basic Document, shall prove to have been false or misleading as of the
time made or furnished in any material and adverse respect and such default
shall continue unremedied for a period of forty-five (45) days after notice
thereof to the Borrower by the Agent; or

                  (d) the Borrower shall default in the performance of any of
its obligations under Article VIII which are not capable of being cured, or
under Sections 8.01, 8.16, 8.17 or 7.01(c); or the Borrower shall default in the
performance of any of its obligations under Article VIII which are capable of
being cured (other than Sections 8.01, 8.16 and 8.17) or any other Article of
this Indenture (other than 7.01(c)) or under any other Basic Document to which
it is a party (other than the payment of amounts due which shall be governed by
Section 10.01(a)) and such default shall continue unremedied for a period of
forty-five (45) days after notice thereof to the Borrower by the Agent; or



                                      -37-
<PAGE>   42


                  (e) any Guarantor shall default in the performance of its
obligation to pay the Liabilities (as defined in the Guaranty Agreement) at
maturity, or any Guarantor shall default in the performance of any of its other
obligations under its Guaranty Agreement and such default shall continue
unremedied for a period of forty-five (45) days after notice thereof to the
Guarantor by the Agent; or

                  (f) the Borrower shall admit in writing its inability to, or
be generally unable to, pay its debts as such debts become due; or

                  (g) the Borrower shall (i) apply for a consent to the
appointment of, or the taking of possession by, a receiver, custodian, trustee
or liquidator of itself or of all or a substantial part of its property, (ii)
make a general assignment for the benefit of its creditors, (iii) commence a
voluntary case under the Federal Bankruptcy Code (as now or hereafter in
effect), (iv) file a petition seeking to take advantage of any other law
relating to bankruptcy, insolvency, reorganization, winding-up, liquidation or
composition or readjustment of debts, (v) fail to controvert in a timely and
appropriate manner, or acquiesce in writing to, any petition filed against it in
an involuntary case under the Federal Bankruptcy Code, or (vi) take any
corporate action for the purpose of effecting any of the foregoing, or

                  (h) a proceeding or case shall be commenced, without the
application or consent of the Borrower, in any court of competent jurisdiction,
seeking (i) its liquidation, reorganization, dissolution or winding-up, or the
composition or readjustment of its debt; (ii) the appointment of a trustee,
receiver, custodian, liquidator or the like of the Borrower of all or any
substantial part of its assets, or (iii) similar relief in respect of the
Borrower under any law relating to bankruptcy, insolvency, reorganization,
winding-up, or composition or adjustment of debts, and such proceeding or case
shall continue undismissed, or an order, judgement or decree approving or
ordering any of the foregoing shall be entered and continue unstayed and in
effect, for a period of 60 days; or an order for relief against the Borrower
shall be entered in an involuntary case under the Federal Bankruptcy Code; or

                  (i) a judgment or judgments for the payment of money in excess
of $2,000,000 in the aggregate shall be rendered by a court against the Borrower
and the same shall not be discharged (or provision shall not be made for such
discharge), or a stay of execution thereof shall not be procured, within
forty-five (45) days from the date of entry thereof and the Borrower shall not,
within said period of 45 days, or such longer period during which execution of
the same shall have been stayed, appeal therefrom and cause the execution
thereof to be stayed during such appeal; or

                  (j) any of the Basic Documents after delivery thereof shall
for any reason, except to the extent permitted by the terms thereof, cease to be
in full force and effect and valid, binding and enforceable in all material
respects in accordance with their terms, or cease in any material respect to
create a valid and perfected Lien of the priority required thereby on any of the
collateral purported to be covered thereby, except to the extent permitted by
the terms of this Indenture, or the Borrower or any Guarantor shall so state in
writing, and such Default shall continue unremedied for a period of forty-five
(45) days after notice thereof to the Borrower by the Agent; or



                                      -38-
<PAGE>   43

                  (k) any Guarantor takes, suffers or permits to exist any of
the events or conditions referred to in paragraphs (f), (g), (h) or (i) hereof
or if any Guaranty Agreement related thereto shall for any reason cease to be
valid and binding on such Guarantor in all material respects or if such
Guarantor shall so state in writing, and such Default shall continue unremedied
for a period of forty-five (45) days after notice thereof to the Guarantor by
the Agent; or

                  (l) there occurs a Change in Control; or

                  (m) any annual audited financial statement delivered to Agent
pursuant to Section 7.01(a) is qualified (as to going concern or similar
qualifications).

         Section 10.02  Remedies.

                  (a) During the continuance of any Event of Default specified
in Section 10.01 (other than clauses (f), (g) or (h) of Section 10.01), or in
clause (k) as it relates to clauses (f), (g) or (h) thereof, the Agent may by
written notice to the Borrower declare the entire principal amount of all
Obligations then outstanding, including interest accrued thereon, to be
immediately due and payable without presentment, demand, protest, notice of
protest or dishonor, notice of intent to accelerate, or other notice of default
of any kind, all of which are hereby expressly waived by the Borrower.

                  (b) Upon the happening of any Event of Default specified in
clauses (f), (g) or (h) of Section 10.01, or clause (k) as it relates to clauses
(f), (g) or (h), the entire principal amount of all Obligations then
outstanding, including interest accrued thereon, shall, without notice or action
by the Trustee, the Agent or the Noteholders be immediately due and payable
without presentment, demand, protest, notice of protest or dishonor, notice of
intent to accelerate or other notice of default of any kind, all of which are
hereby expressly waived by the Borrower.

                  (c) In addition to the foregoing, upon the happening of any of
the events described in subsections (a) and (b) above, the Trustee, at the
direction of the Agent may exercise any of the rights or remedies provided in
the Collateral Documents and other Basic Documents or avail itself of any rights
or remedies provided by applicable law.

                  (d) All proceeds received after maturity of the Notes, whether
by acceleration or otherwise shall be applied first to reimbursement of expenses
and indemnities provided for in the Basic Documents; second to accrued interest
on the Notes; third to fees; fourth pro rata to principal outstanding on the
Notes and other Obligations; and any excess shall be paid to the Borrower or as
otherwise required by any Governmental Requirement.

         Section 10.03 Production and Proceeds. Notwithstanding that, by the
terms of the various Mortgages and other Basic Documents, the Borrower and any
other mortgagors are and will be assigning to the Trustee all of the
Hydrocarbons covered thereby and all of the products thereof and proceeds and
revenues attributable thereto and all payments in lieu of such Hydrocarbons (in
this section collectively called the "Production and Proceeds"), so long as no



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<PAGE>   44

Default has occurred and is continuing (a) the Borrower and such mortgagors may
continue to receive all such Production and Proceeds, subject, however, to the
Liens created under the Mortgages and other Basic Documents, and (b) upon the
Borrower's request the Agent will confirm to any purchasers of Hydrocarbons,
title examiners, or other Persons that the Borrower and such mortgagors continue
to have the right so to receive such Production and Proceeds until notification
by the Agent of the occurrence of a Default. During the continuance of an Event
of Default, however, the Trustee at the direction of the Agent may (subject to
all rights of the Senior Loan Agent and the Senior Lenders under the Senior Loan
Documents) exercise its rights and remedies granted under the Mortgages and the
other Basic Documents, including the rights and remedies granted under the
Mortgages and the other Basic Documents, including the right to obtain
possession of all Production and Proceeds then held by the Borrower and such
mortgagors and to receive directly from the purchasers of Hydrocarbons all other
Production and Proceeds. In no case shall any failure by the Trustee to collect
directly any such Production and Proceeds constitute in any way a release of any
of its or the Agent's rights under the Basic Documents.

         Section 10.04 Set-Off. Upon the occurrence of any Event of Default, any
Noteholder shall have the right to set-off any funds of the Borrower in the
possession of the Noteholder against any Debt (or accrued interest on Debt) then
due by the Borrower to the Noteholder. The Borrower agrees that any holder of
Notes or a participation in the Notes may exercise any and all rights of
counter-claim, set-off, banker's lien and other liens with respect to any and
all monies owing by the Borrower to such holder as fully as if such holder of a
participation were a holder of a Note in the amount of such participation.

                                   ARTICLE XI
                                    THE AGENT

         Section 11.01 Authorization and Action. Each Noteholder hereby appoints
and authorizes the Agent to take such action on behalf of such Noteholder and to
exercise such powers under this Indenture as are delegated to the Agent by the
terms hereof and of the other Basic Documents, together with such powers as are
reasonably incidental thereto. As to any matters not expressly provided for by
this Indenture or any other Basic Document (including, without limitation,
enforcement or collection of the Notes), the Agent shall not be required to
exercise any discretion or take any action, but shall be required to act or to
refrain from acting (and shall be fully protected in so acting or refraining
from acting) only upon the instructions of the Majority Noteholders, and such
instructions shall be binding upon Noteholders; provided, however, that the
Agent shall not be required to take any action which exposes the Agent to
personal liability or which is contrary to this Indenture, any other Basic
Document, or applicable law.

         Section 11.02 Agent's Reliance, Etc. Neither the Agent nor any of the
Agent's directors, officers, agents or employees shall be liable for any action
taken or omitted to be taken (including the Agent's own negligence) by it or
them under or in connection with this Indenture or the other Basic Documents,
except for its or their own gross negligence or willful misconduct. Without
limitation of the generality of the foregoing, the Agent: (a) may treat the
payee of any Note as the holder thereof until the Agent receives written notice
of the 



                                      -40-
<PAGE>   45

assignment or transfer thereof signed by such payee and in form satisfactory to
the Agent; (b) may consult with legal counsel (including counsel for the
Borrower), independent public accountants and other experts selected by it and
shall not be liable for any action taken or omitted to be taken in good faith by
it in accordance with the advice of such counsel, accountants or experts; (c)
makes no warranty or representation to any Noteholder and shall not be
responsible to any Noteholder for any statements, warranties or representations
made in or in connection with this Indenture or the other Basic Documents; (d)
shall not have any duty to ascertain or to inquire as to the performance or
observance of any of the terms, covenants or conditions of this Indenture or any
other Basic Document on the part of the Borrower or any Subsidiary or to inspect
the Property (including the books and records) of such Persons; (e) shall not be
responsible to any Noteholder for the due execution, legality, validity,
enforceability, genuineness, sufficiency or value of this Indenture or any other
Basic Document; and (f) shall incur no liability under or in respect of this
Indenture or any other Basic Document by acting upon any notice, consent,
certificate or other instrument or writing (which may be by telecopy) reasonably
believed by it to be genuine and signed or sent by the proper party or parties.

         Section 11.03 The Agent and Its Affiliates. With respect to its
Participation, and the Note issued to it, the Agent shall have the same rights
and powers under this Indenture as any other Noteholder and may exercise the
same as though it were not an Agent hereunder. The term "Noteholder" or
"Noteholders" shall, unless otherwise expressly indicated, include the Agent in
its individual capacity. The Agent and its Affiliates may accept deposits from,
lend money to, act as trustee under indentures of, and generally engage in any
kind of business with, the Borrower or any Subsidiary, and any Person who may do
business with or own securities of the Borrower, or any Subsidiary, all as if
the Agent were not an agent hereunder and without any duty to account therefor
to the Noteholders.

         Section 11.04 Noteholders Loan Decision. Each Noteholder acknowledges
that it has, independently and without reliance upon the Agent or any other
Noteholder and based on the Financial Statements and such other documents and
information as it has deemed appropriate, made its own credit analysis and
decision to enter into the Basic Documents. Each Noteholder also acknowledges
that it will, independently and without reliance upon the Agent or any other
Noteholder and based on such documents and information as it shall deem
appropriate at the time, continue to make its own credit decisions in taking or
not taking action under this Indenture.

         Section 11.05 Indemnification. The Noteholders severally agree to
indemnify the Agent and each Affiliate thereof and their respective directors,
officers, employees and agents (to the extent not reimbursed by the Borrower),
according to their respective Participations from and against any and all
liabilities, obligations, losses, damages, penalties, actions, judgments, suits,
costs, expenses or disbursements of any kind or nature whatsoever which may be
imposed on, incurred by, or asserted against the Agent in any way relating to or
arising out of this Indenture or any action taken or omitted by the Agent under
this Indenture or any other Basic Document (INCLUDING THE AGENT'S OWN
NEGLIGENCE), provided that no Noteholder shall be liable for any portion of such
liabilities, obligations, losses, damages, penalties, actions, judgments, suits,
costs, expenses or disbursements resulting from the Agent's gross negligence or
willful misconduct. Without limitation of the foregoing, each Noteholder agrees
to reimburse 



                                      -41-
<PAGE>   46

the Agent promptly upon demand for its ratable share of any out-of-pocket
expenses (including counsel fees) incurred by the Agent in connection with the
preparation, execution, delivery, administration, modification, amendment or
enforcement (whether through negotiations, legal proceedings or otherwise) of,
or legal advice in respect of rights or responsibilities under, this Indenture
or any other Basic Document, to the extent that the Agent is not reimbursed for
such expenses by the Borrower.

         Section 11.06 Successor Agent. The Agent may resign at any time by
giving written notice thereof to the Noteholders and the Borrower and may be
removed at any time with cause by the Majority Noteholders upon receipt of
written notice from the Majority Noteholders to such effect. Upon receipt of
notice of any such resignation or removal, the Majority Noteholders shall have
the right to appoint a successor Agent with, if no Default exists, the consent
of the Borrower, which consent shall not be unreasonably withheld. If no
successor Agent shall have been so appointed by the Majority Noteholders with
the consent of the Borrower, if required, and shall have accepted such
appointment, within 30 days after the retiring Agent's giving of notice of
resignation or the Majority Noteholders' removal of the retiring Agent, then the
retiring Agent may, on behalf of the Noteholders and the Borrower, appoint a
successor Agent. Upon the acceptance of any appointment as Agent by a successor
Agent, such successor Agent shall thereupon succeed to and become vested with
all the rights, powers, privileges and duties of the retiring Agent, and the
retiring Agent shall be discharged from its duties and obligations under this
Indenture and the other Basic Documents. After any retiring Agent's resignation
or removal hereunder as Agent, the provisions of this Article XI shall inure to
its benefit as to any actions taken or omitted to be taken by it while it was
Agent this Indenture and the other Basic Documents.


                                   ARTICLE XII
                                     TRUSTEE

         Section 12.01  Duties of Trustee.

                  (a) If an Event of Default has occurred and is continuing, the
Trustee shall exercise such rights and powers vested in it by this Indenture and
use the same degree of care and skill in such exercise as a prudent person would
exercise or use under the circumstances in the conduct of such person's own
affairs.

                  (b) Except during the continuance of an Event of Default:

                           (i) The Trustee need perform only those duties that
         are specifically set forth (or incorporated by reference) in this
         Indenture and no others.

                           (ii) In the absence of bad faith on its part, the
         Trustee may conclusively rely, as to the truth of the statements and
         the correctness of the opinions expressed therein, upon certificates or
         opinions furnished to the Trustee and conforming to the requirements of
         this Indenture. However, in the case of any such certificates or
         opinions which by any provision hereof are specifically required to be
         furnished to the 



                                      -42-
<PAGE>   47

         Trustee, the Trustee shall be under a duty to examine the same to 
         determine whether or not they conform to the requirements of this 
         Indenture (but need not confirm or investigate the accuracy of
         mathematical calculations or other facts stated therein).

                  (c) The Trustee may not be relieved from liability for its own
negligent action, its own negligent failure to act, or its own willful
misconduct, except that:

                           (i)      This paragraph (c) does not limit the effect
         of paragraph (b) of this Section.

                           (ii) The Trustee shall not be liable for any error of
         judgment made in good faith by an officer of the Trustee, unless it is
         proved that the Trustee was negligent in ascertaining the pertinent
         facts.

                           (iii) The Trustee shall not be liable with respect to
         action it takes or omits to take in good faith in accordance with a
         direction received by it from the Agent, and the Trustee shall be
         entitled from time to time to request such a direction.

                  (d) Every provision of this Indenture and each Collateral
Document that in any way relates to the Trustee is subject to paragraphs (a),
(b) and (c) of this Section.

                  (e) The Trustee shall be under no obligation and may refuse to
perform any duty or exercise any right or power unless it receives indemnity
satisfactory to it against any loss, liability or expense. No provision of this
Indenture or any Collateral Document shall require the Trustee to expend or risk
its own funds or otherwise incur financial liability in the performance of any
of its duties hereunder or in the exercise of any of its rights or powers, if it
shall have reasonable grounds to believe that repayment of such funds or
adequate indemnity against such risk or liability is not reasonably assured to
it.

                  (f) The Trustee shall not be liable for interest on any money
received by it except as the Trustee may agree in writing with the Borrower.
Money held in trust by the Trustee need not be segregated from other funds
except to the extent required by law.

                  (g) The Trustee shall not be required to take notice, and
shall not be deemed to have notice, of any Default or Event of Default
hereunder, unless the Trustee shall be notified specifically of the Default or
Event of Default in a written instrument or document delivered to it by the
Borrower or any Guarantor, or by the Agent or the Majority Noteholders.
In the absence of delivery of a notice satisfying those requirements, the
Trustee may assume that there is no Default or Event of Default, except as noted
above.

         Section 12.02  Rights of Trustee.

                  (a) The Trustee may conclusively rely on and shall be fully
protected in acting or refraining from acting upon any document believed by it
to be genuine and to have been signed or presented by the proper person. The
Trustee shall not be bound to make any investigation into the facts or matters
stated in any resolution, certificate, statement, instrument, 



                                      -43-
<PAGE>   48
opinion, report, notice, request, direction, consent, order, bond, debenture or
other paper or document, but the Trustee, in its discretion, may make such
further inquiry or investigation into such facts or matters as it may see fit,
and, if the Trustee shall determine to make such further inquiry or
investigation, it shall be entitled to examine the books, records and premises
of the Borrower, personally or by agent or attorney, to the extent reasonably
required by such inquiry or investigation at the sole expense of the Borrower
and shall incur no liability or additional liability of any kind by reason of
such inquiry or investigation.

                  (b) Before the Trustee acts or refrains from acting, it may
require an Officers' Certificate or an Opinion of Counsel. The Trustee shall not
be liable for any action it takes or omits to take in good faith in reliance on
such certificate or opinion.

                  (c) The Trustee may act through agents and shall not be
responsible for the misconduct or negligence of any agent appointed with due
care.

                  (d) The Trustee shall not be liable for any action it takes or
omits to take in good faith which it believes to be authorized or within its
rights or powers.

                  (e) The Trustee may consult with counsel of its selection and 
the advice of such counsel or any Opinion of Counsel shall be full and complete
authorization and protection in respect of any action taken, suffered or omitted
by it hereunder in good faith and in reliance thereon.

                  (f) The Trustee will not, without the consent of the Agent,
give any consent, waiver or approval required under the Collateral Documents or
by the terms hereof with respect to the Collateral or agree to any amendment or
modification of the Collateral Documents.

                  (g) The Trustee may settle or compromise at any time any and
all claims against it which may be asserted by any governmental body or private
party for the alleged violation of any Environmental Laws affecting any of the
Collateral, and may disclaim (as to itself, but not as to the Indenture or any
successor Trustee) any power (including, without limitation, the power to sell
the Collateral) granted by the Indenture, the Collateral Documents or any
statute or rule of law, the exercise of which power may, in the sole discretion
of the Trustee, as advised by counsel, cause the Trustee to incur corporate or
personal liability under any Environmental Laws.

         Section 12.03 Individual Rights of Trustee. The Trustee in its
individual or any other capacity may become the owner or pledgee of Notes and
may otherwise deal with the Borrower or its Subsidiaries or Affiliates with the
same rights it would have if it were not Trustee. The provision of this Section
shall extend to Affiliates of the Trustee. Any Agent may do the same with like
rights. However, the Trustee must comply with Sections 12.10 and 12.11.

         Section 12.04 Trustee's Disclaimer.

         The Trustee makes no representation as to the value or condition of the
Collateral or any part thereof, or as to the title of the Borrower or any
Subsidiary thereto, or as to the security 



                                      -44-
<PAGE>   49

afforded thereby or hereby, or as to the validity or genuineness of any
Collateral pledged and deposited with the Trustee, or the validity or adequacy
of this Indenture or the Notes, it shall not be accountable for the Borrower's
use of the proceeds from the Notes or any offering memorandum or solicitation
documents, and it shall not be responsible for any statement in the Basic
Documents other than its certificate of authentication.

         Section 12.05  Notice of Defaults.

         If a Default occurs and is continuing and if it is actually known to a
Responsible Officer of the Trustee pursuant to Section 12.01(g), the Trustee
shall mail to each Noteholder and the Agent pursuant to Section 13.05 a notice
of the Default within 90 days after it occurs. Except in the case of a Default
in any payment on any Note, the Trustee may withhold the notice if and so long
as the board of directors, executive committee or a trust committee of officers
in good faith determines that withholding the notice is in the interests of the
Noteholders.

         Section 12.06  Reports by Trustee to Noteholders.

         Within 60 days after each November 15, beginning with the November 15
following the date of this Indenture, the Trustee shall mail to each Noteholder
a brief report dated as of such November 15, that complies with TIA ss.313(a),
but only if such report is required in any year under TIA ss.313(a). The Trustee
also shall comply with TIA ss.ss.313(b) and 313(c).

         A copy of each report at the time of its mailing to Noteholders shall
be filed with the SEC and each stock exchange on which the Notes are listed. The
Borrower shall promptly notify the Trustee in writing when the Notes become
listed on any national securities exchange or of any delisting thereof.

         Section 12.07  Compensation and Indemnity.

         The Borrower and the Guarantors jointly and severally agree to pay the
Trustee from time to time such compensation as shall be agreed in writing
between the Borrower and the Trustee for its services (which compensation shall
not be limited by any provision of law in regard to the compensation of a
trustee of an express trust). The Borrower and the Guarantors jointly and
severally agree to reimburse the Trustee upon request for all reasonable
out-of-pocket expenses, disbursements and advances incurred by it. Such
expenses shall include when applicable the reasonable compensation and expenses
of the Trustee's agents and counsel.

         The Borrower and the Guarantors jointly and severally agree to
indemnify each of the Trustee and any predecessor Trustee against any and all
loss, liability, damage, claim or expenses, including taxes (other than taxes
based on the income of the Trustee) incurred by it arising out of or in
connection with the acceptance and administration of the trust and its duties
hereunder as Trustee and/or Note Registrar, including the costs and expenses of
enforcing this Indenture against the Borrower (including with respect to this
Section 12.07) and of defending itself against any claim or liability in
connection with the exercise or performance of any of its powers or duties
hereunder. The Trustee shall notify the Borrower and the Guarantors of any claim
for which it may seek indemnity; however, unless the position of the Borrower is



                                      -45-
<PAGE>   50

materially prejudiced by such failure, the failure of the Trustee to promptly
notify the Borrower shall not limit its right to indemnification. The Borrower
shall defend each such claim and the Trustee shall cooperate in the defense. The
Trustee may retain separate counsel and the Borrower shall reimburse the Trustee
for the reasonable fees and expenses of such counsel if the Borrower is advised
by an Opinion of Counsel that the Trustee has separate defenses and that
separate representation is appropriate or if the Trustee reasonably determines
that such joint defense would otherwise involve a conflict of interest. The
Borrower need not pay for any settlement made without its consent.

         Neither the Borrower nor the Guarantors shall be obligated to reimburse
any expense or indemnify against any loss or liability incurred by the Trustee
through the Trustee's breach of the applicable standard of care for its conduct
under Section 12.01.

         When the Trustee incurs expenses or renders services after the
occurrence of any Event of Default specified in Sections 10.01(f), (g) or (h),
the expenses and the compensation for the services are intended to constitute
expenses of administration under any Bankruptcy Law.

         The provisions of this Section 12.07 shall survive the satisfaction and
discharge or other termination of this Indenture.

         Section 12.08  Replacement of Trustee.

         The Trustee may resign by so notifying the Borrower and the Guarantors.
The Agent may remove the Trustee by so notifying the Trustee, in writing. The
Borrower may remove the Trustee if.

                  (a)      the Trustee fails to comply with Section 12.10;

                  (b)      the Trustee is adjudged a bankrupt or an insolvent;

                  (c)      a receiver or other public officer takes charge of 
the Trustee or its property; or

                  (d) the Trustee becomes incapable of acting as Trustee
hereunder.

         If the Trustee resigns or is removed or if a vacancy exists in the
office of Trustee for any reason, the Borrower shall promptly appoint a
successor Trustee. Within one year after the successor Trustee takes office, the
Agent may appoint a successor Trustee to replace the successor Trustee appointed
by the Borrower.

         A successor Trustee shall deliver a written acceptance of its
appointment to the retiring Trustee and to the Borrower and the Guarantors.
Immediately after that, the retiring Trustee shall transfer all property held by
it as Trustee to the successor Trustee the resignation or removal of the
retiring Trustee shall become effective, and the successor Trustee shall have
all the rights, powers and duties of the Trustee under this Indenture. A
successor Trustee shall mail notice of its succession to each Noteholder.



                                      -46-
<PAGE>   51


         If a successor Trustee does not take office within 30 days after the
retiring Trustee resigns or is removed, the retiring Trustee, the Borrower or
the Agent may petition, at the expense of the Borrower, any court of competent
jurisdiction for the appointment of a successor Trustee.

         If the Trustee fails to comply with Section 12.10, the Agent may
petition any court of competent jurisdiction for the removal of the Trustee and
the appointment of a successor Trustee. Any successor Trustee shall comply with
TIA ss.310(a)(5).

         Section 12.09  Successor Trustee by Merger, etc.

         If the Trustee consolidates, merges or converts into, or transfers all
or substantially all of its corporate trust business to, another corporation,
the successor corporation without any further act shall be the successor
Trustee; provided such corporation or association shall be otherwise eligible
and qualified under this Article.

         Section 12.10  Eligibility, Disqualification.

         This Indenture shall always have a Trustee which satisfies the
requirements of TIA ss.310(a)(1) and (5). The Trustee shall always have a
combined capital and surplus of at least $50,000,000 as set forth in its most
recent published annual report of condition. The Trustee shall also comply with
TIA ss. 310(b).

         Section 12.11  Preferential Collection of Claims Against Borrower.

         The Trustee shall comply with TIA ss.311(a), excluding any creditor
relationship listed in TIA ss.311(b). A Trustee who has resigned or been removed
shall be subject to TIA ss.311(a) to the extent indicated therein.

         Section 12.12  Appointment of Co-Trustee.

         If the Trustee deems it necessary or desirable in connection with the
Collateral and/or the enforcement of the Collateral Documents, the Trustee may
appoint a co-Trustee with such powers of the Trustee as may be designated by the
Trustee at the time of such appointment (including acting as separate trustee of
any Collateral), and the Borrower shall, on request, execute and deliver to such
co-Trustee any deeds, conveyances or other instruments required by such
co-Trustee so appointed by the Trustee to more fully and certainly vest in and
confirm to such co-Trustee its rights, powers, trusts, duties and obligations
hereunder.

         All rights (including rights to indemnification hereunder), powers,
duties and obligations conferred or imposed upon the Trustee shall be conferred
or imposed upon and exercised or performed by the Trustee or jointly by the
Trustee and such co-Trustees, except to the extent that under any law of any
jurisdiction in which any particular act or acts are to be performed the Trustee
shall be incompetent or unqualified to perform such act or acts, in which event
such rights, powers, duties and obligations shall be exercised and performed by
such co-Trustees. No Trustee or co-Trustee shall be personally liable by reason
of any act or omission of any 



                                      -47-
<PAGE>   52

other Trustee or co-Trustee hereunder. Any co-Trustee appointed pursuant to this
Section 12.12 may be removed by the Trustee pursuant to the terms of this
Indenture and may be removed and may resign pursuant to the provisions of the
applicable Collateral Document and of this Indenture.

         A co-Trustee shall not be responsible for and makes no representation
as to the value or condition of the Collateral or any part thereof, or as to the
title of the Borrower thereto, or as to the security afforded thereby or hereby,
or as to the validity or genuineness of any Collateral pledged and deposited
with such co-Trustee, or the validity or adequacy of this Indenture or the
Notes; a co-Trustee shall not be accountable for the Borrower's use of the
proceeds from the Notes, and it shall not be responsible for any statement of
the Borrower in this Indenture or any document issued in connection with the
sale of the Notes or any statement in the Notes. A co-Trustee makes no
representations with respect to the effectiveness or adequacy of this Indenture
or any Basic Document or the validity or perfection, if any, of Liens granted
under this Indenture or the Collateral Documents. A co-Trustee shall not be
responsible for independently ascertaining or maintaining such validity or
perfection, if any, and shall be fully protected in relying upon certificates
and opinions delivered to it in accordance with the terms of this Indenture or
the Collateral Documents.

         Section 12.13 No Conflict. It is the purpose of this section of the
Indenture to remove any potential conflict of interest in the instance in which
Chase Bank of Texas, National Association ("Chase") is acting as Trustee and, in
its commercial banking capacity, has or may develop a lending relationship with
the Borrower or any of its Subsidiary Guarantors. Accordingly, in the event
that Chase, in its commercial banking capacity, has or may develop a lending
relationship with the Borrower or any of its Subsidiary Guarantors, Chase may,
but is not obligated to, resign as Trustee, such resignation to be effective
automatically upon receipt by the Trustee of notice from the successor Trustee
evidencing its assumption of the duties of Trustee hereunder, without notice to
and without prior approval of any party. In the event Chase resigns as trustee
pursuant to this Section 12.13, First Union National Bank, a national banking
association duly organized and existing under the laws of the United States of
America with a corporate trust office in Jacksonville, Florida, or any
successor appointed pursuant to the "Acceptance of Appointment" attached hereto
as Exhibit 6, has agreed to and shall automatically become successor Trustee
hereunder for all purposes. Chase shall give notice of its resignation in
writing to the Borrower, the Agent and the Noteholders as soon as possible but
in any event not less than forty-five (45) days after its resignation, provided
that failure to give such notice shall not impair the effectiveness of such
resignation. The provisions of this section shall extend to Affiliates of Chase.

                                  ARTICLE XIII
                                  MISCELLANEOUS

         Section 13.01 Interpretation and Survival of Provisions. Article,
Section, Schedule, and Exhibit references are to this Indenture, unless
otherwise specified. All references to instruments, documents, contracts, and
agreements are references to such instruments, documents, contracts, and
agreements as the same may be amended, supplemented, and otherwise modified from
time to time, unless otherwise specified. The word "including" shall mean
"including but not limited to." Whenever the Borrower has an obligation under
the Basic Documents, the expense of complying with that obligation shall be an
expense of the Borrower unless otherwise specified. Whenever any determination,
consent, or approval is to be made or given by the Noteholders, such action
shall be in the Noteholders' sole discretion unless otherwise specified in this
Indenture. If any provision in the Basic Documents is held to be illegal,
invalid, not binding, or unenforceable, such provision shall be fully severable
and the Basic Documents shall be construed and enforced as if such illegal,
invalid, not binding, or unenforceable provision had never comprised a part of
the Basic Documents, and the remaining provisions shall remain in full force and
effect. The Basic Documents have been reviewed and negotiated by sophisticated
parties with access to legal counsel and shall not be construed against the
drafter. The representations, warranties, and covenants made in this Indenture,
the Notes or any other Basic Document shall remain operative and in full force
and effect regardless of (a) any investigation made by or on behalf of the
Borrower or the Noteholders or (b) acceptance of any of the Notes and payment
therefor and repayment or repurchase thereof. All indemnification obligations of
the Borrower and the provisions of Section 13.02 shall remain operative and in
full force and effect unless such obligations are expressly terminated in a
writing referencing those individual Sections, regardless of any purported
general termination of this Indenture or any other Basic Document.



                                      -48-
<PAGE>   53

         Section 13.02  Costs, Expenses and Taxes.

                  (a)       Intentionally Deleted.

                  (b) The Borrower agrees to indemnify the Agent and the
Noteholders, and their respective officers, directors, employees,
representatives, agents, attorneys, and Affiliates (collectively, "Related
Parties") from, hold each of them harmless against and promptly upon demand pay
or reimburse each of them for, any and all actions, suits, proceedings
(including any investigations, litigation, or inquiries), claims, demands, and
causes of action, and, in connection therewith, all reasonable costs, losses,
liabilities, damages, or expenses of any kind or nature whatsoever (collectively
the "Indemnity Matters") which may be incurred by or asserted against or involve
any of them (whether or not any of them is designated a party thereto) as a
result of, arising out of, or in any way related to (i) any actual or proposed
use by the Borrower of the proceeds of any sale of the Notes, (ii) the
operations of the business of the Borrower or any Subsidiary, (iii) any bodily
injury or death or property damage occurring in or upon or in the vicinity of
any Collateral, (iv) any claim by any third Person against any Collateral
assigned to or paid to any Noteholder pursuant to any Collateral Document, (v)
the failure of the Borrower or any Subsidiary to comply with any Governmental
Requirement, or (vi) any other aspect of this Indenture and the other Basic
Documents, including, without limitation, the reasonable fees and disbursements
of counsel and all other reasonable expenses incurred in connection with
investigating, defending or preparing to defend any such action, suit,
proceeding (including any investigations, litigation, or inquiries), or claim
and INCLUDING ALL INDEMNITY MATTERS ARISING BY REASON OF THE ORDINARY NEGLIGENCE
OF ANY INDEMNITEE (but excluding all Indemnity Matters arising solely by reason
of claims between the Noteholders or any Noteholder and the Agent or any
Noteholder's shareholders against the Agent or any Noteholder or by reason of
the gross negligence or wilful misconduct of any Indemnitee).

                  (c) The Borrower agrees to pay and hold the Noteholders
harmless from and against any and all present and future stamp and other similar
taxes with respect to this Indenture and Basic Documents and save the
Noteholders harmless from and against any and all liabilities with respect to or
resulting from any delay or omission to pay such taxes, and will indemnify the
Noteholders for the full amount of taxes paid by the Noteholders in respect of
payments made or to be made under this Indenture, any Note, or any other Basic
Document and any liability (including penalties, interest, and expenses) arising
therefrom or with respect thereto, whether or not such taxes were correctly or
legally asserted.

                  (d) The Borrower agrees to indemnify and hold harmless from
time to time the Noteholders, and their respective Related Parties, together
with the Trustee, from and against any and all losses, claims, cost recovery
actions, administrative orders or proceedings, damages, and liabilities to which
any such Person may become subject (i) under any Environmental Law applicable to
the Borrower, any Subsidiary, or any of their respective Properties, (ii) as a
result of the breach or non-compliance by the Borrower or any Subsidiary with
any Environmental Law applicable to the Borrower or any Subsidiary, or any of
their respective Properties, (iii) due to the ownership by the Borrower or any
Subsidiary of their respective Properties or any activity on any of their
respective Properties, or any past activity on any of their respective
Properties 



                                      -49-
<PAGE>   54

which, though lawful and fully permissible at the time, could result in present
liability, (iv) the presence, use, release, storage, treatment, or disposal of
hazardous substances on or at any of the properties owned or operated by the
Borrower or any Subsidiary, or (v) any other environmental, health, or safety
condition in connection with this Indenture or any other Basic Document.

                  (e) In the case of any indemnification hereunder, the
Noteholder or other Person indemnified hereunder shall give notice to the
Borrower within a reasonable period of time of any such claim or demand being
made against the Noteholder or other indemnified Person and the Borrower at its
sole cost and expense shall provide a defense of such claim, provided, however,
that (i) if the Borrower has failed to assume the defense and employ counsel or
(ii) if the defendants in any such action include both the indemnified party and
the Borrower or any Subsidiary and counsel to the indemnified party shall have
concluded that there may be reasonable defenses available to the indemnified
party that are different from or additional to those available to the Borrower
or such Subsidiary or if the interests of the indemnified party reasonably may
be deemed to conflict with the interests of the Borrower or such Subsidiary,
then the indemnified party shall have the right to select a separate counsel and
to assume such legal defense and otherwise to participate in the defense of such
action, with the expenses and fees of such separate counsel and other expenses
related to such participation to be reimbursed by the Borrower as incurred.

                  (f) No indemnitee may settle any claim to be indemnified
without the consent of the indemnitor, such consent not to be unreasonably
withheld; provided, that the indemnitor may not reasonably withhold consent to
any settlement that an indemnitee proposes if the indemnitor does not have the
financial ability to pay all its obligations outstanding and asserted against
the indemnitee at that time, including the maximum potential claims against the
indemnitee to be indemnified pursuant to this Section 13.02.

                  (g) This Section 13.02 shall not apply to actions, suits,
proceedings, investigations, demands, losses, liabilities, claims, damages,
deficiencies, interest, judgments, costs, or expenses relating to any Property
to the extent arising from the acts or omissions of the Agent or any Noteholder
during the period after which such Person, its successors or assigns shall have
acquired possession of such Property (whether through foreclosure or deed in
lieu of foreclosure, as mortgagee in possession or otherwise).

                  (h) The Borrower's obligations under this Section 13.02 shall
survive any termination of this Indenture and the payment of the Obligations.

         Section 13.03  No Waiver; Modifications in Writing.

                  (a) No failure or delay on the part of the Trustee, the
Borrower, the Agent or the Noteholders in exercising any right, power, or remedy
hereunder shall operate as a waiver thereof, nor shall any single or partial
exercise of any such right, power, or remedy preclude any other or further
exercise thereof or the exercise of any right, power, or remedy. The remedies
provided for herein are cumulative and are not exclusive of any remedies that
may be available to the Borrower, the Trustee, the Agent or the Noteholders at
law or in equity or otherwise.



                                      -50-
<PAGE>   55

                  (b) Except as otherwise provided herein, no amendment, waiver,
consent, modification, or termination of any provision of this Indenture, the
Notes or any other Basic Document, shall be effective unless signed by the
Borrower and the Majority Noteholders. The Noteholders have all rights to take
such actions under this Indenture and the other Basic Documents without the
consent or joinder of any holder of the Acquired Shares or Warrants. Any
amendment, supplement or modification of or to any provision of this Indenture
or the Notes or any other Basic Document, any waiver of any provision of this
Indenture, the Notes or any other Basic Document, and any consent to any
departure by the Borrower from the terms of any provision of this Indenture, the
Notes or any other Basic Document, shall be effective only in the specific
instance and for the specific purpose for which made or given. Except where
notice is specifically required by this Indenture, no notice to or demand on the
Borrower in any case shall entitle the Borrower to any other or further notice
or demand in similar or other circumstances.

         Section 13.04 Binding Effect; Assignment. This Indenture shall be
binding upon the Borrower, the Trustee, the Agent and the Noteholders, and their
respective successors and permitted assigns. Except as expressly provided in
this Indenture, this Indenture shall not be construed so as to confer any right
or benefit upon any Person other than the Borrower, Trustee, Agent and
Noteholders, and their respective successors and permitted assigns. Subject to
applicable federal law and state securities law, all or any portion of the
rights and obligations of the Noteholders under this Indenture with respect to
the Basic Documents may be sold, assigned or pledged by any Noteholder. Upon any
assignment of the Basic Documents, the acquiring Noteholder shall succeed to all
of the selling Noteholder's rights and obligations under the Basic Documents to
the extent assigned and the selling Noteholder shall be automatically released
from any such obligations hereunder with respect to the Basic Documents to the
extent assigned.

         Section 13.05 Communications. All notices and demands provided for
hereunder shall be in writing and shall be given by registered or certified
mail, return receipt requested, telecopy, air courier guaranteeing overnight
delivery or personal delivery to the following addresses:

         If to the Trustee:

         Chase Bank of Texas, National Association
         Global Trust Services
         600 Travis Street, Suite 1150
         Houston, Texas  77002
         Attention:  Mr. Mauri J. Cowen
         Telephone:        (713) 216-6686
         Telecopier:       (713) 216-5474



                                      -51-
<PAGE>   56

         If to the Agent:







         If to the Noteholders:

         and


         If to the Borrower:

         6300 Bridge Point Parkway
         Building 2, Suite 500
         Austin, Texas 78730
         Attention:  Craig M. Fleming
         Telecopier:  (512) 472-3400

or to such other address as the Borrower, Agent or any Noteholder may designate
in writing. All other communications may be by regular mail. All notices and
communications shall be deemed to have been duly given: at the time delivered by
hand, if personally delivered; four days after being sent by certified mail,
return receipt requested, if mailed; when receipt acknowledged, if telecopied;
and on the next Business Day if timely delivered to an air courier guaranteeing
overnight delivery. Notwithstanding the foregoing, notices to the Trustee shall
be effective only upon receipt.



                                      -52-
<PAGE>   57

         Section 13.06 Governing Law. This Indenture will be construed in
accordance with and governed by the laws of the State of Texas without regard to
principles of conflicts of laws.

         Section 13.07  Arbitration.

                  (a) Binding Arbitration. Subject to the provisions of
subparagraph (e), on the request of either the Borrower, the Agent or any
Noteholder, whether made before or after the institution of any legal
proceeding, any action, dispute, claim or controversy of any kind now existing
or hereafter arising between any of the parties hereto in any way arising out
of, pertaining to or in connection with this Indenture (a "Dispute") shall be
resolved by binding arbitration in accordance with the terms hereof. Either the
Borrower, the Agent or any Noteholder may, by summary proceedings, bring an
action in court to compel arbitration of any Dispute.

                  (b) Governing Rules. Any arbitration shall be administered by
the American Arbitration Association (the "AAA") in accordance with the terms of
this Section, the Commercial Arbitration Rules of the AAA, and, to the maximum
extent applicable, the Federal Arbitration Act. Judgment on any award rendered
by an arbitrator may be entered in any court having jurisdiction.

                  (c) Arbitrators. Any arbitration shall be conducted before a
three person panel of neutral arbitrators. Such panel shall consist of one
person from each of the following categories: (1) an attorney who has practiced
in the area of commercial law for at least 10 years or a retired judge at the
Texas or United States District Court or an appellate court level; (2) a person
with at least 10 years experience in commercial lending; and (3) a person with
at least 10 years experience in the energy service industry. The AAA shall
submit a list of persons meeting the criteria outlined above for each category
of arbitrator, and the parties shall select one person from each category in the
manner established by the AAA. If the parties cannot agree on an arbitrator
within 30 days after the request for an arbitration, then any party may request
the AAA to select an arbitrator. The arbitrator may engage engineers,
accountants or other consultants that the arbitrator deems necessary to render a
conclusion in the arbitration proceeding.

                  (d) Conduct of Arbitration. To the maximum extent practicable,
an arbitration proceeding hereunder shall be concluded within 180 days of the
filing of the Dispute with the AAA. Arbitration proceedings shall be conducted
in Houston, Texas. At the conclusion of any arbitration proceeding, the
arbitrator shall make specific written findings of fact and conclusions of law.
The arbitrator shall have the power to award recovery of all costs and fees to
the prevailing party. The Borrower, the Agent and the Noteholders each agree to
keep all Disputes and arbitration proceedings strictly confidential except for
disclosure of information required by applicable law.

                  (e) Parties' Rights. Nothing in the preceding paragraph shall
require arbitration prior to the Agent's or the Noteholders' exercise of any
rights and remedies under Article X. In addition, nothing in this Section 13.07,
nor the exercise of any right to arbitrate thereunder, shall limit the right of
the Borrower, the Agent, the Trustee or any Noteholder: (a)



                                      -53-
<PAGE>   58

to foreclose against any Collateral by the exercise of the power of sale under,
or to secure direct payment of the proceeds of any Collateral as provided under,
any deed of trust, mortgage, or other security agreement or instrument or
applicable law; (b) to exercise self-help remedies such as setoff or
repossession; or (c) to obtain provisional or ancillary remedies or relief such
as replevin, injunctive relief, attachment or appointment of a receiver from a
court having jurisdiction, before, during or after the pendency of any
arbitration proceeding. Any foreclosure action, or the institution and
maintenance of any action for such judicial relief, or pursuit of provisional or
ancillary remedies, or exercise of self-help remedies shall not constitute a
waiver of the right of the exercising party to submit any claim or dispute to
arbitration.

                  (f) Costs of Arbitration. All fees of the arbitrator and any
engineer, accountant or other consultant engaged by the arbitrator, shall be
paid by the Borrower (as to 50%) and the Noteholders (as to 50%) unless
otherwise awarded by the arbitrator.

         Section 13.08 Confidentiality. In the event that the Borrower or any
Guarantor (hereinafter called the "Subject Entities") provides to the Agent or
the Noteholders written confidential information or, if communicated as
confidential, oral confidential information belonging to any Subject Entity, the
Agent and the Noteholders shall thereafter maintain such information in
confidence in accordance with the standards of care and diligence that each
utilizes in maintaining its own confidential information. This obligation of
confidence shall not apply to such portions of the information which (i) are in
the public domain, (ii) hereafter become part of the public domain without the
Agent or the Noteholders breaching their obligation of confidence to any Subject
Entity, (iii) are previously known by the Agent or the Noteholders from some
source other than any Subject Entity, (iv) are hereafter developed by the Agent
or the Noteholders without using a Subject Entity's information, (v) are
hereafter obtained by or available to the Agent or the Noteholders from a third
party who owes no obligation of confidence to any Subject Entity with respect to
such information, (vi) are disclosed with a Subject Entity's consent, (vii) must
be disclosed either pursuant to any Governmental Requirement or to Persons
regulating the activities of the Agent or the Noteholders, or (viii) may be
required to be disclosed by law or regulation or order of any Governmental
Authority in any judicial, arbitration or governmental proceeding. Further, the
Agent or a Noteholder may disclose any such information to any other Noteholder,
any independent petroleum engineers or consultants, any independent certified
public accounts, any legal counsel employed by such Person in connection with
this Indenture or any other Basic Document, including without limitation, the
enforcement or exercise of all rights and remedies thereunder, or, subject to
Section 13.04, any assignee or participant (including prospective assignees and
participants) in the Obligations; provided, however, that the Agent or the
Noteholders shall receive a confidentiality agreement from the Person to whom
such information is disclosed such that said person shall have the same
obligation to maintain the confidentiality of such information as is imposed
upon the Agent or the Noteholders hereunder. Notwithstanding anything to the
contrary provided herein, this obligation of confidence shall cease three (3)
years from the date the information was furnished, unless the Borrower requests
in writing at least thirty (30) days prior to the expiration of such three (3)
year period, to maintain the confidentiality of such information for an
additional three year period.



                                      -54-
<PAGE>   59

         Section 13.09 Execution in Counterparts. This Indenture may be executed
in any number of counterparts and by different parties hereto in separate
counterparts, each of which counterparts, when so executed and delivered, shall
be deemed to be an original and all of which counterparts, taken together, shall
constitute but one and the same Agreement.

         Section 13.10 Trust Indenture Act Controls. Whether prior to or
following the qualification of this Indenture under the TIA, if any provision of
this Indenture limits, qualifies, or conflicts with the duties imposed by
operation of TIA ss. 318(c) upon an Indenture qualified under the TIA, the
imposed duties shall control under this Indenture.

         Section 13.11 Communication by Noteholders with Other Noteholders.
Noteholders may communicate pursuant to TIA ss. 312(b) with other Noteholders
with respect to their rights under this Indenture or the Notes. The Company, the
Guarantors, the Trustee, the Registrar and anyone else shall have the protection
of TIA ss. 312(c).

         Section 13.12 Certificate and Opinion as to Conditions Precedent. Upon
any request or application by the Borrower or any Guarantor to the Trustee to
take any action under this Indenture, the Borrower or such Guarantor, as the
case may be, shall furnish to the Trustee:

                  (a) an Officers' Certificate (which shall include the
statements set forth in Section 13.13) stating that, in the opinion of the
signers, the conditions precedent, if any, provided for in this Indenture
relating to the proposed action have been complied with;

                  (b) an Opinion of Counsel stating that, in the opinion of such
counsel, such conditions precedent have been complied with; and

                  (c) any Opinion of Counsel may assume the existence of
non-existence of facts necessary to support such Opinion unless such counsel has
actual knowledge that such assumption would be contrary to the actual facts.

         Section 13.13 Statements Required in Certificate or Opinion. Each
certificate or opinion with respect to compliance with a condition or covenant
provided for in this Indenture shall include:

                  (a)      a statement that each person making such certificate
or opinion has read such covenant or condition;

                  (b) a brief statement as to the nature and scope of the
examination or investigation upon which the statements or opinions contained in
such certificate or opinion are based;

                  (c) a statement that, in the opinion of each such person, he
has made such examination or investigation as is necessary to enable him to
express an informed opinion as to whether or not such covenant or condition has
been complied with; and



                                      -55-
<PAGE>   60

                  (d) a statement as to whether or not, in the opinion of each
such person, such covenant or condition has been complied with.

         Section 13.14 Rules by Trustee and Agents. The Trustee may make
reasonable rules for action by or a meeting of the Noteholders. The Note
Registrar may make reasonable rules for its functions.

         Section 13.15 Legal Holidays. A "Legal Holiday" is a Saturday, a
Sunday, or a day on which banks and trust companies in the City of New York are
not required by law or executive order to be open. If a payment date is a Legal
Holiday at a place of payment, payment may be made at the place on the next
succeeding day that is not a Legal Holiday, without additional interest.

         IN WITNESS WHEREOF, BRIGHAM EXPLORATION COMPANY has caused this
Indenture to be signed by its President or one of its Vice Presidents, and its
corporate seal to be affixed hereunto, and the same to be attested by its
Secretary or an Assistant Secretary, and CHASE BANK OF TEXAS, NATIONAL
ASSOCIATION has caused this Indenture to be signed by one of its duly authorized
trust officers, all as of the day and year first above written.

                                         BRIGHAM EXPLORATION COMPANY


                                         By:
                                            --------------------------------
                                            Name:
                                                 ---------------------------
                                            Title:
                                                  --------------------------



                                         CHASE BANK OF TEXAS, NATIONAL
                                         ASSOCIATION,
                                         as Trustee


                                         By:
                                            --------------------------------
                                            Name:
                                                 ---------------------------
                                            Title:
                                                  --------------------------




                                      -56-
<PAGE>   61

STATE OF TEXAS          )
                        )
COUNTY OF DALLAS        )

         BEFORE ME, the undersigned authority, a Notary Public in and for said
state, on this day personally appeared ________________ and _____________, known
to me to be the persons and officers whose names are subscribed to the foregoing
instrument and acknowledged to me that the same was the act of the said BRIGHAM
EXPLORATION COMPANY, a Delaware corporation, and that they executed the same as
the act of said corporation for the purposes and consideration therein
expressed, and in the capacity therein stated.

         GIVEN UNDER MY HAND AND SEAL OF OFFICE, this ______ day of August,
1998.


                                    -------------------------------------------
                                    Notary Public in and for the State of Texas

My commission expires:


------------------------------

STATE OF TEXAS          )
                        )
COUNTY OF HARRIS        )

         BEFORE ME, the undersigned authority, a Notary Public in and for said
state, on this day personally appeared ______________ , known to me to be the
person and officer whose names are subscribed to the foregoing instrument and
acknowledged to me that the same was the act of the said CHASE BANK OF TEXAS,
NATIONAL ASSOCIATION, a national banking association, and that she executed the
same as the act of said national banking association for the purposes and
consideration therein expressed, and in the capacity therein stated.

         GIVEN UNDER MY HAND AND SEAL OF OFFICE, this _____ day of ________,
1998.


                                    -------------------------------------------
                                    Notary Public in and for the State of Texas

My commission expires:


------------------------------


                                      -57-
<PAGE>   62
                                                                     EXHIBIT A


                                                                            1998



         THIS INSTRUMENT IS SUBORDINATED TO THE EXTENT AND IN THE MANNER
         PROVIDED IN THE SUBORDINATION AGREEMENT REFERRED TO BELOW.

         NOTWITHSTANDING THE PROVISIONS OF SECTION 2.05 OF THE SECURITIES
         PURCHASE AGREEMENT REFERRED TO BELOW, THE INITIAL PRINCIPAL BALANCE OF
         THIS NOTE IS $____________, AND SUCH PRINCIPAL AMOUNT SHALL BE
         INCREASED BY THE AMOUNT OF ANY PAYMENTS OF INTEREST ON THIS NOTE IN
         KIND.  FOR MORE INFORMATION, CONTACT THE COMPANY AT THE ADDRESS
         SPECIFIED IN THE SECURITIES PURCHASE AGREEMENT.

                                ________________

                   Senior Subordinated Secured Note due 2003

No. __                                                            Houston, Texas
$_________                                                       August __, 1998

         BRIGHAM EXPLORATION COMPANY, a Delaware corporation ("Company"), for
value received, hereby promises to pay to the order of ___________
("Purchaser"), to its account at __________________, ABA No. _________, Account
No. __________, or such other account or address in the State of Texas as may
be specified by the Purchaser, the principal amount of ___________ DOLLARS
($________), or, if less, the aggregate unpaid principal balance of this Note
(including any additions to such principal balance as a result of the payment
of interest owing in respect of this Note in kind, as more fully described
below), together with interest on the unpaid balance of such principal amount
in accordance with the Indenture dated as of August __, 1998 (the "Indenture"),
between the Company, and ________________, as Trustee (the "Trustee").  The
Indenture is being executed in connection with the Securities Purchase
Agreement dated as of August __, 1998 (as modified from time to time, the
"Securities Purchase Agreement", and together with the Indenture, the
"Securities Purchase Documents") among the Company, the Purchaser and the other
purchasers party thereto (together with the Purchaser, referred to collectively
as the "Noteholders"), and ______________________________, as agent for the
Noteholders ("Agent").
<PAGE>   63
         The Securities Purchase Documents provide for the making of loans by
the Noteholders to the Company in exchange for, among other things, the
issuance by the Company of the Notes and Warrants (as defined in the Securities
Purchase Documents).  The Company hereby acknowledges and agrees that, as of
the date of the issuance of this Note and notwithstanding the provisions of
Section 2.05 of the Securities Purchase Agreement, the aggregate outstanding
principal balance of this Note is $_________. In addition, the Securities
Purchase Documents provide that payment of a portion of the interest owing by
the Company in respect of the Notes may be made by the Company in kind.  The
Company hereby acknowledges and agrees that any such payments of interest in
kind in respect of this Note shall be deemed to be additional principal
advanced by the Purchaser under this Note and such additional principal shall
be added to the unpaid principal amount of this Note owing by the Company to
Purchaser in respect of this Note.  The loan made by the Purchaser to the
Company under this Note (including, without limitation, loans deemed to be made
as a result of any payments of interest in kind) and all payments made on
account of the principal amount of such loans shall be entered by the Purchaser
in its records or on the grid attached hereto which is part of this Note;
provided that, the failure of the Purchaser to make any such notation shall not
impair or otherwise affect the Company's obligations under this Note.

         This Note is subject to optional prepayments, in whole or in part and
without premium or penalty, as specified in the Securities Purchase Documents.
Payments of principal and interest on this Note are subordinated to the extent
provided in the Subordination Agreement dated as of August __, 1998
("Subordination Agreement") among the Noteholders, the Agent and Bank of
Montreal, as agent for certain senior bank lenders.  Payments of principal and
interest due on this Note shall be made in lawful money of the United States of
America in accordance with the Securities Purchase Documents.

         This Note is issued pursuant to the Securities Purchase Documents and
is subject to and entitled to the benefits of the Securities Purchase Documents
and the security and support therefor, and the holder of this Note may enforce
such rights in accordance with the Securities Purchase Documents.  Without
limiting the foregoing, upon the occurrence of an Event of Default (as defined
in the Indenture), payments due under this Note may be accelerated in the
manner and with the effect provided in the Securities Purchase Documents.

         It is the intention of the Purchaser and the Company to conform
strictly to any applicable usury laws.  Accordingly, the terms of the
Securities Purchase Documents relating to the prevention of usury will be
strictly followed.

         THIS NOTE SHALL BE GOVERNED BY AND CONSTRUED AND ENFORCED IN
ACCORDANCE WITH THE LAWS OF THE STATE OF TEXAS.



                                     -2-
<PAGE>   64


                                        BRIGHAM EXPLORATION COMPANY



                                        By:
                                           ------------------------------
                                        Name: Craig M. Fleming
                                        Title: Chief Financial Officer

TRUSTEE'S CERTIFICATE
OF AUTHENTICATION

This is one of the securities referred to
in the within-mentioned Indenture

CHASE BANK OF TEXAS, NATIONAL ASSOCIATION


By: 
   ------------------------------
       Authorized Signatory

Dated:
      ------------------



                                      -3-
<PAGE>   65
LOAN, MATURITIES, AND PAYMENTS OF PRINCIPAL



<TABLE>
<CAPTION>
----------------------------------------------------------------------------------------
Date     Amount of   Maturity of      Amount of        Unpaid Principal    Notation Made
           Loan         Loan        Principal Paid          Balance               By
                                     or Prepaid
----------------------------------------------------------------------------------------
<S>      <C>         <C>            <C>                <C>                 <C>

----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------
</TABLE>



                                      -4-
<PAGE>   66



                                   EXHIBIT B

                               GUARANTY AGREEMENT


                                       BY


                 _____________________________________________


                                  IN FAVOR OF



                           __________________________




                                AUGUST ___, 1998
<PAGE>   67
                               TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                                                     Page
                                                                                                                     ----
<S>              <C>                                                                                                   <C>
ARTICLE 1        GENERAL TERMS
Section 1.1      Terms Defined Above  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Section 1.2      Certain Definitions  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Section 1.3      Credit Agreement Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

ARTICLE 2        THE GUARANTY
Section 2.1      Liabilities Guaranteed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Section 2.2      Nature of Guaranty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Section 2.3      Collateral Agent's Rights  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Section 2.4      Guarantor's Waivers  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Section 2.5      Maturity of Liabilities; Payment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Section 2.6      Collateral Agent's and Noteholders' Expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Section 2.7      Liability  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Section 2.8      Events and Circumstances Not Reducing or Discharging Guarantor's 
                 Obligations  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Section 2.9      Right of Subrogation and Contribution  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

ARTICLE 3        REPRESENTATIONS AND WARRANTIES
Section 3.1      By Guarantor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Section 3.2      No Representation by Noteholders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

ARTICLE 4        SUBORDINATION OF INDEBTEDNESS
Section 4.1      Subordination of All Guarantor Claims  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Section 4.2      Claims in Bankruptcy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Section 4.3      Payments Held in Trust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Section 4.4      Liens Subordinate  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10

ARTICLE 5        MISCELLANEOUS
Section 5.1      Successors and Assigns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
Section 5.2      Notices  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
Section 5.3      Business and Financial Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
Section 5.4      Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
Section 5.5      Invalidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
Section 5.6      Subordination Agreement  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
Section 5.7      ENTIRE AGREEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
</TABLE>





                                      -i-
<PAGE>   68
                               GUARANTY AGREEMENT


         THIS GUARANTY AGREEMENT by ______________________________ (hereinafter
called "Guarantor"), is in favor of __________________________________________
as agent (the "Agent") for the ratable benefit of itself and the Noteholders
(hereinafter defined).

                              W I T N E S S E T H:

         A.      BRIGHAM EXPLORATION COMPANY, a Delaware corporation
(hereinafter called "Borrower") has entered into (i) the Indenture dated as of
August __, 1998 (as the same may be amended from time to time, the "Indenture")
between the Borrower and _________, as Trustee ("Trustee"), and (ii) the
Securities Purchase Agreement dated as of August __, 1998 (as the same may be
amended from time to time, the "Securities Purchase Agreement," and together
with the Indenture, the "Securities Purchase Documents") among the Borrower,
the purchasers named therein ("Noteholders"), and the Agent, in connection with
the Borrower's Senior Subordinated Notes due 2003; and

         B.      One of the terms and conditions stated in the Securities
Purchase Documents for the making of the loans described therein is the
execution and delivery to the Agent for the ratable benefit of itself and the
Noteholders of this Guaranty Agreement;

         NOW, THEREFORE, (i) in order to comply with the terms and conditions
of the Securities Purchase Documents, (ii) to induce the Noteholders, at any
time or from time to time, to loan monies, with or without security to or for
the account of Borrower in accordance with the terms of the Securities Purchase
Documents, (iii) at the special insistence and request of the Noteholders, and
(iv) for other good and valuable consideration, the receipt and sufficiency of
which is hereby acknowledged, Guarantor hereby agrees as follows:

                                   ARTICLE 1
                                 GENERAL TERMS

         Section 1.1      Terms Defined Above.  As used in this Guaranty
Agreement, the terms "Agent", Borrower", "Guarantor", "Indenture", "Trustee"
and "Securities Purchase Documents" shall have the meanings indicated above.

         Section 1.2      Certain Definitions.  As used in this Guaranty
Agreement, the following terms shall have the following meanings, unless the
context otherwise requires:

         "Contribution Obligation" shall mean an amount equal, at any time and
         from time to time and for each respective Subsidiary Guarantor, to the
         product of (a) its Contribution Percentage times (b) the sum of all
         payments made previous to or at the time of calculation





                                      -1-
<PAGE>   69
         by all Subsidiary Guarantors in respect of the Liabilities, as a
         Subsidiary Guarantor (less the amount of any such payments previously
         returned to any Subsidiary Guarantor by operation of law or otherwise,
         but not including payments received by any Subsidiary Guarantor by way
         of its rights of subrogation and contribution under Section 2.9 of the
         other Guaranty Agreements), provided, however, such Contribution
         Obligation for any Subsidiary Guarantor shall in no event exceed such
         Subsidiary Guarantor's Maximum Guaranteed Amount, as defined in the
         respective Guaranty Agreement of such Subsidiary Guarantor.

         "Contribution Percentage" shall mean for any Subsidiary Guarantor for
         any applicable date as of which such percentage is being determined,
         an amount equal to the quotient of (a) the Net Worth of such
         Subsidiary Guarantor as of such date, divided by (b) the sum of the
         Net Worth of all the Subsidiary Guarantors as of such date.

         "Guarantor Claims" shall have the meaning indicated in Section 4.1
         hereof.

         "Guaranty Agreement" shall mean this Guaranty Agreement, and where the
         context indicates, the Guaranty Agreement of any other Subsidiary
         Guarantor, as the same may from time to time be amended or
         supplemented.

         "Liabilities" shall mean:

                 (a)      any and all indebtedness, obligations and liabilities
         of the Borrower to the Agent and the Noteholders pursuant to the
         Securities Purchase Documents, including without limitation, the
         unpaid principal of and interest on the Notes (as defined in the
         Securities Purchase Documents);

                 (b)      any additional Obligations (as defined in the
         Securities Purchase Documents) owing to the Agent and the Noteholders;
         and

                 (c)       all renewals, rearrangements, increases, extensions
         for any period, amendments or supplements in whole or in part of the
         Notes or any documents evidencing the above.

         "Maximum Guaranteed Amount" shall mean, for the Guarantor, the greater
         of (a) the "reasonably equivalent value" or "fair consideration" (or
         equivalent concept) received by the Guarantor in exchange for the
         obligation incurred hereunder, within the meaning of any applicable
         state or federal fraudulent conveyance or transfer laws; or (b) the
         lesser of (i) the maximum amount that will not render the Guarantor
         insolvent, or (ii) the maximum amount that will not leave the
         Guarantor with any property deemed an unreasonably small capital.
         Clauses (i) and (ii) are and shall be determined pursuant to and as of
         the appropriate date mandated by such applicable state or federal
         fraudulent conveyance or transfer laws and to the extent allowed by





                                      -2-
<PAGE>   70
         law take into account the rights to contribution and subrogation under
         Section 2.9 in each Guaranty Agreement so as to provide for the
         largest Maximum Guaranteed Amount possible.

         "Net Payments" shall mean an amount equal, at any time and from time
         to time and for each respective Subsidiary Guarantor, to the
         difference of (a) the sum of all payments made previous to or at the
         time of calculation by such Subsidiary Guarantor in respect to the
         Liabilities, as a Subsidiary Guarantor, and in respect of its
         obligations contained in this Guaranty Agreement, less (b) the sum of
         all such payments previously returned to such Subsidiary Guarantor by
         operation of law or otherwise and including payments received by such
         Subsidiary Guarantor by way of its rights of subrogation and
         contribution under Section 2.9 of the other Guaranty Agreements.

         "Net Worth" shall mean for any Subsidiary Guarantor, calculated on and
         as of any applicable date on which such amount is being determined,
         the difference between (a) the sum of all such Subsidiary Guarantor's
         property, at a fair valuation and as of such date, minus (b) the sum
         of all such Subsidiary Guarantor's debts, at a fair valuation and as
         of such date, excluding the Liabilities.

         "Noteholders" shall mean the holders of the Notes from time to time,
         and the holders of any promissory note or notes given in substitution
         or replacement thereof, including, without limitation, pursuant to
         Section 2.06 of the Indenture.

         "Subsidiary Guarantors" shall mean the Guarantors as defined in the
         Securities Purchase Documents, including the Guarantor.

         Section 1.3      Securities Purchase Documents Definitions.  Unless
otherwise defined herein, all terms beginning with a capital letter which are
defined in the Securities Purchase Documents shall have the same meanings
herein as therein.

                                   ARTICLE 2
                                  THE GUARANTY

         Section 2.1      Liabilities Guaranteed.  Guarantor hereby irrevocably
and unconditionally guarantees the prompt payment of the Liabilities when due,
whether at maturity or otherwise, provided, however, that, notwithstanding
anything herein or in any other Loan Document to the contrary, the maximum
liability of Guarantor hereunder shall in no event exceed the Maximum
Guaranteed Amount.

         Section 2.2      Nature of Guaranty.  This Guaranty Agreement is an
absolute, irrevocable, completed and continuing guaranty of payment and not a
guaranty of collection, and no notice of the Liabilities or any extension of
credit already or hereafter contracted by or extended to Borrower need





                                      -3-
<PAGE>   71
be given to Guarantor.  This Guaranty Agreement may not be revoked by Guarantor
and shall continue to be effective with respect to debt under the Liabilities
arising or created after any attempted revocation by Guarantor and shall remain
in full force and effect until the Liabilities are paid in full.  Borrower and
the Noteholders may modify, alter, rearrange, extend for any period and/or
renew from time to time, the Liabilities, and the Noteholders may waive any
Default or Events of Default without notice to the Guarantor and in such event
Guarantor will remain fully bound hereunder on the Liabilities.  This Guaranty
Agreement shall continue to be effective or be reinstated, as the case may be,
if at any time any payment of the Liabilities is rescinded or must otherwise be
returned by any of the Noteholders upon the insolvency, bankruptcy or
reorganization of Borrower or otherwise, all as though such payment had not
been made. This Guaranty Agreement may be enforced by Trustee, Agent and any
holder of any of the Liabilities and shall not be discharged by the assignment
or negotiation of all or part of the Liabilities.  Guarantor hereby expressly
waives presentment, demand, notice of non-payment, protest and notice of
protest and dishonor, notice of Default or Event of Default, and also notice of
acceptance of this Guaranty Agreement, acceptance on the part of the
Noteholders being conclusively presumed by the Noteholders' request for this
Guaranty Agreement and delivery of the same to Trustee.

         Section 2.3      Trustee's Rights.  Guarantor authorizes Trustee,
without notice or demand and without affecting Guarantor's liability hereunder,
to take and hold security for the payment of this Guaranty Agreement and/or the
Liabilities, and exchange, enforce, waive and release any such security; and to
apply such security and direct the order or manner of sale thereof as Trustee
in its discretion may determine; and to obtain a guaranty of the Liabilities
from any one or more Persons and at any time or times to enforce, waive,
rearrange, modify, limit or release any of such other Persons from their
obligations under such guaranties.

         Section 2.4      Guarantor's Waivers.  Guarantor waives any right to
require any of the Noteholders to (i) proceed against Borrower or any other
person liable on the Liabilities, (ii) enforce any of their rights against any
other guarantor of the Liabilities (iii) proceed or enforce any of their rights
against or exhaust any security given to secure the Liabilities (iv) have
Borrower joined with Guarantor in any suit arising out of this Guaranty
Agreement and/or the Liabilities, or (v) pursue any other remedy in the
Noteholders' powers whatsoever.  The Noteholders shall not be required to
mitigate damages or take any action to reduce, collect or enforce the
Liabilities.  Guarantor waives any defense arising by reason of any disability,
lack of corporate authority or power, or other defense of Borrower or any other
guarantor of the Liabilities, and shall remain liable hereon regardless of
whether Borrower or any other guarantor be found not liable thereon for any
reason.  Whether and when to exercise any of the remedies of the Noteholders
under any of the Loan Documents shall be in the sole and absolute discretion of
the Agent, acting on behalf of itself and the Noteholders, and no delay by the
Agent in enforcing any remedy, including delay in conducting a foreclosure
sale, shall be a defense to the Guarantor's liability under this Guaranty
Agreement.

         Section 2.5      Maturity of Liabilities; Payment.  Guarantor agrees
that if the maturity of any of the Liabilities is accelerated by bankruptcy or
otherwise, such maturity shall also be deemed accelerated for the purpose of
this Guaranty Agreement without demand or notice to Guarantor.





                                      -4-
<PAGE>   72
Guarantor will, forthwith upon notice from the Agent, pay to the Agent the
amount due and unpaid by Borrower and guaranteed hereby.  The failure of the
Agent to give this notice shall not in any way release Guarantor hereunder.

         Section 2.6      Agent's and Noteholders' Expenses.  If Guarantor
fails to pay the Liabilities after notice from Agent of Borrower's failure to
pay any Liabilities at maturity, and if the Agent or any Noteholder obtains the
services of an attorney for collection of amounts owing by Guarantor hereunder,
or obtaining advice of counsel in respect of any of their rights under this
Guaranty Agreement, or if suit is filed to enforce this Guaranty Agreement, or
if proceedings are had in any bankruptcy, probate, receivership or other
judicial proceedings for the establishment or collection of any amount owing by
Guarantor hereunder, or if any amount owing by Guarantor hereunder is collected
through such proceedings, Guarantor agrees to pay to Agent and Noteholder, the
Agent's and the Noteholder's respective reasonable attorneys' fees.

         Section 2.7      Liability.  It is expressly agreed that the liability
of the Guarantor for the payment of the Liabilities guaranteed hereby shall be
primary and not secondary.

         Section 2.8      Events and Circumstances Not Reducing or Discharging
Guarantor's Obligations.  Guarantor hereby consents and agrees to each of the
following to the fullest extent permitted by law, and agrees that Guarantor's
obligations under this Guaranty Agreement shall not be released, diminished,
impaired, reduced or adversely affected by any of the following, and waives any
rights (including without limitation rights to notice) which Guarantor might
otherwise have as a result of or in connection with any of the following:

                 (a)      Modifications, etc.  Any renewal, extension,
modification, increase, decrease, alteration or rearrangement of all or any
part of the Liabilities, or of the Notes, or the Securities Purchase Documents
or any instrument executed in connection therewith, or any contract or
understanding between Borrower and any of the Noteholders, or any other Person,
pertaining to the Liabilities;

                 (b)      Adjustment, etc.  Any adjustment, indulgence,
forbearance or compromise that might be granted or given by any Trustee, Agent
or any Noteholder to Borrower or Guarantor or any Person liable on the
Liabilities;

                 (c)      Condition of Borrower or Guarantor.  The insolvency,
bankruptcy arrangement, adjustment, composition, liquidation, disability,
dissolution, death or lack of power of Borrower or Guarantor or any other
Person at any time liable for the payment of all or part of the Liabilities; or
any dissolution of Borrower or Guarantor, or any sale, lease or transfer of any
or all of the assets of Borrower or Guarantor, or any changes in the
shareholders, partners, or members of Borrower or Guarantor; or any
reorganization of Borrower or Guarantor;

                 (d)      Invalidity of Liabilities.  The invalidity,
illegality or unenforceability of all or any part of the Liabilities, or any
document or agreement executed in connection with the





                                      -5-
<PAGE>   73
Liabilities, for any reason whatsoever, including without limitation the fact
that the Liabilities, or any part thereof, exceed the amount permitted by law,
the act of creating the Liabilities or any part thereof is ultra vires, the
officers or representatives executing the documents or otherwise creating the
Liabilities acted in excess of their authority, the Liabilities violate
applicable usury laws, the Borrower has valid defenses, claims or offsets
(whether at law, in equity or by agreement) which render the Liabilities wholly
or partially uncollectible from Borrower, the creation, performance or
repayment of the Liabilities (or the execution, delivery and performance of any
document or instrument representing part of the Liabilities or executed in
connection with the Liabilities, or given to secure the repayment of the
Liabilities) is illegal, uncollectible, legally impossible or unenforceable, or
the Securities Purchase Documents or other documents or instruments pertaining
to the Liabilities have been forged or otherwise are irregular or not genuine
or authentic;

                 (e)      Release of Obligors.  Any full or partial release of
the liability of Borrower on the Liabilities or any part thereof, of any
co-guarantors, or any other Person now or hereafter liable, whether directly or
indirectly, jointly, severally, or jointly and severally, to pay, perform,
guarantee or assure the payment of the Liabilities or any part thereof, it
being recognized, acknowledged and agreed by Guarantor that Guarantor may be
required to pay the Liabilities in full without assistance or support of any
other Person, and Guarantor has not been induced to enter into this Guaranty
Agreement on the basis of a contemplation, belief, understanding or agreement
that other parties other than the Borrower will be liable to perform the
Liabilities, or the Noteholders will look to other parties to perform the
Liabilities.

                 (f)      Other Security.  The taking or accepting of any other
security, collateral or guaranty, or other assurance of payment, for all or any
part of the Liabilities;

                 (g)      Release of Collateral, etc.  Any release, surrender,
exchange, subordination, deterioration, waste, loss or impairment (including
without limitation negligent, willful, unreasonable or unjustifiable
impairment) of any collateral, property or security, at any time existing in
connection with, or assuring or securing payment of, all or any part of the
Liabilities;

                 (h)      Care and Diligence.   The failure of the Noteholders
or any other Person to exercise diligence or reasonable care in the
preservation, protection, enforcement, sale or other handling or treatment of
all or any part of such collateral, property or security;

                 (i)      Status of Liens.  The fact that any collateral,
security, security interest or lien contemplated or intended to be given,
created or granted as security for the repayment of the Liabilities shall not
be properly perfected or created, or shall prove to be unenforceable or
subordinate to any other security interest or lien, it being recognized and
agreed by Guarantor that Guarantor is not entering into this Guaranty Agreement
in reliance on, or in contemplation of the benefits of, the validity,
enforceability, collectibility or value of any of the collateral for the
Liabilities;





                                      -6-
<PAGE>   74
                 (j)      Payments Rescinded.  Any payment by Borrower to the
Agent or the Noteholders is held to constitute a preference under the
bankruptcy laws, or for any reason the Agent or the Noteholders are required to
refund such payment or pay such amount to Borrower or someone else; or

                 (k)      Other Actions Taken or Omitted.  Any other action
taken or omitted to be taken with respect to the Securities Purchase Documents,
the Liabilities, or the security and collateral therefor, whether or not such
action or omission prejudices Guarantor or increases the likelihood that
Guarantor will be required to pay the Liabilities pursuant to the terms hereof;
it being the unambiguous and unequivocal intention of Guarantor that Guarantor
shall be obligated to pay the Liabilities when due, notwithstanding any
occurrence, circumstance, event, action, or omission whatsoever, whether
contemplated or uncontemplated, and whether or not otherwise or particularly
described herein, except for the full and final payment and satisfaction of the
Liabilities.

         Section 2.9      Right of Subrogation and Contribution.  If Guarantor
makes a payment in respect of the Liabilities, it shall be subrogated to the
rights of the Noteholders against the Borrower with respect to such payment and
shall have the rights of contribution against the other Subsidiary Guarantors
set forth in Section 2.9 of the Subsidiary Guarantors' Guaranty Agreements;
provided that Guarantor shall not enforce its rights to any payment by way of
subrogation or by exercising its rights of contribution or reimbursement or the
right to participate in any security now or hereafter held by or for the
benefit of the Noteholders until the Liabilities have been paid in full.  The
Guarantor agrees that after all the Liabilities have been paid in full that if
its then current Net Payments are less than the amount of its then current
Contribution Obligation, Guarantor shall pay to the other Subsidiary Guarantors
an amount (together with any payments required of the other Subsidiary
Guarantors by Section 2.9 of each other Guaranty Agreement) such that the Net
Payments made by all Subsidiary Guarantors in respect of the Liabilities shall
be shared among all of the Subsidiary Guarantors in proportion to their
respective Contribution Percentage.

                                   ARTICLE 3
                         REPRESENTATIONS AND WARRANTIES

         Section 3.1      By Guarantor.  In order to induce the Agent and the
Noteholders to accept this Guaranty Agreement, Guarantor represents and
warrants to the Agent and the Noteholders (which representations and warranties
will survive the creation of the Liabilities and any extension of credit
thereunder) that:

                 (a)      Benefit to Guarantor.  Guarantor's guaranty pursuant
to this Guaranty Agreement reasonably may be expected to benefit, directly or
indirectly, Guarantor.

                 (b)      Existence.  Guarantor is duly organized, legally
existing and in good standing under the laws of the state of its formation and
is duly qualified as a foreign entity in all jurisdictions wherein the property
owned or the business transacted by it makes such qualification necessary.





                                      -7-
<PAGE>   75
                 (c)      Power and Authorization.  Guarantor is duly
authorized and empowered to execute, deliver and perform this Guaranty
Agreement and all corporate or other organizational action on Guarantor's part
requisite for the due execution, delivery and performance of this Guaranty
Agreement has been duly and effectively taken.

                 (d)      Binding Obligations.  This Guaranty Agreement
constitutes valid and binding obligations of Guarantor, enforceable in
accordance with its terms (except that enforcement may be subject to any
applicable bankruptcy, insolvency or similar laws generally affecting the
enforcement of creditors' rights or by general principles of equity).

                 (e)      No Consent.  Guarantor's execution, delivery and
performance of this Guaranty Agreement does not require the consent or approval
of any other Person, including without limitation any regulatory authority or
governmental body of the United States or any state thereof or any political
subdivision of the United States or any state thereof.

                 (f)      Solvency.  The Guarantor hereby represents that (i)
it is not insolvent as of the date hereof and will not be rendered insolvent as
a result of this Guaranty Agreement, (ii) it is not engaged in business or a
transaction, or about to engage in a business or a transaction, for which any
property or assets remaining with such Guarantor is unreasonably small capital,
and (iii) it does not intend to incur, or believe it will incur, debts that
will be beyond its ability to pay as such debts mature.

                 (g)      Litigation.  Except as disclosed to the Noteholders
in Schedule 4.03 of the Securities Purchase Agreement, at the Closing Date
there is no litigation, legal, administrative or arbitral proceeding,
investigation or other action of any nature pending or, to the knowledge of the
Guarantor threatened against the Guarantor or any of its Subsidiaries which
involves the possibility of any judgment or liability against the Guarantor or
any of its Subsidiaries not fully covered by insurance (except for normal
deductibles), and which would be more likely than not to have a Material
Adverse Effect.

                 (h)      No Breach.  Neither the execution and delivery of
this Guaranty Agreement, nor compliance with the terms and provisions hereof
will conflict with or result in a breach of, or require any consent which has
not been obtained as of the Closing Date under, the respective charter or
by-laws or other constituent documents of the Guarantor or any of its
Subsidiaries or any Governmental Requirement or any material agreement or
instrument to which the Guarantor or any of its Subsidiaries is a party or by
which it is bound or to which it or its Properties are subject, or constitute a
default under any such agreement or instrument, or result in the creation or
imposition of any Lien upon any of the material revenues or assets of the
Guarantor or any of its Subsidiaries pursuant to the terms of any such
agreement or instrument other than the Liens created by the Loan Documents.





                                      -8-
<PAGE>   76
         Section 3.2      No Representation by Noteholders.  Neither the
Noteholders nor any other Person has made any representation, warranty or
statement to the Guarantor in order to induce the Guarantor to execute this
Guaranty Agreement.

                                   ARTICLE 4
                         SUBORDINATION OF INDEBTEDNESS

         Section 4.1      Subordination of All Guarantor Claims.  As used
herein, the term "Guarantor Claims" shall mean all debts and liabilities of
Borrower to Guarantor, whether such debts and liabilities now exist or are
hereafter incurred or arise, or whether the obligation of Borrower thereon be
direct, contingent, primary, secondary, several, joint and several, or
otherwise, and irrespective of whether such debts or liabilities be evidenced
by note, contract, open account, or otherwise, and irrespective of the person
or persons in whose favor such debts or liabilities may, at their inception,
have been, or may hereafter be created, or the manner in which they have been
or may hereafter be acquired by Guarantor.  The Guarantor Claims shall include
without limitation all rights and claims of Guarantor against Borrower arising
as a result of subrogation or otherwise as a result of Guarantor's payment of
all or a portion of the Liabilities.  If any Default exists and is continuing,
and if Agent gives notice thereof to the Guarantor requiring the Guarantor
Claims not be paid, then, for so long as any Default continues to exist,
Guarantor shall not receive or collect, directly or indirectly, from Borrower
or any other party any amount upon the Guarantor Claims.

         Section 4.2      Claims in Bankruptcy.  In the event of receivership,
bankruptcy, reorganization, arrangement, debtor's relief, or other insolvency
proceedings involving Borrower as debtor, the Noteholders shall have the right
to prove their claim in any proceeding, so as to establish its rights hereunder
and receive directly from the receiver, trustee or other court custodian,
dividends and payments which would otherwise be payable upon Guarantor Claims.
Guarantor hereby assigns such dividends and payments to the Noteholders.
Should Agent or any Noteholder receive, for application upon the Liabilities,
any such dividend or payment which is otherwise payable to Guarantor, and
which, as between Borrower and Guarantor, shall constitute a credit upon the
Guarantor Claims, then upon payment in full of the Liabilities, Guarantor shall
become subrogated to the rights of Agent or the Noteholders, as applicable, to
the extent that such payments to Agent or the Noteholders, as applicable, on
the Guarantor Claims have contributed toward the liquidation of the
Liabilities, and such subrogation shall be with respect to that proportion of
the Liabilities which would have been unpaid if Agent or Noteholders, as
applicable,  had not received dividends or payments upon the Guarantor Claims.

         Section 4.3      Payments Held in Trust.  In the event that
notwithstanding Sections 4.1 and 4.2 above, Guarantor should receive any funds,
payments, claims or distributions which are prohibited by such Sections,
Guarantor agrees to hold in trust for the Noteholders an amount equal to the
amount of all funds, payments, claims or distributions so received, and agrees
that it shall have absolutely no dominion over the amount of such funds,
payments, claims or distributions except to pay them promptly to Agent, and
Guarantor covenants promptly to pay the same to Agent.





                                      -9-
<PAGE>   77
         Section 4.4      Liens Subordinate.  Guarantor agrees that any liens,
security interests, judgment liens, charges or other encumbrances upon
Borrower's assets securing payment of the Guarantor Claims shall be and remain
inferior and subordinate to any liens, security interests, judgment liens,
charges or other encumbrances upon Borrower's assets securing payment of the
Liabilities, regardless of whether such encumbrances in favor of Guarantor,
Agent or the Noteholders presently exist or are hereafter created or attach.
Without the prior written consent of the Noteholders, Guarantor shall not (a)
exercise or enforce any creditor's right it may have against the Borrower, or
(b) foreclose, repossess, sequester or otherwise take steps or institute any
action or proceeding (judicial or otherwise, including without limitation the
commencement of or joinder in any liquidation, bankruptcy, rearrangement,
debtor's relief or insolvency proceeding) to enforce any lien, mortgages, deeds
of trust, security interest, collateral rights, judgments or other encumbrances
on assets of Borrower held by Guarantor.

                                   ARTICLE 5
                                 MISCELLANEOUS

         Section 5.1      Successors and Assigns.  This Guaranty Agreement is
and shall be in every particular available to the successors and assigns of
Trustee, Agent and the Noteholders and is and shall always be fully binding
upon the legal representatives, heirs, successors and assigns of Guarantor,
notwithstanding that some or all of the monies, the repayment of which this
Guaranty Agreement applies, may be actually advanced after any bankruptcy,
receivership, reorganization, death, disability or other event affecting
Guarantor.

         Section 5.2      Notices.  Any notice or demand to Guarantor under or
in connection with this Guaranty Agreement may be given and shall conclusively
be deemed and considered to have been given and received in accordance with
Section 12.06 of the Securities Purchase Agreement, addressed to Guarantor at
the address on the signature page hereof or at such other address provided to
Trustee and Agent in writing.

         Section 5.3      Business and Financial Information.  Subject to any
applicable confidentiality agreements, the Guarantor will promptly furnish to
Trustee, Agent and the Noteholders from time to time upon request such
information regarding the business and affairs and financial condition of the
Guarantor and its subsidiaries as Trustee, Agent and the Noteholders may
reasonably request.

         Section 5.4      Construction.  This Guaranty Agreement is a contract
made under and shall be construed in accordance with and governed by the laws
of the State of Texas.

         Section 5.5      Invalidity.  In the event that any one or more of the
provisions contained in this Guaranty Agreement shall, for any reason, be held
invalid, illegal or unenforceable in any respect, such invalidity, illegality
or unenforceability shall not affect any other provision of this Guaranty
Agreement.





                                      -10-
<PAGE>   78
         Section 5.6      Subordination Agreement.  The rights and remedies of
Agent and the Noteholders under this Guaranty Agreement are subject to the
terms and conditions of that certain Subordination Agreement dated as of even
date herewith, made by the Agent, the Noteholders and the Bank of Montreal.

         Section 5.7      ENTIRE AGREEMENT.   THIS WRITTEN GUARANTY AGREEMENT
EMBODIES THE ENTIRE AGREEMENT AND UNDERSTANDING AMONG THE AGENT, THE
NOTEHOLDERS AND THE GUARANTOR AND SUPERSEDES ALL OTHER AGREEMENTS AND
UNDERSTANDINGS BETWEEN SUCH PARTIES RELATING TO THE SUBJECT MATTER HEREOF AND
THEREOF.  THIS WRITTEN GUARANTY AGREEMENT REPRESENTS THE FINAL AGREEMENT
BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR,
CONTEMPORANEOUS, OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES.  THERE ARE NO
UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.





                                      -11-
<PAGE>   79
     WITNESS THE EXECUTION HEREOF, as of this the ____ day of August, 1998.

                                     ----------------------



                                     By:
                                        ----------------------------
                                     Name:
                                          --------------------------
                                     Title:
                                           -------------------------

                                     Address:
                                             -----------------------
                                             -----------------------
                                             -----------------------

                                     Telecopier No.:
                                                    ----------------
                                     Telephone No.:
                                                   -----------------
                                     Attention:
                                               ---------------------





                                      -12-
<PAGE>   80
                                   EXHIBIT C
                               INTERCREDITOR AND
                            SUBORDINATION AGREEMENT


         THIS INTERCREDITOR AND SUBORDINATION AGREEMENT (the "Agreement") is
made as of August __, 1998, by  __________ ("__"), ___________ ("___" and
together with ___, the "Subordinated Lender"), and ____, as agent for the
Subordinated Lender (in such capacity, the "Subordinated Agent"), and BANK OF
MONTREAL, as agent (in such capacity, and together with any successor in such
capacity, the "Senior Agent") for each of the lenders that is a signatory to, or
which becomes a signatory to, the Senior Credit Agreement (as defined below)
(collectively, the "Senior Lender"), for the benefit of the Senior Agent and
Senior Lender.

         BRIGHAM EXPLORATION COMPANY, a Delaware corporation (the "Parent),
BRIGHAM OIL & GAS, L.P., a Delaware limited partnership ("BOG"), BRIGHAM, INC.,
a Nevada corporation ("BI"), BRIGHAM HOLDINGS I, LLC, a Nevada limited
liability company ("BH-I") and BRIGHAM HOLDINGS II, LLC, a Nevada limited
liability company ("BH-II", and together with BI and BH-I, the "Obligors") are
signatories hereto solely for the purpose of evidencing their acknowledgment
and consent to the terms and conditions of this Agreement and their agreement
to make payment of the Senior Indebtedness and Subordinated Indebtedness (as
such terms are defined below) in accordance with Section 2.2 of this Agreement.

                                    RECITALS

         A.      BOG, as the borrower, the Senior Agent and the Senior Lender
are parties to that certain Credit Agreement dated as of January 26, 1998, as
amended by (i) that certain First Amendment to Credit Agreement dated as of
________ ,1998 and (ii) that certain Second Amendment to Credit Agreement dated
as of _______, 1998 (such agreement, as the same may be from time to time
further amended, supplemented, restated, refinanced or replaced, the "Senior
Credit Agreement"), pursuant to which the Senior Lender has made certain credit
available to and on behalf of BOG.

         B.       BOG has heretofore executed and may hereafter execute one or
more Mortgage, Deed of Trust, Assignment of Production, Security Agreement and
Financing Statements and one or more Security Agreements (such agreements, as
the same may be from time to time amended, supplemented or replaced, the
"Senior Mortgage") dated as of January 26, 1998 in favor of the Senior Agent to
secure, inter alia, the obligations outstanding under the Senior Credit
Agreement.

         C.      Parent, BI, BH-I and BH-II have each executed a Guaranty
Agreement dated as of January 26, 1998 (such Guaranty Agreements, as the same
may be from time to time further amended,





                                      -1-
<PAGE>   81
supplemented or replaced, being referred to herein as the "Senior Guaranty
Agreements"), in favor of the Senior Agent and the Senior Lender to guarantee,
inter alia, the obligations of BOG under the Senior Credit Agreement.

         D.      Parent has executed a Security Agreement date as of January
26, 1998 (such Security Agreement, as the same may be from time to time further
amended, supplemented or replaced, the "Senior Parent Security Agreement") in
favor of the Senior Agent and the Senior Lender to secure, inter alia, the
obligations of BOG under the Senior Credit Agreement. The Senior Credit
Agreement, the Senior Mortgage, the Senior Guaranty Agreements, the Senior
Parent Security Agreement and any other documents or instruments given in
connection therewith being collectively referred to herein as the "Senior Loan
Documents").

         E.      Of even date herewith, Parent, as the borrower, the
Subordinated Lender and the Subordinated Agent have executed a Securities
Purchase Agreement (the "Securities Purchase Agreement") pursuant to which the
Subordinated Lender will make certain advances to the Parent in accordance with
the terms and conditions of an Indenture of even date herewith executed by the
Parent (the "Indenture"), such advances to be evidenced by one or more
promissory notes executed by the Parent in accordance with the Securities
Purchase Agreement and the Indenture (the "Subordinated Notes ").

         F.      In connection with the execution and delivery of the
Securities Purchase Agreement, the Indenture and the Subordinated Notes, BOG
has executed one or more Mortgage, Deed of Trust, Assignment of Production,
Security Agreement and Financing Statements, granting subordinated liens in the
properties subject to the Senior Mortgage (such agreements, as the same may be
from time to time amended, supplemented or replaced, the "Subordinated
Mortgage") in favor of the Trustee under the Indenture ("Trustee"), for the
benefit of the Subordinated Agent and the Subordinated Lender, to secure, inter
alia, the obligations outstanding under the Subordinated Loan Documents (as
defined below).

         G.      In connection with the execution and delivery of the
Securities Purchase Agreement, BOG, BI, BH-I and BH-II have each executed a
Guaranty Agreement dated as of even date herewith (such Guaranty Agreements, as
the same may be from time to time further amended, supplemented or replaced,
being referred to herein as the "Subordinated Guaranty Agreements"), in favor
of the Trustee, for the benefit of the Subordinated Agent and the Subordinated
Lender to guarantee, inter alia, the obligations of the Parent under the
Subordinated Loan Documents.

         H.      In connection with the execution and delivery of the
Securities Purchase Agreement and the Indenture, the Parent has executed a
Security Agreement dated of even date herewith (such Security Agreement, as the
same may be from time to time further amended, supplemented or replaced, being
referred to herein as the "Subordinated Parent Security Agreement"), in favor
of the Trustee, for the benefit of the Subordinated Agent and the Subordinated
Lender, to secure, inter alia,





                                      -2-
<PAGE>   82
the obligations of the Parent under the Subordinated Loan Documents. The
Securities Purchase Agreement, the Indenture, the Subordinated Notes, the
Subordinated Mortgage, the Subordinated Guaranty Agreements, the Subordinated
Parent Security Agreement and those other documents or instruments given in
connection therewith, including those identified on Exhibit "A" attached hereto
being collectively referred to herein as the "Subordinated Loan Documents").

         H.      One of the conditions to the Senior Agent and the Senior
Lender executing the Second Amendment to Credit Agreement referred to above is
the execution and delivery of this Agreement.

         I.      Therefore, (i) in order to comply with the terms and
conditions of the Second Amendment to Credit Agreement, (ii) at the special
insistence and request of the Senior Agent and the Senior Lender, and (iii) for
other good and valuable consideration, the receipt and sufficiency of which are
hereby acknowledged, the Subordinated Agent, the Subordinated Lender, the
Senior Agent on behalf of the Senior Lender, and the Parent, BOG and the
Obligors agree as follows:

                                   ARTICLE I
                                  Definitions

         Section 1.1      Terms Defined Above. As used in this Agreement, the
terms defined above shall have the meanings respectively assigned to them.

         Section 1.2      Certain Definition. As used in this Agreement the
following terms shall have the following meanings, unless the context otherwise
requires:

         "Hedging Agreement" shall mean the ISDA Master Agreement between BOG
         and Bank of Montreal now or hereafter entered into, and any hedging
         transactions entered into pursuant to the terms thereof.

         "Lien" shall mean any interest in Property securing an obligation owed
         to, or a claim by, a Person other than the owner of the Property,
         whether such interest is based on the common law, statute or contract,
         and whether such obligation or claim is fixed or contingent, and
         including but not limited to the lien or security interest arising
         from a mortgage, encumbrance, pledge, security agreement, conditional
         sale or trust receipt or a lease, consignment or bailment for security
         purposes.

         "Payment Blockage Period" means the period commencing on (i) the date
         on which a default in the payment of any principal of or interest on
         the Senior Indebtedness occurs or (ii) the date on which a Payment
         Blockage Notice (as defined below) is given, and expiring on the date
         which is 60 days following the first day of the Payment Blockage
         Period.





                                      -3-
<PAGE>   83
         "Oil and Gas Properties" shall have the meaning attributed to such
         term in the Senior Credit Agreement.

         "Person" shall mean any individual, corporation, company, voluntary
         association, partnership, joint venture, trust, limited liability
         company, unincorporated organization or government or any agency,
         instrumentality or political subdivision thereof, or any other form of
         entity.

         " Property" shall mean any interest in any kind of property or asset,
         whether real, personal or mixed, or tangible or intangible.

         "Senior Indebtedness" shall mean the principal balance of all loans
         advanced to or letters of credit issued for the account of BOG
         pursuant to the terms and conditions of the Senior Loan Documents, not
         to exceed $75,000,000 plus such additional amounts as are permitted
         under Section 2.6(a)(ii) of this Agreement, and accrued but unpaid
         interest thereon, all fees, expenses, reimbursement obligations,
         liabilities, indemnities or other monetary obligations of BOG, the
         Parent or any Obligor under any Senior Loan Document, and all swap
         settlement amounts or other amounts due and payable under the Hedging
         Agreement, whether any of the foregoing is (i) absolute or contingent,
         direct or indirect, joint, several or independent, (ii) now
         outstanding or owing or which may hereafter be existing or incurred,
         (iii) due or to become due, or (iv) held or to be held by the Senior
         Agent or any Senior Lender, and all renewals, extensions,
         rearrangements, refundings and modifications thereof permitted by the
         terms hereof.

         "Subordinated Indebtedness" shall mean the principal balance of all
         loans advanced to the Parent pursuant to the terms and conditions of
         the Subordinated Loan Documents (including interest paid in kind as
         permitted by the Subordinated Loan Documents), and accrued but unpaid
         interest thereon, and all fees, expenses, reimbursement obligations,
         liabilities, indemnities or other monetary obligations of BOG, the
         Parent or any Obligor under any Subordinated Loan Document, whether
         any of the foregoing is (i) absolute or contingent, direct or
         indirect, joint, several or independent, (ii) now outstanding or owing
         or hereafter existing or incurred, (iii) due or to become due, or (iv)
         held or to be held by the Subordinated Agent or any Subordinated
         Lender, and all renewals, extensions, rearrangements, refundings and
         modifications thereof permitted by the terms hereof.

                                   ARTICLE II
                                 Subordination

         Section 2.1      Agreement to Subordinate. The payment of any and all
Subordinated Indebtedness and the Subordinated Loan Documents are expressly
subordinated to the extent and in the manner set forth in Sections 2.2 through
2.8 hereof to the Senior Indebtedness and the Senior Loan Documents.





                                      -4-
<PAGE>   84
         Section 2.2      Payment Subordination upon Default.

                 (a)      The Subordinated Agent and the Subordinated Lender
agree, that:

                 (i)      the Subordinated Indebtedness is subordinate in right
         of payment, to the extent and in the manner provided in this
         Agreement, to the prior payment in full of all Senior Indebtedness
         (whether outstanding on the date hereof or hereafter created,
         incurred, assumed or guaranteed);

                 (ii)     the Parent, BOG and the Obligors may not make any
         payment (whether by redemption, purchase, retirement, defeasance,
         set-off or otherwise) upon or in respect of the Subordinated
         Indebtedness, until all principal and other obligations with respect
         to the Senior Indebtedness have been paid in full if:

                 (A)      a default in the payment of any principal of or
                          interest on the Senior Indebtedness occurs; or

                 (B)      the payment of the Subordinated Indebtedness would
                          result in a default or event of default under the
                          Senior Loan Documents or any other default has
                          occurred and is continuing with respect to the Senior
                          Indebtedness that permits, or with the giving of
                          notice or passage of time or both (unless cured or
                          waived) would permit, the Senior Agent or the Senior
                          Lender to accelerate its maturity and the
                          Subordinated Agent receives a notice of the default
                          (a "Payment Blockage Notice") from the Parent, BOG,
                          any Obligor, the Senior Agent or any Senior Lender
                          with regard to the foregoing.

                 (iii)    the Parent, BOG and each Obligor may resume payments
         on and distributions in respect of the Subordinated Indebtedness upon:

                 (A)      in the case of a default referred to in Section
                          2.2(a)(ii)(A), the date upon which the default is
                          cured or waived, or

                 (B)      in the case of a default referred to in Section
                          2.2(a)(ii)(B), the earliest of (1) the date on which
                          such nonpayment default is cured or waived or (2) the
                          expiration of the applicable Payment Blockage Period
                          unless the maturity of the Senior Indebtedness has
                          been accelerated.

                 (iv)     Upon any payment or distribution of property or
         securities to creditors of the Parent, BOG or any Obligor in a
         liquidation or dissolution of such person or its property, or in an
         assignment for the benefit of creditors or any marshaling of its
         assets and liabilities:





                                      -5-
<PAGE>   85
                 (A)      the Senior Lender shall be entitled to receive
                 payment in full of all Senior Indebtedness (including interest
                 after the commencement of any such proceeding at the rate
                 specified in the Senior Loan Documents, whether or not a claim
                 for such interest would be allowed in such proceeding) before
                 the Subordinated Agent and/or Subordinated Lender shall be
                 entitled to receive any payment with respect to the
                 Subordinated Indebtedness; and

                 (B)      until the Senior Indebtedness is paid in full, any
                 payment or distribution to which the Subordinated Agent and/or
                 the Subordinated Lender would be entitled shall be made to the
                 Senior Agent for its benefit and the benefit of the Senior
                 Lender.

                 (C)      Under the circumstances described in this clause
                 (iv), the Parent, BOG, any Obligor, or any receiver, trustee
                 in bankruptcy, liquidating trustee, agent or other similar
                 Person making any payment or distribution of cash or other
                 property or securities is authorized or instructed to make any
                 payment or distribution to which the Subordinated Agent and/or
                 the Subordinated Lender would otherwise be entitled (other
                 than securities that are subordinated at least to the same
                 extent as the Subordinated Indebtedness) directly to the
                 Senior Agent for its benefit and the benefit of the Senior
                 Lender to the extent necessary to pay all Senior Indebtedness
                 in full, after giving effect to any concurrent payment,
                 distribution or provision therefor to or for the Senior Agent
                 and the Senior Lender.

                 (b)      The Senior Agent and the Senior Lender shall have the
right, in their sole and absolute discretion, to waive the conditions of
Section 2.2(a) prohibiting the payment of the Subordinated Indebtedness whether
in an enforcement action brought by the Senior Agent or Senior Lender on the
Senior Indebtedness or otherwise.

                 (c)      The foregoing provisions of Section 2.2 shall not
impair or prohibit the rights of the Subordinated Lender to receive payments in
the form of equity securities or additional subordinated debt (including the
payment of interest in kind as permitted by the Subordinated Loan Documents)
that is subordinated to the Senior Indebtedness in accordance with the terms of
this Agreement. Nothing in this Agreement shall limit or restrict the accrual
or charging of default interest on any of the Subordinated Indebtedness not
paid when due. In addition, the foregoing provisions of this Section 2.2 shall
not prevent the Subordinated Agent or any Subordinated Lender from exercising
its available remedies upon a default or event of default under the
Subordinated Loan Documents, subject to (y) the rights of the Senior Agent and
the Senior Lender to receive distributions and payments otherwise payable to
the Subordinated Lenders, and (z) the expiration of any then applicable Payment
Blockage Period.





                                      -6-
<PAGE>   86
         Section 2.3      Payments Received or Made in Violation of this 
Agreement.

                 (a)      In the event the Subordinated Agent or any
Subordinated Lender shall receive any payment or distribution on account of the
Subordinated Indebtedness which it is not entitled to receive under the
provisions of Section 2.2, the Subordinated Agent or such Subordinated Lender
will hold any amount so received in trust for the Senior Lender and will
forthwith turn over such payment to the Senior Agent in the form received by it
(together with any necessary endorsement) to be applied to the Senior
Indebtedness. In the event of any failure by the Subordinated Agent or any
Subordinated Lender to make any such endorsement, the Senior Agent is hereby
irrevocably authorized and granted a power of attorney (which is irrevocable
and coupled with interest) to make the same.

                 (b)      If the Parent or any Obligor shall become aware that
a "Default" or an "Event of Default" has occurred under Senior Credit Agreement
then such Person shall give the Senior Agent, the Senior Lender and the
Subordinated Agent prompt written notice thereof.

                 (c)      This Agreement defines the relative rights of the
Senior Agent and the Senior Lender and the Subordinated Agent and Subordinated
Lender. Nothing in this Agreement shall: (i) impair, as between the Parent, BOG
or any Obligor, the Subordinated Agent and the Subordinated Lender, the
obligations of the Parent, BOG and each Obligor, which are absolute and
unconditional, to pay the Subordinated Indebtedness in accordance with the
terms of the Subordinated Loan Documents, or (ii) prevent the Subordinated
Agent or any Subordinated Lender from exercising its available remedies subject
to any applicable Payment Blockage Period.

         Section 2.4      Liens Subordinate.

                 (a)      The Subordinated Agent and the Subordinated Lender
agree that any Liens upon the Property of any of the Parent, BOG or any Obligor
securing payments of the Subordinated Indebtedness are and shall be and remain
inferior and subordinated to any Liens securing payments of the Senior
Indebtedness in such Property regardless of whether such encumbrances in favor
of the Subordinated Agent or any Subordinated Lender or the Senior Agent and
the Senior Lender presently exist or are hereafter created or attached and
regardless of the date of execution and delivery or the date of filing or
recording. Any obligation of the Parent, BOG or any Obligor under the
Subordinated Loan Documents to deliver possession of any Property to the
Trustee under the Indenture, the Subordinated Agent or the Subordinated Lender,
whether for purposes of perfection or realization of any rights thereunder
shall be subordinate in all respects to the Parent's, BOG's or any Obligor's
obligation to deliver possession of any such Property to the Senior Loan Agent
or Senior Lender under the Senior Loan Documents for such purposes.





                                      -7-
<PAGE>   87
                 (b)      The Subordinated Agent and the Subordinated Lender
covenant and agree not to contest or dispute, whether in any proceeding or
otherwise, the validity, enforceability, attachment, priority or perfected
status of any Lien granted in favor of the Senior Agent or any Senior Lender or
take any steps or actions, including the institution of any proceedings, to
enjoin or restrain the Senior Agent or any Senior Lender from the exercise of
the remedies afforded them under the Senior Loan Documents or applicable law in
and to any of the Senior Lender Collateral.

         Section 2.5      Agreement Not to Pursue Action.

                 (a)      Following the commencement of any Payment Blockage
Period, the Subordinated Agent and each Subordinated Lender covenants that it
will not, until the earlier of the date (1) of expiration of the applicable
Payment Blockage Period, (2) the Senior Indebtedness is paid in full or the
event which gave rise to the Payment Blockage Period is cured or waived, (3)
there occurs an event which would cause an automatic acceleration of the
Subordinated Indebtedness under any of Sections 10.01(f), (g), (h) or (k) of
the Indenture, or (4) the Senior Indebtedness is accelerated and the Senior
Agent or Senior Lender takes any action to enforce any of their respective
rights under the Senior Credit Agreement, do any of the following unless the
Senior Agent or Senior Lender shall also join in such action or commence a
similar action: (i) commence any action or proceeding against the Parent, BOG
or any Obligor to recover all or any part of the Subordinated Indebtedness or
join with any other creditor in bringing any proceedings against such Person
under any bankruptcy, reorganization, readjustment of debt, arrangement of
debt, receivership, liquidation or insolvency law or statute of the Federal or
any state government, (ii) accelerate the maturity of any Subordinated
Indebtedness, or (iii) foreclose, repossess, sequester or otherwise take steps
or institute any action or proceeding to enforce any Lien, collateral right,
judgment or other encumbrances on any Property of the Parent, BOG or any
Obligor held by the Subordinated Agent or any Subordinated Lender, or to take
possession of any such Property; provided the foregoing will not prohibit (A)
such presentment as may be necessary to prevent the discharge of any liable
parties on any instrument, (B) the filing of claims or notices to prevent the
running of any applicable statute of limitations, or (C) or similar actions
necessary to preserve the legal rights of the Subordinated Lender and/or the
Subordinated Agent.

                 (b)      Notwithstanding anything contained in this Agreement
to the contrary, the Subordinated Agent and Subordinated Lender shall not be
prohibited at any time, whether during a Payment Blockage Period or otherwise,
from delivering any notice of default to the Parent, BOG or any Obligor, and
the existence of any Payment Blockage Period shall not prevent, abate or delay
the running of any applicable cure period under the Subordinated Loan Documents
following any default or notice of any default under the Subordinated Loan
Documents.

                 (c)      The Senior Lender and Senior Agent may enforce no
more than two (2) Payment Blockage Periods during any 365 day period.





                                      -8-
<PAGE>   88
         Section 2.6      Rights of the Senior Agent and the Senior Lender. The
Senior Agent and the Senior Lender may, at any time, and from time to time,
without the consent of or notice to the Subordinated Agent or any Subordinated
Lender, without incurring responsibility to the Subordinated Agent and/or any
Subordinated Lender, without impairing or releasing any of the Senior Agent or
the Senior Lender's rights or any of the obligations of the Subordinated Agent
and the Subordinated Lender under this Agreement:

                 (a)      change the amount, manner, place or terms of payment,
or change or extend for any period the time of payment of, or renew, increase
or otherwise alter the Senior Indebtedness or any Senior Loan Document or any
other instrument or agreement now or hereafter executed or evidencing any of
the Senior Indebtedness in any manner, or enter into or amend in any manner any
other agreement relating to the Senior Indebtedness, except as follows:

                          (i)     To increase the rate of interest or modify
                 the interest payment schedule unless, on a pro forma basis,
                 for the four fiscal quarters of the Parent occurring after the
                 effective date of such increase or modification, the interest
                 coverage test in Section 8.16 of the Indenture is satisfied;
                 or

                          (ii)    To increase the principal amount of the
                 Senior Indebtedness above $75,000,000 unless the Senior
                 Indebtedness (as increased) is (A) funded by financial
                 institutions and (B) permitted to be incurred under Section
                 8.01 of the Indenture; or

                          (iii)   To further restrict (beyond those
                 restrictions in the Senior Credit Agreement as in effect on
                 the date hereof) any payment of dividends or similar
                 distributions by any subsidiary of the Parent to the Parent or
                 the granting of any Lien or other security interest securing
                 payment of the Subordinated Indebtedness or any guarantees of
                 the Subordinated Indebtedness; or

                          (iv)    To restrict any payments of the Subordinated
                 Indebtedness except as provided in Section 2.2 above;

                 (b)      sell, exchange, release or otherwise deal with all or
any part of any Property by whomsoever at any time pledged or mortgaged to
secure, howsoever securing, the Senior Indebtedness;

                 (c)      release any Person liable in any manner for payment
or collection of the Senior Indebtedness;

                 (d)      exercise or refrain from exercising any rights
against the Parent, BOG or any other Obligor or others, including the
Subordinated Agent and the Subordinated Lender; and





                                      -9-
<PAGE>   89
                 (e)      apply any sums received by the Senior Agent and/or
Senior Lender, paid by any Person and however realized, to payment of the
Senior Indebtedness in such a manner as the Senior Agent and the Senior Lender,
in their sole discretion, may deem appropriate.

Upon request by the Senior Agent prior to the funding of any Senior
Indebtedness in excess of $75,000,000, if permitted under Section 2.6(a)(ii)
above, the Subordinated Lender will confirm, based upon the information
available to it, whether or not such proposed additional Senior Indebtedness is
permitted under Section 2.6(a)(ii).

         Section 2.7      Subordination May Not Be Impaired by the Parent, BOG
or the Obligors. No right of any present or future Senior Agent or Senior
Lender to enforce the subordination as provided in this Agreement will at any
time or in any way be prejudiced or impaired by any act or failure to act on
the part of the Parent, BOG or any Obligor or by any act or failure to act, in
good faith, by the Senior Agent or any Senior Lender, or by any noncompliance
by the Parent, BOG or any Obligor with the terms of any Subordinated Loan
Document, regardless of any knowledge thereof that the Senior Agent or any
Senior Lender may have or otherwise be charged with. The provisions of this
Section 2.7 are intended to be for the benefit of, and shall be enforceable
directly by, the Senior Agent or the Senior Lender.

         Section 2.8      Authorization to File Proof of Claim. If the
Subordinated Agent or any Subordinated Lender does not file a proper proof of
claim or proof of debt in the form required in any proceeding referred to in
Section 2.2(a)(iv) hereof at least 30 days before the expiration of the time to
file such claim, the Senior Agent is hereby authorized to file an appropriate
claim for and on behalf of the Subordinated Agent and the Subordinated Lender.

                                  ARTICLE III
                    Representations. Warranties and Covenant

         Section 3.1      Representations of Subordinated Agent and
Subordinated Lender. The Subordinated Agent and each Subordinated Lender
represent and warrant that:

                 (a)      neither the execution nor delivery of this Agreement
nor fulfillment of or compliance with the terms and provisions hereof will
conflict with, or result in a breach of the terms, conditions or provisions of,
or constitute a default under, any agreement or instrument which it is now
subject to;

                 (b)      it has all requisite authority to execute, deliver
and perform its obligations under this Agreement; and

                 (c)      this Agreement constitutes the legal, valid, and
binding obligation of the





                                      -10-
<PAGE>   90
Subordinated Agent and the Subordinated Lender, enforceable in accordance with
its terms, subject to applicable bankruptcy, insolvency or similar laws and
general principles of equity.

         Section 3.2      Representations of Senior Agent. The Senior Agent
represents and warrants that:

                 (a)      neither the execution nor delivery of this Agreement
nor fulfillment of or compliance with the terms and provisions hereof will
conflict with, or result in a breach of the terms, conditions or provisions of,
or constitute a default under, any of the Senior Loan Documents or any other
agreement or instrument which it is now subject to;

                 (b)      it has all requisite authority for itself and as
agent acting on behalf of the Senior Lender, to execute, deliver and perform
its and the Senior Lender's obligations under this Agreement; and

                 (c)      this Agreement constitutes the legal, valid, and
binding obligation of the Senior Agent, enforceable in accordance to its terms,
subject to applicable bankruptcy, insolvency or similar laws and general
principles of equity.

         Section 3.3      Subordinated Agent, Subordinated Lender Covenants.
The Subordinated Agent and each Subordinated Lender covenant that so long as
any of the Senior Indebtedness remains outstanding and until the termination of
the "Aggregate Commitments" (as defined in the Senior Credit Agreement), it
will:

                 (a)      cause any note, debenture, or instrument evidencing
or securing the Subordinated Indebtedness to contain a statement or legend to
the effect that such note, debenture, or other instrument is subordinated to
the Senior Indebtedness in the manner and to the extent set forth in this
Agreement;

                 (b)      not assign or transfer to others the Subordinated
Indebtedness or any claim it has or may have against the Parent, BOG or any
other Obligor as long as any of the Senior Indebtedness remains outstanding,
unless such assignment or transfer is expressly made subject to this Agreement;

                 (c)      not amend, supplement or otherwise modify the terms
of the Subordinated Indebtedness without the express written consent of the
Senior Agent, which consent will not be unreasonably withheld, which has the
effect of (i) increasing the principal amount of the Subordinated Indebtedness,
provided that the foregoing shall not affect the Parent's right to make payment
in kind of accrued interest or the Subordinated Lender's ability to accept
payment in kind as provided in the Subordinated Loan Documents, thereby
increasing the principal amount of the Subordinated Indebtedness and (ii)
increasing the rate of interest or any fees charged on the Subordinated





                                      -11-
<PAGE>   91
Indebtedness (provided that the foregoing shall not prohibit any fees or
changes in the rate of interest contemplated by the terms of the Securities
Purchase Agreement);

                 (d)      not ask for, sue for, take, or demand any payment on
such indebtedness, except as permitted hereby; and

                 (e)      execute any and all other instruments necessary as
reasonably required by the Senior Agent or the Senior Lender to effect the
subordinations intended hereby.

                                   ARTICLE IV
                                 Miscellaneous

         Section 4.1      Acceptance by the Senior Agent and the Senior Lender.
The foregoing subordination provisions are, and are intended to be, an
inducement and a consideration to the Senior Agent and each Senior Lender,
whether such Senior Lender's Senior Indebtedness is created or acquired before
or after the issuance of Subordinated Indebtedness, to acquire and continue to
hold, or to continue to hold, such Senior Indebtedness and each such Senior
Lender shall be deemed conclusively to have relied on such subordination
provisions in acquiring and continuing to hold, or in continuing to hold, such
Senior Indebtedness. Notice of acceptance of this Agreement is waived,
acceptance on the part of the Senior Agent and the Senior Lender being
conclusively presumed by their request for this Agreement and delivery of the
same to them.

         Section 4.2      Assignment by the Senior Agent and the Senior Lender.
This Agreement may be assigned by the Senior Agent and the Senior Lender in
connection with any assignment or transfer of the Senior Indebtedness or any
replacement or refinancing of the Senior Loan.

         Section 4.3      Notice. All notices and other communications provided
for herein shall be given or made by telecopy, courier or U.S. Mail or in
writing and telecopied, mailed or delivered to the intended recipient at the
"Address for Notices" specified below its name on the signature pages hereof or
at such other address as shall be designated by such party in a notice to each
other party; and in the case of the Senior Agent or any Senior Lender in care
of the Senior Agent at the following address:

                          Bank of Montreal, as Agent
                          700 Louisiana, Suite 4400
                          Houston, Texas 77002
                          Telecopier No.: (713) 223-4007
                          Telephone No.: (713) 546-9700
                          Attention: Client Services Group

or at such other address as shall be designated by the Senior Agent in a notice
to each other party.





                                      -12-
<PAGE>   92
Except as otherwise provided in this Agreement, all such communications shall
be deemed to have been duly given when transmitted by telecopier, delivered to
the telegraph or cable office or personally delivered or, in the case of a
mailed notice, five (5) days after the date deposited in the mails, postage
prepaid, in each case given or addressed as aforesaid.

         Section 4.4      Amendments and Waivers. The Senior Agent's,
Subordinated Agent's, any Senior Lender's or Subordinated Lender's acceptance
of partial or delinquent payments or any forbearance, failure or delay by any
of the foregoing in exercising any right, power or remedy hereunder shall not
be deemed a waiver of any obligation of the Parent, BOG or any Obligor or the
Senior Agent, Senior Lender, Subordinated Agent or any Subordinated Lender, or
of any right, power or remedy of the Senior Agent, Senior Lender, Subordinated
Agent or Subordinated Lender; and no partial exercise of any right, power or
remedy shall preclude any other or further exercise thereof. The Subordinated
Agent and the Subordinated Lender hereby agree that if the Senior Agent and/or
any Senior Lender agrees to a waiver of any provision hereunder, or an exchange
of or release of collateral, or the addition or release of any Person as an
Obligor, any such action shall not constitute a waiver of any of the Senior
Agent's and/or any Senior Lender's other rights or of the Subordinated Agent's
or any Subordinated Lender's obligations hereunder. This Agreement may be
amended only by an instrument in writing executed jointly by the Subordinated
Agent and the Senior Agent and may be supplemented only by documents delivered
or to be delivered in accordance with the express terms hereof.

         Section 4.5      Parties to the Agreement. The provisions of this
Agreement are and are intended solely for the purpose of defining the relative
rights of the Subordinated Agent, the Subordinated Lender, the Senior Agent and
the Senior Lender, and are solely for the benefit of the Senior Agent, the
Senior Lender, the Subordinated Agent and the Subordinated Lender (including
their respective assignees and successors); and may not be relied upon or
enforced by any other Person. The Parent, BOG and each Obligor have joined
herein solely for the purpose of evidencing their acknowledgment and consent to
the terms and conditions of this Agreement and their agreement to make payment
of the Senior Indebtedness and Subordinated Indebtedness in accordance with the
terms of Section 2.2.

         Section 4.6      Reinstatement. To the extent that any payments on the
Senior Indebtedness or proceeds of any collateral are subsequently invalidated,
declared to be fraudulent or preferential, set aside or required to be repaid
by the Senior Agent or any Senior Lender to a trustee, debtor in possession,
receiver or other Person under any bankruptcy law, common law or equitable
cause, then to such extent, obligations hereunder with respect to the Senior
Indebtedness so satisfied shall be revived and continue as if such payment or
proceeds had not been received and the Senior Agent's and the Senior Lender's
Liens, interests, rights, powers and remedies under the Senior Loan Documents
and this Agreement shall continue in full force and effect. In such event, each
Senior Loan Document and this Agreement shall be automatically reinstated and
the Parent, BOG, the Obligors, the Subordinated Agent and the Subordinated
Lender shall take such action as may be





                                      -13-
<PAGE>   93
reasonably requested by the Senior Agent and the Senior Lender to effect such
reinstatement. Any Senior Lender which has assigned its rights hereunder shall
continue to be entitled to the benefits of this Section notwithstanding such
assignment.

         Section 4.7      Governing Law. THIS AGREEMENT SHALL BE GOVERNED BY,
AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF TEXAS.

         Section 4.8      ENTIRE AGREEMENT. THIS WRITTEN AGREEMENT EMBODIES THE
ENTIRE AGREEMENT AND UNDERSTANDING BETWEEN THE SENIOR AGENT AND THE SENIOR
LENDER, THE SUBORDINATED AGENT AND THE SUBORDINATED LENDER AND SUPERSEDES ALL
OTHER AGREEMENTS AND UNDERSTANDINGS BETWEEN SUCH PARTIES RELATING TO THE
SUBJECT MATTER HEREOF AND THEREOF. THIS WRITTEN AGREEMENT REPRESENTS THE FINAL
AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR,
CONTEMPORANEOUS, OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO
UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.

         Section 4.9      References and Title. All references in this
Agreement to articles, sections, subsections and other subdivisions refer to
the articles, sections, subsections and other subdivisions of this Agreement
unless expressly provided otherwise. Titles appearing at the beginning of any
subdivisions are for convenience only and do not constitute any part of such
subdivisions and shall be disregarded in construing the language contained in
such subdivisions.

         Section 4.10     Severability. All rights, remedies and powers
provided herein may be exercised only to the extent that the exercise thereof
does not violate any applicable provision of law; and all the provisions hereof
are intended (a) to be subject to all applicable mandatory provisions of law
which may be controlling and (b) to be limited to the extent necessary so that
they will not render this Agreement invalid under the provisions of any
applicable law.  If any term or provision of this Agreement shall be determined
to be illegal or unenforceable, all other terms and provisions of this
Agreement shall nevertheless remain effective and shall be enforced to the
fullest extent permitted by applicable law and the parties agree to promptly
meet and negotiate in good faith to establish new arrangements which have the
effect of preserving in the economic and commercial benefits established by
this Agreement.

         Section 4.11     Subrogation. Subject to the terms of Section 4.6,
after all Senior Indebtedness is paid in full and until the Subordinated
Indebtedness has been paid in full, the Subordinated Lender shall be subrogated
to the rights of the Senior Agent and the Senior Lender to receive
distributions and payments applicable to the Senior Indebtedness to the extent
that distributions and payments otherwise payable to the Subordinated Lender
have been applied to the payment of Senior Indebtedness. A payment or
distribution made under this Agreement to the Senior Agent and/or the





                                      -14-
<PAGE>   94
Senior Lender that otherwise would have been made to the Subordinated Lender is
not, as between Parent, BOG or any Obligor and the Subordinated Agent and
Subordinated Lender, a payment on the Subordinated Indebtedness.





                                      -15-
<PAGE>   95
WITNESS THE EXECUTION HEREOF, as of this the _____ day of August, 1998.

                                       SENIOR AGENT:

                                       BANK OF MONTREAL

                                       By: 
                                          -------------------------
                                       Name: 
                                            -----------------------
                                       Title:
                                             ----------------------





                                      -16-
<PAGE>   96
                                       PARENT:

                                       BRIGHAM EXPLORATION COMPANY,
                                       a Delaware corporation

                                       By:
                                          ------------------------
                                          Craig M. Fleming
                                          Chief Financial Officer

                                       BOG:

                                       BRIGHAM OIL & GAS, L.P.,
                                       a Delaware limited partnership

                                       By:  Brigham, Inc., a Nevada
                                            corporation, its General Partner


                                            By:
                                               -----------------------
                                               Craig M. Fleming
                                               Chief Financial Officer





                                      -18-
<PAGE>   97
                                       OBLIGORS:

                                       BRIGHAM, INC.,
                                       a Nevada corporation

                                       By: 
                                          --------------------------
                                          Craig M. Fleming
                                          Chief Financial Officer

                                       BRIGHAM HOLDINGS I, LLC,
                                       a Nevada limited liability company

                                       By: 
                                          --------------------------
                                       Name: 
                                            ------------------------
                                       Title: 
                                             -----------------------

                                       BRIGHAM HOLDINGS II, LLC,
                                       a Nevada limited liability company


                                       By: 
                                          --------------------------
                                       Name: 
                                            ------------------------
                                       Title: 
                                             -----------------------



                                       Addresses for notices of the Parent, BOG
                                       and each Obligor:

                                       6300 Bridge Point Parkway
                                       Building 2, Suite 500
                                       Austin, Texas 78730
                                       Telecopy No: 512-427-3400





                                    -19-
<PAGE>   98
                                   EXHIBIT A

                           Subordinated Loan Document

1.       The Securities Purchase Agreement.

2.       Subordinated Note(s) in the aggregate face amount of $50,000,000
         issued by the Parent in favor of the Subordinated Lender(s).

3.       Mortgage, Deed of Trust, Assignment of Production, Security Agreement
         and Financing Statement dated as of August __, 1998 executed by BOG in
         favor of the Subordinated Agent, for its benefit and the benefit of
         Subordinated Lender.

5.       Guaranty Agreement dated as of August __, 1998 executed by BOG in
         favor of the Subordinated Agent and Subordinated Lender.

6.       Guaranty Agreement dated as of August __, 1998 executed by Brigham,
         Inc. in favor of the Subordinated Agent and Subordinated Lender.

7.       Guaranty Agreement dated as of August __, 1998 executed by Brigham
         Holdings I, LLC in favor of the Subordinated Agent and Subordinated
         Lender.

8.       Guaranty Agreement dated as of August __, 1998 executed by Brigham
         Holdings II, LLC in favor of the Subordinated Agent and Subordinated
         Lender.

9.

10.

11.

12.
<PAGE>   99
--------------------------------------------------------------------------------

                                   Exhibit D
                                 ------------    
                               SECURITY AGREEMENT



                                    Between



                  ----------------------------------------

                                      and

                                           , as Trustee
                       --------------------


                                August __, 1998




--------------------------------------------------------------------------------

<PAGE>   100
                               SECURITY AGREEMENT


         THIS SECURITY AGREEMENT (this "Agreement") is made as of August __,
1998, between ___________________ ("Pledgor"); and _________ having an address
at __________ ("Secured Party") as trustee and as collateral agent for the
ratable benefit of Agent and the Noteholders (each as defined in the Securities
Purchase Documents described below).

                                    RECITALS
         A.      [The Pledgor] [Brigham Exploration Company, a Delaware
corporation] ("Borrower")  is executing (i) the Securities Purchase Agreement
dated as of August __, 1998 (such agreement, as may from time to time be
amended or supplemented, being hereinafter called the "Securities Purchase
Agreement") among the [Pledgor] [Borrower], the purchasers named therein
("Noteholders") and __________________, as agent for such Noteholders ("Agent"),
and (ii) the Indenture dated as of August __, 1998 ("Indenture," and together 
with the Securities Purchase Agreement, collectively referred to herein as the 
"Securities Purchase Documents") between the [Pledgor] [Borrower] and the 
Trustee, pursuant to which, upon the terms and conditions stated therein, 
Noteholders agree to make loans to [Pledgor[ [Borrower].

         B.      The Noteholders have conditioned their respective obligations
under the Securities Purchase Documents upon the execution and delivery by
Pledgor of this Agreement, and Pledgor has agreed to enter into this Agreement.

         C.      Therefore, in order to comply with the terms and conditions of
the Securities Purchase Documents and for other good and valuable
consideration, the receipt and sufficiency of which are hereby acknowledged,
Pledgor hereby agrees with Secured Party as follows:

                                   ARTICLE 1

                               SECURITY INTEREST

         Section 1.01     Pledge.  Pledgor hereby pledges, assigns and grants
to Secured Party a security interest in and right of set-off against the assets
referred to in Section 1.02 (the "Collateral") to secure the prompt payment and
performance of the "Obligations" (as defined in Section 2.02) and the
performance by Pledgor of this Agreement.

         Section 1.02     Collateral.  The Collateral consists of the following
types or items of property which are owned by Pledgor.

                 (a)      The securities described or referred to in Exhibit A
         attached hereto and made a part hereof.

                 (b)      (i) the certificates or instruments, if any,
         representing such securities, (ii) all dividends (cash, stock or
         otherwise), cash, instruments, rights to subscribe,



                                     -1-
<PAGE>   101
         purchase or sell and all other rights and property from time to time
         received, receivable or otherwise distributed in respect of or in
         exchange for any or all of such securities, (iii) all replacements,
         additions to and substitutions for any of the property referred to in
         this Section 1.02, including, without limitation, claims against third
         parties, (iv) the proceeds, interest, profits and other income of or
         on any of the property referred to in this Section 1.02 and (v) all
         books and records relating to any of the property referred to in this
         Section 1.02.

It is expressly contemplated that additional securities or other property of
the type described in this Section 1.02 may from time to time be pledged,
assigned or granted to Secured Party as additional security for the
Obligations, and the term "Collateral" as used herein shall be deemed for all
purposes hereof to include all such additional securities and property,
together with all other property of the types described above related thereto.

         Section 1.03     Transfer of Collateral.  All certificates or
instruments representing or evidencing the Pledged Securities shall, subject
to, that certain Security Agreement dated January 26, 1998 from [Pledgor]
[Borrower] to the Senior Loan Agreement (the "Senior Security Agreement") and
the terms of the Subordination Agreement, be delivered to and held pursuant
hereto by Secured Party or a Person designated by Secured Party and shall be in
suitable form for transfer by delivery, or shall be accompanied by duly
executed instruments of transfer or assignment in blank, or (in the case of
either certificated or uncertificated securities) Secured Party shall, subject
to the Liens created under the Senior Security Agreement and to the terms of
the Subordination Agreement, have been provided with evidence that the Pledged
Securities have been otherwise transferred to Secured Party in accordance with
Section 8.301 of the Code, all in form and substance satisfactory to Secured
Party.  Notwithstanding the preceding sentence, and subject to the terms of the
Subordination Agreement, at Secured Party's discretion, all Pledged Securities
must be delivered or transferred in such manner as to permit Secured Party to
be a "protected purchaser" to the extent of its security interest as provided
in Section 8.303 of the Code.  Secured Party shall have the right, at any time
in its discretion and without notice to Pledgor but subject to the Liens
created under the Senior Security Agreement and to the terms of the
Subordination Agreement, to transfer to or to register in the name of Secured
Party or any of its nominees any or all of the Pledged Securities, subject only
to the revocable rights specified in Section 6.06.  In addition, Secured Party
shall have the right at any time to exchange certificates or instruments
representing or evidencing Pledged Securities for certificates or instruments
of smaller or larger denominations.

                                   ARTICLE 2

                                  DEFINITIONS

         Section 2.01     Terms Defined Above or in the Securities Purchase
Documents.  As used in this Agreement, the terms defined above shall have the
meanings respectively assigned to them.  Other capitalized terms which are
defined in the Securities Purchase





                                      -2-
<PAGE>   102
Documents but which are not defined herein shall have the same meanings as
defined in the Securities Purchase Documents.

         Section 2.02     Certain Definitions.  As used in this Agreement, the
following terms shall have the following meanings, unless the context otherwise
requires:

                 "Agreement" means this Security Agreement, as the same may
         from time to time be amended or supplemented.

                 "Code" means the Uniform Commercial Code as presently in
         effect in the State of Texas, Business and Commerce Code, Chapters 1
         through 9.  Unless otherwise indicated by the context herein, all
         uncapitalized terms which are defined in the Code shall have their
         respective meanings as used in Chapters 8 and 9 of the Code.

                 "Event of Default" means any event specified in Section 6.01.

                 "Obligations" means:

                          (a)     any and all indebtedness, obligations and
                 liabilities now or hereafter incurred by the Pledgor pursuant
                 to the Securities Purchase Documents, including without
                 limitation, the unpaid principal of and interest on the Notes;

                          (b)     payment of and performance of any and all
                 present or future obligations of Borrower according to the
                 terms of any Hedging Agreement now or hereafter arising
                 between the Pledgor and any Noteholder;

                          (c)     any additional "Obligations" (as defined in
                 the Securities Purchase Documents) owing to the Agent and the
                 Noteholders;

                          (d)     all renewals, rearrangements, increases,
                 extensions for any period, amendments or supplement in whole
                 or in part of the Notes or any documents evidencing the above;
                 and

                          (e)     all interest, charges, expenses, attorneys'
                 or other fees and any other sums payable to or incurred by
                 Agent and the Noteholders in connection with the execution,
                 administration or enforcement of Agent's or any of the
                 Noteholders' rights and remedies hereunder or any other
                 agreement with Pledgor.

                 "Obligor" means any Person, other than Pledgor, liable
         (whether directly or indirectly, primarily or secondarily) for the
         payment or performance of any of the Obligations whether as maker,
         co-maker, endorser, guarantor, accommodation party, general partner or
         otherwise.





                                      -3-
<PAGE>   103
                 "Pledged Securities" means all of the securities and other
         property (whether or not the same constitutes a "security" under the
         Code) referred to in Section 1.02 and all additional securities (as
         that term is defined in the Code), if any, constituting Collateral
         under this Agreement.

                                   ARTICLE 3

                         REPRESENTATIONS AND WARRANTIES

         In order to induce Secured Party, the Agent and the Noteholders to
accept this Agreement, Pledgor represents and warrants to Secured Party, the
Agent and the Noteholders (which representations and warranties will survive
the creation and payment of the Obligations) that:

         Section 3.01     Ownership of Collateral; Encumbrances.  Pledgor is
the legal and beneficial owner of the Collateral free and clear of any adverse
claim, lien, security interest, option or other charge or encumbrance except
for the security interest created by this Agreement and the security interest
granted to the Senior Loan Agent pursuant to the Senior Security Agreement, and
Pledgor has full right, power and authority to pledge, assign and grant a
security interest in the Collateral to Secured Party.

         Section 3.02     No Required Consent.  No authorization, consent,
approval or other action by, and no notice to or filing with, any governmental
authority or regulatory body (other than the filing of financing statements) is
required for (a) the due execution, delivery and performance by Pledgor of this
Agreement, (b) the grant by Pledgor of the security interest granted by this
Agreement, (c) the perfection of such security interest or (d) the exercise by
Secured Party of its rights and remedies under this Agreement.

         Section 3.03     Pledged Securities.  The Pledged Securities have been
duly authorized and validly issued, and are fully paid and non-assessable.

         Section 3.04     Security Interest.  The pledge of Pledged Securities
pursuant to this Agreement creates a valid and perfected second priority
security interest subordinate only to the first priority security interest of
the Senior Loan Agent, in the Collateral, enforceable against Borrower and all
third parties and securing payment of the Obligations.

         Section 3.05     Collateral.  All statements or other information
provided by Pledgor to Secured Party, Agent or any Noteholder describing or
with respect to the Collateral is or (in the case of subsequently furnished
information) will be when provided correct and complete in all material
respects.





                                      -4-
<PAGE>   104

                                   ARTICLE 4

                            COVENANTS AND AGREEMENTS

         Pledgor will at all times comply with the covenants and agreements
contained in this Article 4, from the date hereof and for so long as any part
of the Obligations are outstanding.

         Section 4.01     Sale, Disposition or Encumbrance of Collateral.
Except as permitted by the Indenture, Pledgor will not in any way encumber any
of the Collateral (or permit or suffer any of the Collateral to be encumbered)
or sell, pledge, assign, lend or otherwise dispose of or transfer any of the
Collateral to or in favor of any Person other than Secured Party or to the
Senior Loan Agent pursuant to the Senior Security Agreement and in accordance
with the terms of the Subordination Agreement.

         Section 4.02     Dividends or Distributions.  So long as no Event of
Default shall have occurred and be continuing:  Pledgor shall be entitled to
receive and retain any and all dividends and interest paid in respect of the
Collateral, provided, however, that any and all

                 (a)      dividends and interest paid or payable other than in
         cash in respect of, and instruments and other property received,
         receivable or otherwise distributed in respect of, or in exchange for
         (including, without limitation, any certificate or share purchased or
         exchanged in connection with a tender offer or merger agreement), any
         Collateral,

                 (b)      dividends and other distributions paid or payable in
         cash in respect of any Collateral in connection with a partial or
         total liquidation or dissolution or in connection with a reduction of
         capital, capital surplus or paid-in surplus, or reclassification, and

                 (c)      cash paid, payable or otherwise distributed in
         respect of principal of, or in redemption of, or in exchange for, any
         Collateral,

shall, subject to the Liens created under the Senior Security Agreement and to
the terms of the Subordination Agreement, be, and shall be forthwith delivered
to Secured Party to hold as, Collateral and shall, subject to the Liens created
under the Senior Security Agreement and to the terms of the Subordination
Agreement, if received by Pledgor, be received in trust for the benefit of
Secured Party, be segregated from the other property or funds of Pledgor, and
be forthwith delivered to Secured Party as Collateral in the same form as so
received (with any necessary indorsement).





                                      -5-
<PAGE>   105
         Section 4.03     Records and Information.  Pledgor shall keep accurate
and complete records of the Collateral (including proceeds, payments,
distributions, income and profits).  Pledgor will promptly provide written
notice to Secured Party of all information which in any way relates to or
affects the filing of any financing statement or other public notices or
recordings, or the delivery and possession of items of Collateral for the
purpose of perfecting a security interest in the Collateral.

         Section 4.04     Certain Liabilities.  Pledgor hereby assumes all
liability for the Collateral, the security interest created hereunder and any
use, possession, maintenance, management, enforcement or collection of any or
all of the Collateral.

         Section 4.05     Further Assurances.  Upon the request of Secured
Party, Pledgor shall (at Pledgor's expense) execute and deliver all such
assignments, certificates, instruments, securities, financing statements,
notifications to financial intermediaries, clearing corporations, issuers of
securities or other third parties or other documents and give further
assurances and do all other acts and things as Secured Party may reasonably
request to perfect Secured Party's interest in the Collateral or to protect,
enforce or otherwise effect Secured Party's rights and remedies hereunder.

         Section 4.06     Stock Powers.  Pledgor shall furnish to Secured Party
such stock powers and other instruments as may be required by Secured Party to
assure the transferability of the Collateral when and as often as may be
requested by Secured Party.

         Section 4.07     Rights to Sell.  If Secured Party shall determine to
exercise its rights to sell all or any of the Collateral pursuant to its rights
hereunder subject to the Senior Security Agreement and in accordance with the
terms of the Subordination Agreement, Pledgor agrees that, upon request of
Secured Party, Pledgor will, at its own expense:

                 (a)      execute and deliver, and use its best efforts to
         cause each issuer of the Collateral contemplated to be sold and the
         directors and officers thereof to execute and deliver, all such
         instruments and documents, and do or cause to be done all such other
         acts and things, as may be necessary or, in the opinion of Secured
         Party, advisable to register such Collateral under the provisions of
         the Securities Act of 1933, as from time to time amended (the
         "Securities Act"), if such registration is, in the opinion of Secured
         Party, necessary or advisable to effect a public distribution of the
         Collateral, and to cause the registration statement relating thereto
         to become effective and to remain effective for such period as
         prospectuses are required by law to be furnished, and to make all
         amendments and supplements thereto and to the related prospectus
         which, in the opinion of Secured Party, are necessary or advisable,
         all in conformity with the





                                      -6-
<PAGE>   106
         requirements of the Securities Act and the rules and regulations of
         the Securities and Exchange Commission applicable thereto;

                 (b)      use its best efforts to qualify the Collateral under
         the state securities or "Blue Sky" laws and to obtain all necessary
         governmental approvals for the sale of the Collateral, as requested by
         Secured Party;

                 (c)      use its best efforts to cause each such issuer to
         make available to its security holders, as soon as practicable, an
         earnings statement which will satisfy the provisions of Section 11(a)
         of the Securities Act; and

                 (d)      use its best efforts to do or cause to be done all
         such others acts and things as may be necessary to make such sale of
         the Collateral or any part thereof valid and binding and in compliance
         with applicable law.

Pledgor further acknowledges the impossibility of ascertaining the amount of
damages which would be suffered by Secured Party and the Noteholders by reason
of the failure by Pledgor to perform any of the covenants contained in this
Section 4.07 and consequently agrees that if Pledgor shall fail to perform any
of such covenants, it shall pay, as liquidated damages, and not as penalty, an
amount (in no event to exceed the amount of Obligations then outstanding) equal
to the value of the Collateral on the date the Secured Party shall demand
compliance with this Section 4.07.

         Section 4.08     Voting and Other Consensual Rights.  Except to the
extent otherwise provided in subsection 6.06(d), Pledgor shall be entitled to
exercise any and all voting and other consensual rights pertaining to the
Collateral or any part thereof for any purpose not inconsistent with the terms
of this Agreement; provided however, that Pledgor shall not exercise or refrain
from exercising any such right if such action would have a material adverse
effect on the value of the Collateral or any part thereof, and, provided,
further, that upon request of Secured Party at any time or from time to time,
Pledgor shall give Secured Party prompt written notice of the manner in which
Pledgor has exercised, or the reasons for refraining from exercising, any such
right.

                                   ARTICLE 5

                   RIGHTS, DUTIES AND POWERS OF SECURED PARTY

         The following rights, duties and powers of Secured Party are
applicable irrespective of whether an Event of Default occurs and is
continuing:

         Section 5.01     Discharge Encumbrances.  Secured Party may, at its
option, discharge any taxes, liens, security interests or other encumbrances at
any time levied or





                                      -7-
<PAGE>   107
placed on the Collateral.  Pledgor agrees to reimburse Secured Party upon
demand for any payment so made, plus interest thereon from the date of Secured
Party's demand at the Post-Default Rate.

         Section 5.02     Transfer of Collateral.  Secured Party may transfer
any or all of the Obligations, and upon any such transfer Secured Party may
transfer its interest in any or all of the Collateral and shall be fully
discharged thereafter from all liability therefor.  Any transferee of the
Collateral shall be vested with all rights, powers and remedies of Secured
Party hereunder.

         Section 5.03     Cumulative and Other Rights.  The rights, powers and
remedies of Secured Party hereunder are, subject to the Liens under the Senior
Security Agreement and the terms of the Subordination Agreement, in addition to
all rights, powers and remedies given by law or in equity.  The exercise by
Secured Party of any one or more of the rights, powers and remedies herein
shall not be construed as a waiver of any other rights, powers and remedies,
including, without limitation, any other rights of set-off.  If any of the
Obligations are given in renewal, extension for any period or rearrangement, or
applied toward the payment of debt secured by any lien, Secured Party shall be,
and is hereby, subrogated (to the maximum extent permitted by law) to all the
rights, titles, interests and liens securing the debt so renewed, extended,
rearranged or paid.

         Section 5.04     Disclaimer of Certain Duties.  The powers conferred
upon Secured Party by this Agreement are to protect its interest in the
Collateral and shall not impose any duty upon Secured Party, Agent or any
Noteholder to exercise any such powers.  Pledgor hereby agrees that Secured
Party shall not be liable for, nor shall the indebtedness evidenced by the
Obligations be diminished by, Secured Party's delay or failure to collect upon,
foreclose, sell, take possession of or otherwise obtain value for the
Collateral.

         Section 5.05     Custody and Preservation of the Collateral.  Secured
Party shall be deemed to have exercised reasonable care in the custody and
preservation of the Collateral in its possession if the Collateral is accorded
treatment substantially equal to that which comparable secured parties accord
comparable collateral, it being understood and agreed, however, that neither
Secured Party, Agent nor any Noteholder shall have responsibility for (a)
ascertaining or taking action with respect to calls, conversions, exchanges,
maturities, tenders or other matters relative to any Collateral, whether or not
Secured Party has or is deemed to have knowledge of such matters, or (b) taking
any necessary steps to preserve rights against Persons or entities with respect
to any Collateral.





                                      -8-
<PAGE>   108
                                   ARTICLE 6

                               EVENTS OF DEFAULT

         Section 6.01     Events.  It shall constitute an Event of Default
under this Agreement if an Event of Default occurs and is continuing under the
Securities Purchase Documents.

         Section 6.02     Remedies.  Upon the occurrence and during the
continuance of any Event of Default, Secured Party may, subject to the Liens
created under the Senior Security Agreement and to the terms of the
Subordination Agreement, take any or all of the following actions without
notice (except where expressly required below or in the Securities Purchase
Documents) or demand to Pledgor:

                 (a)      Declare all or part of the indebtedness pursuant to
         the Obligations immediately due and payable as provided in the
         Securities Purchase Documents and enforce payment of the same by
         Pledgor or any Obligor.

                 (b)      Sell, in one or more sales and in one or more
         parcels, or otherwise dispose of any or all of the Collateral in any
         commercially reasonable manner as Secured Party may elect, in a public
         or private transaction, at any location as deemed reasonable by
         Secured Party either for cash or credit or for future delivery at such
         price as Secured Party may deem fair, and (unless prohibited by the
         Code, as adopted in any applicable jurisdiction) Secured Party, Agent
         or any Noteholder may be the purchaser of any or all Collateral so
         sold and may apply upon the purchase price therefor any Obligations
         secured hereby.  Any such sale or transfer by Secured Party either to
         itself or to any other Person shall be absolutely free from any claim
         of right by Pledgor, including any equity or right of redemption, stay
         or appraisal which Pledgor has or may have under any rule of law,
         regulation or statute now existing or hereafter adopted.  Upon any
         such sale or transfer, Secured Party shall have the right to deliver,
         assign and transfer to the purchaser or transferee thereof the
         Collateral so sold or transferred.  If Secured Party deems it
         advisable to do so, it may restrict the bidders or purchasers of any
         such sale or transfer to Persons or entities who will represent and
         agree that they are purchasing the Collateral for their own account
         and not with the view to the distribution or resale of any of the
         Collateral.  Secured Party may, at its discretion, provide for a
         public sale, and any such public sale shall be held at such time or
         times within ordinary business hours and at such place or places as
         Secured Party may fix in the notice of such sale.  Secured Party shall
         not be obligated to make any sale pursuant to any such notice.
         Secured Party may, without notice or publication, adjourn any public
         or private sale by announcement at any time and place fixed for such
         sale, and such sale may be made at any time or place to which the same
         may be so adjourned.  In the event any sale or transfer hereunder is
         not completed or is defective in the opinion of Secured Party, such





                                      -9-
<PAGE>   109
         sale or transfer shall not exhaust the rights of Secured Party
         hereunder, and Secured Party shall have the right to cause one or more
         subsequent sales or transfers to be made hereunder.  If only part of
         the Collateral is sold or transferred such that the Obligations remain
         outstanding (in whole or in part), Secured Party's rights and remedies
         hereunder shall not be exhausted, waived or modified, and Secured
         Party is specifically empowered to make one or more successive sales
         or transfers until all the Collateral shall be sold or transferred and
         all the Obligations are paid.  In the event that Secured Party elects
         not to sell the Collateral, Secured Party retains its rights to
         dispose of or utilize the Collateral or any part or parts thereof in
         any manner authorized or permitted by law or in equity, and to apply
         the proceeds of the same towards payment of the Obligations.

                 (c)      Apply proceeds of the disposition of the Collateral
         to the Obligations in any manner elected by Secured Party and
         permitted by the Code or otherwise permitted by law or in equity.
         Such application may include, without limitation, the reasonable
         attorneys' fees and legal expenses incurred by Secured Party and the
         Noteholders.

                 (d)      Appoint any Person as agent to perform any act or
         acts necessary or incident to any sale or transfer by Secured Party of
         the Collateral.

                 (e)      Receive, change the address for delivery, open and
         dispose of mail addressed to Pledgor, and to execute, assign and
         endorse negotiable and other instruments for the payment of money,
         documents of title or other evidences of payment, shipment or storage
         for any form of Collateral on behalf of and in the name of Pledgor.

                 (f)      Exercise all other rights and remedies permitted by 
         law or in equity.

         Section 6.03     Attorney-in-Fact.  Pledgor hereby irrevocably
appoints Secured Party as Pledgor's attorney-in- fact, with full authority in
the place and stead of Pledgor and in the name of Pledgor or otherwise, from
time to time in Secured Party's discretion upon the occurrence and during the
continuance of an Event of Default and subject to the terms of the
Subordination Agreement, but at Pledgor's cost and expense and without notice
to Pledgor, to take any action and to execute any assignment, certificate,
financing statement, stock power, notification, document or instrument which
Secured Party may deem necessary or advisable to accomplish the purposes of
this Agreement, including, without limitation, to receive, endorse and collect
all instruments made payable to Pledgor representing any dividend, interest
payment or other distribution in respect of the Collateral or any part thereof
and to give full discharge for the same.





                                      -10-
<PAGE>   110
         Section 6.04     Liability for Deficiency.  If any sale or other
disposition of Collateral by Secured Party in compliance with the Loan
Documents and applicable law or any other action of Secured Party or any
Noteholder hereunder in compliance with the Loan Documents and applicable law
results in reduction of the Obligations, such action will not release Pledgor
from its liability to Secured Party and the Noteholders for any unpaid
Obligations, including costs, charges and expenses incurred in the liquidation
of Collateral, together with interest thereon, and the same shall be
immediately due and payable to Secured Party at Secured Party's address set
forth in the opening paragraph hereof.

         Section 6.05     Reasonable Notice.  If any applicable provision of
any law requires Secured Party or any Noteholder to give reasonable notice of
any sale or disposition or other action, Pledgor hereby agrees that ten days'
prior written notice shall constitute reasonable notice thereof.  Such notice,
in the case of public sale, shall state the time and place fixed for such sale
and, in the case of private sale, the time after which such sale is to be made.

         Section 6.06     Pledged Securities.  Upon the occurrence and during
the continuance of an Event of Default and subject to the Liens created under
the Senior Security Agreement and to the terms of the Subordination Agreement:

                 (a)      All rights of Pledgor to receive the dividends and
         interest payments which it would otherwise be authorized to receive
         and retain pursuant to Section 4.02 shall cease, and all such rights
         shall thereupon become vested in Secured Party who shall thereupon
         have the sole right to receive and hold as Collateral such dividends
         and interest payments, but Secured Party shall have no duty to receive
         and hold such dividends and interest payments and shall not be
         responsible for any failure to do so or delay in so doing.

                 (b)      All dividends and interest payments which are
         received by Pledgor contrary to the provisions of this Section 6.06
         shall be received in trust for the benefit of Secured Party, shall be
         segregated from other funds of Pledgor and shall be forthwith paid
         over to Secured Party as Collateral in the same form as so received
         (with any necessary indorsement).

                 (c)      Secured Party may exercise any and all rights of
         conversion, exchange, subscription or any other rights, privileges or
         options pertaining to any of the Pledged Securities as if it were the
         absolute owner thereof, including without limitation, the right to
         exchange at its discretion, any and all of the Pledged Securities upon
         the merger, consolidation, reorganization, recapitalization or other
         readjustment of any issuer of such Pledged Securities or upon the
         exercise by any such issuer or Secured Party of any right, privilege
         or option pertaining to any of the Pledged Securities, and in
         connection therewith, to deposit and deliver any and all of the
         Pledged Securities with any committee, depository, transfer agent,
         registrar or other designated agency upon such terms and conditions as
         it may determine, all without liability except to account for property
         actually received by it, but Secured Party shall





                                      -11-
<PAGE>   111
         have no duty to exercise any of the aforesaid rights, privileges or
         options and shall not be responsible for any failure to do so or delay
         in so doing.

                 (d)      If the issuer of any Pledged Securities is the
         subject of bankruptcy, insolvency, receivership, custodianship or
         other proceedings under the supervision of any court or governmental
         agency or instrumentality, then all rights of Pledgor to exercise the
         voting and other consensual rights which Pledgor would otherwise be
         entitled to exercise pursuant to Section 4.08 with respect to the
         Pledged Securities issued by such issuer shall cease, and all such
         rights shall thereupon become vested in Secured Party who shall
         thereupon have the sole right to exercise such voting and other
         consensual rights, but Secured Party shall have no duty to exercise
         any such voting or other consensual rights and shall not be
         responsible for any failure to do so or delay in so doing.

         Section 6.07     Non-judicial Enforcement.  To the extent permitted by
law, Secured Party may enforce its rights hereunder without prior judicial
process or judicial hearing, and to the extent permitted by law Pledgor
expressly waives any and all legal rights which might otherwise require Secured
Party to enforce its rights by judicial process.

                                   ARTICLE 7

                            MISCELLANEOUS PROVISIONS

         Section 7.01     Notices.  Any notice required or permitted to be
given under or in connection with this Agreement shall be given in accordance
with the notice provisions of the Securities Purchase Documents.

         Section 7.02     Amendments and Waivers.  Secured Party's acceptance
of partial or delinquent payments or any forbearance, failure or delay by
Secured Party in exercising any right, power or remedy hereunder shall not be
deemed a waiver of any obligation of Pledgor or any Obligor, or of any right,
power or remedy of Secured Party; and no partial exercise of any right, power
or remedy shall preclude any other or further exercise thereof.  Secured Party
may remedy any Event of Default hereunder or in connection with the Obligations
without waiving the Event of Default so remedied.  Pledgor hereby agrees that
if Secured Party agrees to a waiver of any provision hereunder, or an exchange
of or release of the Collateral, or the addition or release of any Obligor or
other Person, any such action shall not constitute a waiver of any of Secured
Party's other rights or of Pledgor's obligations hereunder.  This Agreement may
be amended only by an instrument in writing executed jointly by Pledgor and
Secured Party and may be supplemented only by documents delivered or to be
delivered in accordance with the express terms hereof.

         Section 7.03     Copy as Financing Statement.  A photocopy or other
reproduction of this Agreement may be delivered by Pledgor or Secured Party to
any financial intermediary





                                      -12-
<PAGE>   112
or other third party for the purpose of transferring or perfecting any or all
of the Pledged Securities to Secured Party or its designee or assignee.

         Section 7.04     Possession of Collateral.  Secured Party shall be
deemed to have possession of any Collateral in transit to it or set apart for
it (or, in either case, any of its agents, affiliates or correspondents).

         Section 7.05     Redelivery of Collateral.  If any sale or transfer of
Collateral by Secured Party results in full satisfaction of the Obligations,
and after such sale or transfer and discharge there remains a surplus of
proceeds, Secured Party will deliver to Pledgor such excess proceeds in a
commercially reasonable time; provided, however, that neither Secured Party nor
any Noteholder shall have any liability for any interest, cost or expense in
connection with any delay in delivering such proceeds to Pledgor.

         Section 7.06     Governing Law; Jurisdiction.  This Agreement and the
security interest granted hereby shall be construed in accordance with and
governed by the laws of the State of Texas (except to the extent that the laws
of any other jurisdiction govern the perfection and priority of the security
interests granted hereby).

         Section 7.07     Continuing Security Agreement.

         (a)     Except as may be expressly applicable pursuant to Section
9.505 of the Code, no action taken or omission to act by Secured Party or the
Noteholders hereunder, including, without limitation, any exercise of voting or
consensual rights pursuant to Section 4.08 or any other action taken or
inaction pursuant to Section 6.02, shall be deemed to constitute a retention of
the Collateral in satisfaction of the Obligations or otherwise to be in full
satisfaction of the Obligations, and the Obligations shall remain in full force
and effect, until Secured Party and the Noteholders shall have applied payments
(including, without limitation, collections from Collateral) towards the
Obligations in the full amount then outstanding or until such subsequent time
as is hereinafter provided in subsection (b) below.

         (b)     To the extent that any payments on the Obligations or proceeds
of the Collateral are subsequently invalidated, declared to be fraudulent or
preferential, set aside or required to be repaid to a trustee, debtor in
possession, receiver or other Person under any bankruptcy law, common law or
equitable cause, then to such extent the Obligations so satisfied shall be
revived and continue as if such payment or proceeds had not been received by
Secured Party or the Noteholders, and Secured Party's and the Noteholders'
security interests, rights, powers and remedies hereunder shall continue in
full force and effect.  In such event, this Agreement shall be automatically
reinstated if it shall theretofore have been terminated pursuant to Section
7.08.

         Section 7.08     Termination.  The grant of a security interest
hereunder and all of Secured Party's and the Noteholders' rights, powers and
remedies in connection therewith shall remain in full force and effect until
Secured Party has (a) retransferred and delivered





                                      -13-
<PAGE>   113
all Collateral in its possession to Pledgor, and (b) executed a written release
or termination statement and reassigned to Pledgor without recourse or warranty
any remaining Collateral and all rights conveyed hereby.  Upon the complete
payment of the Obligations and the compliance by Pledgor with all covenants and
agreements hereof, Secured Party, at the written request and expense of
Pledgor, will release, reassign and transfer the Collateral to Pledgor and
declare this Agreement to be of no further force or effect.  Notwithstanding
the foregoing, the reimbursement and indemnification provisions of Section 4.04
and the provisions of subsection 7.07(b) shall survive the termination of this
Agreement.

         Section 7.08     Subordination Agreement.  The rights and remedies of
the Agent and the Noteholders under this Agreement are subject to the terms and
conditions of that certain Subordination Agreement dated as of August __, 1998,
made by Secured Party, the Agent, the Noteholders and the Bank of Montreal.

         Section 7.09     Counterparts, Effectiveness.  This Agreement may be
executed in two or more counterparts.  Each counterpart is deemed an original,
but all such counterparts taken together constitute one and the same
instrument.  This Agreement becomes effective upon the execution hereof by
Pledgor and delivery of the same to Secured Party, Agent or the Noteholders,
and it is not necessary for Secured Party, Agent or any Noteholder to execute
any acceptance hereof or otherwise signify or express its acceptance hereof.

PLEDGOR:
                                    ----------------------------------



                                    By:
                                       -------------------------------
                                    Name: 
                                         -----------------------------
                                    Title:
                                          ----------------------------





                                      -14-
<PAGE>   114
                              FINANCING STATEMENT


         This Financing Statement is presented to a filing officer for filing
pursuant to the Uniform Commercial Code.

1.       The name and address of the Debtor is:

         [DEBTOR'S NAME]
         6300 Bridge Point Parkway
         Building 2, Suite 500
         Austin, Texas 78730

2.       The name and address of the Secured Party is:

         -----------------------

         -----------------------

         -----------------------
         Federal Tax I.D. 
                          ------
3.       This Financing Statement covers the following Collateral:

                 (a) The securities described or referred to in Exhibit A
         attached hereto and made a part hereof.

                 (b) (i) the certificates or instruments, if any, representing
         such securities, (ii) all dividends (cash, stock or otherwise), cash,
         instruments, rights to subscribe, purchase or sell and all other
         rights and property from time to time received, receivable or
         otherwise distributed in respect of or in exchange for any or all of
         such securities, (iii) all replacements, additions to and
         substitutions for any of the property referred to in this paragraph 3,
         including, without limitation, claims against third parties, (iv) the
         proceeds, interest, profits and other income of or on any of the
         property referred to in this paragraph 3 and (v) all books and records
         relating to any of the property referred to in this paragraph 3.

PLEDGOR  :                          
                                    ----------------------------------


                                    By:
                                       -------------------------------
                                    Name: 
                                         -----------------------------
                                    Title:
                                          ----------------------------






                                      -15-
<PAGE>   115
                                   EXHIBIT A

                               PLEDGED SECURITIES


         ______ shares of capital stock of _______________evidenced by
Certificate No. ___, such shares representing _______ of the capital stock of
_______________





                                      -16-
<PAGE>   116



                                   EXHIBIT  E


                               SECURITY AGREEMENT

           (Accounts, Inventory, Equipment, Chattel Paper, Documents,
              Instruments, General Intangibles and Other Property)



                                    Between

                            BRIGHAM OIL & GAS, L.P.

                                      and

                                _______________,
                                   as Trustee



                                August __, 1998
<PAGE>   117
                               SECURITY AGREEMENT

           Accounts, Inventory, Equipment, Chattel Paper, Documents,
              Instruments, General Intangibles and Other Property

         THIS SECURITY AGREEMENT (this "Agreement") is made as of August __,
1998, between BRIGHAM OIL & GAS L.P., a Delaware limited partnership with
principal offices at 6300 Bridge Point Parkway, Bldg. 2, Suite 500, Austin,
Texas 78730 ("Debtor"); and _________ having an address at __________ ("Secured
Party") as trustee and as collateral agent for the ratable benefit of Agent and
the Noteholders (each as defined in the Securities Purchase Documents described
below).

                                    RECITALS

         A.      Brigham Exploration Company, a Delaware corporation
("Borrower")  is executing (i) the Securities Purchase Agreement dated as of
August __, 1998 (such agreement, as may from time to time be amended or
supplemented, being hereinafter called the "Securities Purchase Agreement")
among the Borrower, the purchasers named therein ("Noteholders") and _________ 
___________________________________________________________, as agent for such
Noteholders ("Agent"), and (ii) the Indenture dated as of August __, 1998
("Indenture," and together with the Securities Purchase Agreement, collectively
referred to herein as the "Securities Purchase Documents") between the Borrower
and the Trustee, pursuant to which, upon the terms and conditions stated
therein, the Noteholders agree to make loans to the Debtor.

         B.      The Noteholders have conditioned their respective obligations
under the Securities Purchase Documents upon (1) the execution and delivery by
Debtor of the Guaranty Agreement dated as of August __, 1998 ("Guaranty
Agreement") made by the Debtor for the benefit of the Agent and the Noteholders
and providing for the guarantee by the Debtor of the Borrower's obligations
under the Securities Purchase Documents, and (2) the execution and delivery by
Debtor of this Agreement in order to secured its guaranty obligations, and
Debtor has agreed to enter into this Agreement.

         C.      Therefore, in order to comply with the terms and conditions of
the Securities Purchase Documents and for other good and valuable
consideration, the receipt and sufficiency of which are hereby acknowledged,
Debtor hereby agrees with Secured Party as follows:





                                      -1-
<PAGE>   118
                                   ARTICLE 1

                               SECURITY INTEREST

         Section 1.01     Grant of Security Interest.  Debtor hereby assigns
and grants to Secured Party a security interest in and right of set-off against
the assets referred to in Section 1.02 (the "Collateral") to secure the prompt
payment and performance of the "Obligations" (as defined in Section 2.02) and
the performance by Debtor of this Agreement.

         Section 1.02     Collateral.  The Collateral consists of the following
types or items of property which are owned by Debtor (including property
hereafter acquired by Debtor as well as property which Debtor now owns or in
which Debtor has rights):

                 (a)      All of Debtor's accounts, inventory, equipment,
         chattel paper, documents, instruments and general intangibles.

                 (b)      (i) Any related or additional property from time to
         time delivered to or deposited with Secured Party by or for the
         account of Debtor; (ii) all certificates of title or other documents
         evidencing ownership or possession of or otherwise relating to any
         property referred to in this Section 1.02; (iii) all property used or
         usable in connection with any property referred to in this Section
         1.02; (iv) all policies of insurance (whether or not required by
         Secured Party) covering any property referred to in this Section 1.02;
         (v) all goods which were at any time included in the Collateral and
         which are returned to or for the account of Debtor following their
         sale, lease or other disposition; (vi) all proceeds, products,
         replacements, additions to, substitutions for, accessions of, and
         property necessary for the operation of any of the property referred
         to in this Section 1.02, including, without limitation, insurance
         payable as a result of loss or damage to any of the property referred
         to in this Section 1.02, refunds of unearned premiums of any such
         insurance policy and claims against third parties; and (vii) all books
         and records related to any of the property referred to in this Section
         1.02, including, without limitation, any and all books of account,
         customer lists and other records relating in any way to the accounts,
         chattel paper, instruments or inventory referred to in this Section
         1.02.

                 (c)      All general intangibles related to any property
         referred to in this Section 1.02, including, without limitation, all
         (i) letters of credit, bonds, guaranties, purchase or sales agreements
         and other contractual rights, rights to performance, and claims for
         damages, refunds (including tax refunds) or other monies due or to
         become due; (ii) orders, franchises, permits, certificates, licenses,
         consents, exemptions, variances, authorizations or other approvals by
         any governmental agency or court; (iii) consulting, engineering and
         technological information and specifications, design data, patent
         rights, trade secrets, literary rights, copyrights, trademarks,
         labels, trade names and other intellectual property;





                                      -2-
<PAGE>   119
         (iv) business records, computer tapes and computer software; (v)
         goodwill; and (vi) other intangible personal property, whether similar
         or dissimilar to the property referred to in this Section 1.02.

It is expressly contemplated that additional property may from time to time be
pledged, assigned or granted to Secured Party as additional security for the
Obligations, and the term "Collateral" as used herein shall be deemed for all
purposes hereof to include all such additional property, together with all
other property of the types described above related thereto.  The term
"Collateral" does not, however, include any geological or geophysical data or
other property to the extent that the assignment thereof or granting of a
security interest therein would violate any contracts or other restrictions
applicable thereto.

                                   ARTICLE 2

                                  DEFINITIONS

         Section 2.01     Terms Defined Above or in the Securities Purchase
Documents.  As used in this Agreement, the terms defined above shall have the
meanings respectively assigned to them.  Other capitalized terms which are
defined in the Securities Purchase Documents but which are not defined herein
shall have the same meanings as defined in the Securities Purchase Documents.

         Section 2.02     Certain Definitions.  As used in this Agreement, the
following terms shall have the following meanings, unless the context otherwise
requires:

                 "Accounts" means all accounts, chattel paper and instruments
         (as such terms are defined in the Code) at any time included in the
         Collateral.

                 "Account Debtor" means any Person liable (whether directly or
         indirectly, primarily or secondarily) for the payment or performance
         of any obligations included in the Collateral, whether as an account
         debtor (as defined in the Code), obligor on an instrument, issuer of
         documents or securities, guarantor or otherwise.

                 "Agreement" means this Security Agreement, as the same may
         from time to time be amended or supplemented.

                 "Code" means the Uniform Commercial Code as presently in
         effect in the State of Texas, Business and Commerce Code, Chapters 1
         through 9.  Unless otherwise indicated by the context herein, all
         uncapitalized terms which are defined in the Code shall have their
         respective meanings as used in Chapter 9 of the Code.





                                      -3-
<PAGE>   120
                 "Disclosure - Restricted Collateral" means any Collateral in
         which Debtor is permitted to grant a security interest but which
         Debtor is not permitted, under confidentiality agreements or
         restrictions from time to time in effect, to disclosure to Secured
         Party or Noteholders.

                 "Event of Default" means any event specified in Section 6.01.

                 "Inventory" means all inventory (as defined in the Code) at
         any time included in the Collateral.

                 "Obligations" means:

                 (a)      any and all indebtedness, obligations and liabilities
         now or hereafter incurred by the Debtor pursuant to the Guaranty
         Agreement;

                 (b)      payment of and performance of any and all present or
         future obligations of Debtor according to the terms of any Hedging
         Agreement now or hereafter arising between the Debtor and any
         Noteholder;

                 (c)      any additional "Obligations", (as defined in the
         Securities Purchase Documents) owing to the Agent and the Noteholders;

                 (d)      all renewals, rearrangements, increases, extensions
         for any period, amendments or supplement in whole or in part of the
         Notes or any documents evidencing the above; and

                 (e)      all interest, charges, expenses, attorneys' or other
         fees and any other sums payable to or incurred by the Agent and the
         Noteholders in connection with the execution, administration or
         enforcement of Secured Party's or any of the Noteholders' rights and
         remedies hereunder or any other agreement with Debtor.

                 "Obligor" means any Person, other than Debtor, liable (whether
         directly or indirectly, primarily or secondarily) for the payment or
         performance of any of the Obligations whether as maker, co-maker,
         endorser, guarantor, accommodation party, general partner or
         otherwise.





                                      -4-
<PAGE>   121
                                   ARTICLE 3

                         REPRESENTATIONS AND WARRANTIES

         In order to induce Secured Party to accept this Agreement, Debtor
represents and warrants to Secured Party (which representations and warranties
will survive the creation and payment of the Obligations) that:

         Section 3.01     Ownership of Collateral; Encumbrances.  Debtor is the
legal and beneficial owner of the Collateral free and clear of any adverse
claim, lien, security interest, option or other charge or encumbrance except
for the matters permitted under or otherwise disclosed in the Securities
Purchase Documents and the security interest created by this Agreement, and
Debtor has full right, power and authority to assign and grant a security
interest in the Collateral to Secured Party.

         Section 3.02     No Required Consent.  Except for any consents or
waivers required in connection with Disclosure-Restricted Collateral, no
authorization, consent, approval or other action by, and no notice to or filing
with, any governmental authority or regulatory body (other than the filing of
financing statements) is required for (a) the due execution, delivery and
performance by Debtor of this Agreement, (b) the grant by Debtor of the
security interest granted by this Agreement, (c) the perfection of such
security interest or (d) the exercise by Secured Party of its rights and
remedies under this Agreement.

         Section 3.03     Priority Security Interest.  Subject only to the
matters permitted under or otherwise disclosed in the Securities Purchase
Documents and to the terms of the Subordination Agreement, the grant of the
security interest in the Collateral pursuant to this Agreement creates a valid
and perfected priority security interest in the Collateral, enforceable against
Debtor and all third parties and securing payment of the Obligations, and
second only to the security interest granted to Senior Loan Agent, including
without limitation pursuant to that certain Security Agreement dated January
26, 1998 from Pledgor to the Senior Loan Agent (the "Senior Security
Agreement").

         Section 3.04     No Filings By Third Parties.  No unexpired financing
statement or other public notice or recording covering the Collateral is on
file in any public office (other than any financing statement or other public
notice or recording naming Secured Party or the Senior Loan Agent as the
secured party therein), and Debtor will not execute any such financing
statement or other public notice or recording so long as any of the Obligations
are outstanding.

         Section 3.05     No Name Changes.  Debtor has not, during the
preceding five years, entered into any contract, agreement, security instrument
or other document using a name other than, or been known by or otherwise used
any name other than, the name used by Debtor herein.





                                      -5-
<PAGE>   122
         Section 3.06     Location of Debtor and Collateral.  Debtor's chief
executive office and Debtor's records concerning the Collateral are located at
the address or location set forth in the opening paragraph hereof.  As of the
date hereof, the Collateral is located at Debtor's address set forth in the
opening paragraph hereof or in the states set forth on Schedule 3.06 attached
hereto.

         Section 3.07     Collateral.  All statements or other information
provided by Debtor to Secured Party or any Noteholder describing or with
respect to the Collateral is or (in the case of subsequently furnished
information) will be when provided correct and complete in all material
respects.

         Section 3.08     Delivery of Documents or Letters of Credit.  With
respect to any Inventory or other Collateral covered by one or more
certificates of title or other documents evidencing ownership or possession
thereof, and with respect to any Accounts or other Collateral supported by
letters of credit, each of such certificates, documents or letters of credit
has, if requested by Secured Party, been delivered to the Secured Party, except
that such documents or instruments may, if there are outstanding amounts owing
under the Senior Loan Agreement, be delivered to the Senior Loan Agent who
shall maintain first priority status of such security interest according to the
terms of the Senior Loan Agreement (provided that all certificates, documents
and letters of credit referred to in Section 1.02 shall be subject to the
security interest created by this Agreement irrespective of whether or not such
delivery shall have been made).

                                   ARTICLE 4

                            COVENANTS AND AGREEMENTS

         Debtor will at all times comply with the covenants and agreements
contained in this Article 4, from the date hereof and for so long as any part
of the Obligations are outstanding.

         Section 4.01     Change in Location of Collateral or Debtor.  Debtor
will notify Secured Party on or before the date of any change in location of
the Collateral to a place outside the states listed on Schedule 3.06.  Debtor
will give Secured Party 30 days' prior written notice of (a) the opening or
closing of any place of Debtor's business or (b) any change in the location of
Debtor's chief executive office or address.

         Section 4.02     Change in Debtor's Name or Corporate Structure.
Debtor will not change its name, identity or corporate structure (including,
without limitation, any merger, consolidation or sale of substantially all of
its assets) without notifying Secured Party of such change in writing at least
30 days prior to the effective date of such change.  Without the express
written consent of Secured Party, however, Debtor will not engage in any other
business or transaction with respect to the Collateral herein under any name
other than Debtor's name hereunder or "Brigham Exploration Company" unless the
Debtor has notified the Secured Party of such other name and executed or





                                      -6-
<PAGE>   123
caused to be executed financing statements or other documentation required by
the Secured Party to continue the perfection of the Security Interest herein.

         Section 4.03     Documents; Collateral in Possession of Third Parties.
If certificates of title or other documents evidencing ownership or possession
of the Collateral are issued or outstanding, Debtor will, upon Secured Party's
request, cause the interest of Secured Party to be properly noted thereon and
will, forthwith upon receipt and subject to the Liens under the Senior Security
Agreement and to the terms of the Subordination Agreement, deliver same to
Secured Party.  If any Collateral is at any time in the possession or control
of any warehouseman, bailee, agent or independent contractor, Debtor shall,
upon Secured Party's request, notify such Person of Secured Party's security
interest in such Collateral.  Upon Secured Party's request, Debtor shall
instruct any such Person to hold all such Collateral for Secured Party's
account subject to Debtor's instructions and the terms of the Subordination
Agreement, or, if an Event of Default shall have occurred, subject to Secured
Party's instructions and the Liens under the Senior Security Agreement and to
the terms of the Subordination Agreement.

         Section 4.04     Delivery of Letters of Credit and Instruments.
Debtor will, upon Secured Party's request and subject to the Liens under the
Senior Security Agreement and to the terms of the Subordination Agreement,
deliver each letter of credit, if any, included in the Collateral to Secured
Party, in each case forthwith upon receipt by or for the account of Debtor.  If
any Account becomes evidenced by a promissory note, trade acceptance or any
other instrument for the payment of money (other than checks or drafts in
payment of Accounts collected by Debtor in the ordinary course of business
prior to notification by Secured Party under Section 6.02(h)), Debtor will,
upon Secured Party's request and subject to the Liens under the Senior Security
Agreement and to the terms of the Subordination Agreement, immediately deliver
such instrument to Secured Party appropriately endorsed and, regardless of the
form of presentment, demand, notice of dishonor, protest and notice of protest
with respect thereto, Debtor will remain liable thereon until such instrument
is paid in full.

         Section 4.05     Encumbrance of Collateral.  Except as permitted by
Section 4.10 or as permitted by the Securities Purchase Documents with Secured
Party's prior written consent, Debtor will not in any way encumber any of the
Collateral (or permit or suffer any of the Collateral to be encumbered) to or
in favor of any Person other than Secured Party.

         Section 4.06     Proceeds of Collateral.  Upon Secured Party's request
during the continuance of a Default, Debtor will, subject to the Liens under
the Senior Security Agreement and to the terms of the Subordination Agreement,
deliver to Secured Party promptly upon receipt all proceeds delivered to Debtor
from the sale or disposition of any Collateral.  If chattel paper, documents or
instruments are received as proceeds, which are required to be delivered to
Secured Party, they will be, subject to the Liens under the Senior Security
Agreement and to the terms of the Subordination Agreement, immediately, in such
circumstances, properly endorsed or assigned and delivered to Secured Party as
Collateral.  This Section 4.06 shall not be construed to permit sales or
dispositions





                                      -7-
<PAGE>   124
of Collateral except as may be elsewhere expressly permitted by this Agreement
or the Securities Purchase Documents.

         Section 4.07     Records and Information.  Debtor shall keep accurate
and complete records of the Collateral (including proceeds).  These records
shall reflect complete and accurate records of the Inventory and all facts
concerning each Account.

         Section 4.08     Certain Liabilities.  Debtor hereby assumes all
liability for the Collateral, the security interests created hereunder and any
use, possession, maintenance, management, enforcement or collection of any or
all of the Collateral.

         Section 4.09     Further Assurances.  Upon the request of Secured
Party, Debtor shall (at Debtor's expense) execute and deliver all such
assignments, certificates, financing statements or other documents and give
further assurances and do all other acts and things as Secured Party may
reasonably request to perfect Secured Party's interest in the Collateral or to
protect, enforce or otherwise effect Secured Party's rights and remedies
hereunder.

         Section 4.10     Accounts.

         (a)     Prior to notification by Secured Party under Section 6.02(h),
Debtor will collect the Accounts in the ordinary course of its business and may
retain the proceeds of such collections (subject to Section 4.04).

         (b)     Debtor will duly perform or cause to be performed all of
Debtor's obligations with respect to the Accounts and the underlying sales of
goods or other transactions giving rise to the Accounts.

         Section 4.11     Collateral Attached to Other Property.  In the event
that the Collateral is to be attached or affixed to any real property, Debtor
hereby agrees that this Agreement may be filed for record in any appropriate
real estate records as a financing statement which is a fixture filing.  In
connection therewith, Debtor will take whatever action is required by Section
4.09.  If Debtor is not the record owner of such real property, Debtor will
provide Secured Party with any additional security agreements or financing
statements necessary for the perfection of Secured Party's security interest in
the Collateral.

                                   ARTICLE 5

                   RIGHTS, DUTIES AND POWERS OF SECURED PARTY

         The following rights, duties and powers of Secured Party are
applicable irrespective of whether an Event of Default occurs and is
continuing:





                                      -8-
<PAGE>   125
         Section 5.01     Discharge Encumbrances.  Secured Party may, at its
option, discharge any taxes, liens, security interests or other encumbrances at
any time levied or placed on the Collateral, may pay for insurance on the
Collateral and may pay for the reasonable maintenance and preservation of the
Collateral.  Debtor agrees to reimburse Secured Party upon demand for any
payment so made, plus interest thereon from the date of Secured Party's demand
at the Post-Default Rate.

         Section 5.02     Transfer of Collateral.  Secured Party may transfer
any or all of the Obligations, and upon any such transfer Secured Party may
transfer its interest in any or all of the Collateral and shall be fully
discharged thereafter from all liability therefor.  Any transferee of the
Collateral shall be vested with all rights, powers and remedies of Secured
Party hereunder.

         Section 5.03     Licenses and Rights to Use Collateral.  In connection
with any transfer or sale (to Secured Party or any other Person) of the
Collateral, Secured Party is hereby granted a transferable license or other
right to use, without any charge but subject to the terms of the Subordination
Agreement, any of Debtor's labels, patents, copyrights, trade names, trade
secrets, trademarks or other similar property (excluding, however, all
Disclosure-Restricted Collateral) in completing production, advertising or
selling such Collateral.  Debtor's rights under all licenses and franchise
agreements shall inure to the benefit of Secured Party and any transferee of
all or any part of the Collateral.

         Section 5.04     Cumulative and Other Rights.  The rights, powers and
remedies of Secured Party hereunder are subject to the Liens under the Senior
Security Agreement and to the terms of the Subordination Agreement, in addition
to all rights, powers and remedies given by law or in equity.  The exercise by
Secured Party of any one or more of the rights, powers and remedies herein
shall not be construed as a waiver of any other rights, powers and remedies,
including, without limitation, any other rights of set-off.  If any of the
Obligations are given in renewal, extension for any period or rearrangement, or
applied toward the payment of debt secured by any lien, Secured Party shall be,
and is hereby, subrogated (to the maximum extent permitted by law) to all the
rights, titles, interests and liens securing the debt so renewed, extended,
rearranged or paid.

         Section 5.05     Disclaimer of Certain Duties.

         (a)     The powers conferred upon Secured Party by this Agreement are
to protect its interest in the Collateral and shall not impose any duty upon
Secured Party or any Noteholder to exercise any such powers.  Debtor hereby
agrees that Secured Party shall not be liable for, nor shall the indebtedness
evidenced by the Obligations be diminished by, Secured Party's delay or failure
to collect upon, foreclose, sell, take possession of or otherwise obtain value
for the Collateral.

         (b)     Secured Party shall, subject to the terms of the Subordination
Agreement, be under no duty whatsoever to make or give any presentment, notice
of dishonor, protest, demand for





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<PAGE>   126
performance, notice of non-performance, notice of intent to accelerate, notice
of acceleration, or other notice or demand in connection with any Collateral or
the Obligations, or to take any steps necessary to preserve any rights against
any Obligor, Account Debtor or other Person.  Debtor waives any right of
marshaling in respect of any and all Collateral, and waives any right to
require Secured Party or any Noteholder to proceed against any Obligor, Account
Debtor or other Person, exhaust any Collateral or enforce any other remedy
which Secured Party or any Noteholder now has or may hereafter have against any
Obligor or other Person.

         Section 5.06     Modification of Obligations; Other Security.  Debtor
waives (a) any and all notice of acceptance, creation, modification,
rearrangement, renewal or extension for any period of any instrument executed
by any Obligor in connection with the Obligations and (b) any defense of any
Obligor by reason of disability, lack of authorization, cessation of the
liability of any Obligor or for any other reason.  Debtor authorizes Secured
Party, without notice or demand and without any reservation of rights against
Debtor and without affecting Debtor's liability hereunder or on the
Obligations, from time to time to (i) take and hold other property, other than
the Collateral, as security for the Obligations, and exchange, enforce, waive
and release any or all of the Collateral, (ii) apply the Collateral in the
manner permitted by this Agreement and (iii) renew, extend for any period,
accelerate, amend or modify, supplement, enforce, compromise, settle, waive or
release the obligations of any Obligor or any instrument or agreement of such
other Person with respect to any or all of the Obligations or Collateral.

                                   ARTICLE 6

                               EVENTS OF DEFAULT

         Section 6.01     Events.  It shall constitute an Event of Default
under this Agreement if an Event of Default occurs and is continuing under the
Securities Purchase Documents.

         Section 6.02     Remedies.  Upon the occurrence and during the
continuance of any Event of Default and subject to the Liens under the Senior
Security Agreement and to the terms of the Subordination Agreement, Secured
Party may take any or all of the following actions without notice (except where
expressly required below or in the Securities Purchase Documents) or demand to
Debtor:

                 (a)      Declare all or part of the indebtedness pursuant to
         the Obligations immediately due and payable as provided in the
         Securities Purchase Documents, and enforce payment of the same by
         Debtor or any Obligor.

                 (b)      Take possession of the Collateral, or at Secured
         Party's request Debtor shall, at Debtor's cost, assemble the
         Collateral and make it available at a location to be specified by
         Secured Party which is reasonably convenient to Debtor and Secured
         Party.  Secured





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<PAGE>   127
         Party may, at its option, render any equipment unusable that may be
         included in the Collateral, or, at Secured Party's request, Debtor
         will render it unusable.  In any event, Debtor shall bear the risk of
         accidental loss or damage to or diminution in value of the Collateral,
         and neither Secured Party nor any Noteholder will have any liability
         whatsoever for failure to obtain or maintain insurance, nor to
         determine whether any insurance ever in force is adequate as to amount
         or as to risk insured.

                 (c)      Sell or lease, in one or more sales or leases and in
         one or more parcels, or otherwise dispose of any or all of the
         Collateral in its then condition or in any other commercially
         reasonable manner as Secured Party may elect, in a public or private
         transaction, at any location as deemed reasonable by Secured Party
         (including, without limitation, Debtor's premises), either for cash or
         credit or for future delivery at such price as Secured Party may deem
         fair, and (unless prohibited by the Code, as adopted in any applicable
         jurisdiction) Secured Party or any Noteholder may be the purchaser of
         any or all Collateral so sold and may apply upon the purchase price
         therefor any Obligations secured hereby.  Any such sale or transfer by
         Secured Party either to itself or to any other Person shall be
         absolutely free from any claim of right by Debtor, including any
         equity or right of redemption, stay or appraisal which Debtor has or
         may have under any rule of law, regulation or statute now existing or
         hereafter adopted.  Upon any such sale or transfer, Secured Party
         shall have the right to deliver, assign and transfer to the purchaser
         or transferee thereof the Collateral so sold or transferred.  It shall
         not be necessary that the Collateral or any part thereof be present at
         the location of any such sale or transfer.  Secured Party may, at its
         discretion, provide for a public sale, and any such public sale shall
         be held at such time or times within ordinary business hours and at
         such place or places as Secured Party may fix in the notice of such
         sale.  Secured Party shall not be obligated to make any sale pursuant
         to any such notice.  Secured Party may, without notice or publication,
         adjourn any public or private sale by announcement at any time and
         place fixed for such sale, and such sale may be made at any time or
         place to which the same may be so adjourned.  In the event any sale or
         transfer hereunder is not completed or is defective in the opinion of
         Secured Party, such sale or transfer shall not exhaust the rights of
         Secured Party hereunder, and Secured Party shall have the right to
         cause one or more subsequent sales or transfers to be made hereunder.
         In the event that any of the Collateral is sold or transferred on
         credit, or to be held by Secured Party for future delivery to a
         purchaser or transferee, the Collateral so sold or transferred may be
         retained by Secured Party until the purchase price or other
         consideration is paid by the purchaser or transferee thereof, but in
         the event that such purchaser or transferee fails to pay for the
         Collateral so sold or transferred or to take delivery thereof, neither
         Secured Party nor any Noteholder shall incur any liability in
         connection therewith.  If only part of the Collateral is sold or
         transferred such that the Obligations remain outstanding (in whole or
         in part), Secured Party's rights and remedies hereunder shall not be
         exhausted, waived or modified, and Secured Party is specifically
         empowered to make one or more successive sales or transfers until all
         the Collateral shall be sold or transferred and all the Obligations
         are paid.





                                      -11-
<PAGE>   128
         In the event that Secured Party elects not to sell the Collateral,
         Secured Party retains its rights to lease or otherwise dispose of or
         utilize the Collateral or any part or parts thereof in any manner
         authorized or permitted by law or in equity, and to apply the proceeds
         of the same towards payment of the Obligations.

                 (d)      Take possession of all books and records of Debtor
         pertaining to the Collateral.  Secured Party shall have the authority
         to enter upon any real property or improvements thereon in order to
         obtain any such books or records, or any Collateral located thereon,
         and remove the same therefrom without liability.

                 (e)      Apply proceeds of the disposition of the Collateral
         to the Obligations in any manner elected by Secured Party and
         permitted by the Code or otherwise permitted by law or in equity.
         Such application may include, without limitation, the reasonable
         expenses of retaking, holding, preparing for sale or other
         disposition, and the reasonable attorneys' fees and legal expenses
         incurred by Secured Party and the Noteholders.

                 (f)      Appoint any Person as agent to perform any act or
         acts necessary or incident to any sale or transfer by Secured Party of
         the Collateral.  Additionally, any sale or transfer hereunder may be
         conducted by an auctioneer or any officer or agent of Secured Party.

                 (g)      Receive, change the address for delivery, open and
         dispose of mail addressed to Debtor, and to execute, assign and
         endorse negotiable and other instruments for the payment of money,
         documents of title or other evidences of payment, shipment or storage
         for any form of Collateral on behalf of and in the name of Debtor.

                 (h)      Notify or require Debtor to notify Account Debtors
         that the Accounts have been assigned to Secured Party and direct such
         Account Debtors to make payments on the Accounts directly to Secured
         Party.  To the extent Secured Party does not so elect, Debtor shall
         continue to collect the Accounts.  Secured Party or its designee shall
         also have the right, in its own name or in the name of Debtor, to do
         any of the following: (i) to demand, collect, receipt for, settle,
         compromise any amounts due, give acquittances for, prosecute or defend
         any action which may be in relation to any monies due or to become due
         by virtue of, the Accounts; (ii) to sell, transfer or assign or
         otherwise deal in the Accounts or the proceeds thereof or the related
         goods, as fully and effectively as if Secured Party were the absolute
         owner thereof; (iii) to extend the time of payment of any of the
         Accounts, to grant waivers and make any allowance or other adjustment
         with reference thereto; (iv) to endorse the name of Debtor on notes,
         checks or other evidences of payments on Collateral that may come into
         possession of Secured Party; (v) to take control of cash and other
         proceeds of any Collateral; (vi) to sign the name of Debtor on any
         invoice or bill of lading relating to any Collateral, or any drafts
         against Account Debtors or other persons making payment with respect
         to





                                      -12-
<PAGE>   129
         Collateral; (vii) to send a request for verification of Accounts to
         any Account Debtor; and (viii) to do all other acts and things
         necessary to carry out the intent of this Agreement.

                 (i)      Exercise all other rights and remedies permitted by 
         law or in equity.

                 Notwithstanding the foregoing, Secured Party may not knowingly
         do anything hereunder which would violate the rights known to the
         Secured Party of third parties with respect to Disclosure-Restricted
         Collateral.

         Section 6.03     Attorney-in-Fact.  Debtor hereby irrevocably appoints
Secured Party as Debtor's attorney-in-fact, with full authority in the place
and stead of Debtor and in the name of Debtor or otherwise, from time to time
in Secured Party's discretion upon the occurrence and during the continuance of
an Event of Default and subject to the terms of the Subordination Agreement,
but at Debtor's cost and expense and without notice to Debtor:

                 (a)      To obtain, adjust, sell and cancel any insurance with
         respect to the Collateral, and endorse any draft drawn by insurers of
         the Collateral.  Secured Party may apply any proceeds or unearned
         premiums of such insurance to the Obligations (whether or not due).

                 (b)      To take any action and to execute any assignment,
         certificate, financing statement, notification, document or instrument
         which Secured Party may deem necessary or advisable to accomplish the
         purposes of this Agreement, including, without limitation, to receive,
         endorse and collect all instruments made payable to Debtor
         representing any payment or other distribution in respect of the
         Collateral or any part thereof and to give full discharge for the
         same.

         Section 6.04     Account Debtors.  Any payment or settlement of an
Account made by an Account Debtor will be, to the extent of such payment or to
the extent provided under such settlement, a release, discharge and acquittance
of the Account Debtor with respect to such Account, and Debtor shall take any
action as may be required by Secured Party in connection therewith.  No Account
Debtor on any Account will ever be bound to make inquiry as to the termination
of this Agreement or the rights of Secured Party to act hereunder, but shall be
fully protected by Debtor in making payment directly to Secured Party.

         Section 6.05     Liability for Deficiency.  If any sale or other
disposition of Collateral by Secured Party in compliance with the Loan
Documents and applicable law or any other action of Secured Party or any
Noteholder hereunder in compliance with the Loan Documents and applicable law
results in reduction of the Obligations, such action will not release Debtor
from its liability to Secured Party and the Noteholders for any unpaid
Obligations, including costs, charges and expenses incurred in the liquidation
of Collateral, together with interest thereon, and the same shall be





                                      -13-
<PAGE>   130
immediately due and payable to Secured Party at Secured Party's address set
forth in the opening paragraph hereof.

         Section 6.06     Reasonable Notice.  If any applicable provision of
any law requires Secured Party or any Noteholder to give reasonable notice of
any sale or disposition or other action, Debtor hereby agrees that ten days'
prior written notice shall constitute reasonable notice thereof.  Such notice,
in the case of public sale, shall state the time and place fixed for such sale
and, in the case of private sale, the time after which such sale is to be made.

         Section 6.07     Non-judicial Enforcement.  To the extent permitted by
law, Secured Party may enforce its rights hereunder without prior judicial
process or judicial hearing, and to the extent permitted by law Debtor
expressly waives any and all legal rights which might otherwise require Secured
Party to enforce its rights by judicial process.

                                   ARTICLE 7

                            MISCELLANEOUS PROVISIONS

         Section 7.01     Notices.  Any notice required or permitted to be
given under or in connection with this Agreement shall be given in accordance
with the notice provisions of the Securities Purchase Documents.

         Section 7.02     Amendments and Waivers.  Secured Party's acceptance
of partial or delinquent payments or any forbearance, failure or delay by
Secured Party in exercising any right, power or remedy hereunder shall not be
deemed a waiver of any obligation of Debtor or any Obligor, or of any right,
power or remedy of Secured Party; and no partial exercise of any right, power
or remedy shall preclude any other or further exercise thereof.  Secured Party
may remedy any Event of Default hereunder or in connection with the Obligations
without waiving the Event of Default so remedied.  Debtor hereby agrees that if
Secured Party agrees to a waiver of any provision hereunder, or an exchange of
or release of the Collateral, or the addition or release of any Obligor or
other Person, any such action shall not constitute a waiver of any of Secured
Party's other rights or of Debtor's obligations hereunder.  This Agreement may
be amended only by an instrument in writing executed jointly by Debtor and
Secured Party and may be supplemented only by documents delivered or to be
delivered in accordance with the express terms hereof.

         Section 7.03     Copy as Financing Statement.  A photocopy or other
reproduction of this Agreement or any financing statement covering the
Collateral is sufficient as a financing statement, and the same may be filed
with any appropriate filing authority for the purpose of perfecting Secured
Party's security interest in the Collateral.





                                      -14-
<PAGE>   131
         Section 7.04     Possession of Collateral.  Secured Party shall be
deemed to have possession of any Collateral in transit to it or set apart for
it (or, in either case, any of its agents, affiliates or correspondents).

         Section 7.05     Redelivery of Collateral.  If any sale or transfer of
Collateral by Secured Party results in full satisfaction of the Obligations,
and after such sale or transfer and discharge there remains a surplus of
proceeds, Secured Party will deliver to Debtor such excess proceeds in a
commercially reasonable time; provided, however, that neither Secured Party nor
any Noteholder shall have any liability for any interest, cost or expense in
connection with any delay in delivering such proceeds to Debtor.

         Section 7.06     Governing Law; Jurisdiction.  This Agreement and the
security interest granted hereby shall be construed in accordance with and
governed by the laws of the State of Texas (except to the extent that the laws
of any other jurisdiction govern the perfection and priority of the security
interests granted hereby).

         Section 7.07     Continuing Security Agreement.

         (a)     Except as may be expressly applicable pursuant to Section
9.505 of the Code, no action taken or omission to act by Secured Party or the
Noteholders hereunder, including, without limitation, any action taken or
inaction pursuant to Section 6.02, shall be deemed to constitute a retention of
the Collateral in satisfaction of the Obligations or otherwise to be in full
satisfaction of the Obligations, and the Obligations shall remain in full force
and effect, until Secured Party and the Noteholders shall have applied payments
(including, without limitation, collections from Collateral) towards the
Obligations in the full amount then outstanding or until such subsequent time
as is hereinafter provided in subsection (b) below.

         (b)     To the extent that any payments on the Obligations or proceeds
of the Collateral are subsequently invalidated, declared to be fraudulent or
preferential, set aside or required to be repaid to a trustee, debtor in
possession, receiver or other Person under any bankruptcy law, common law or
equitable cause, then to such extent the Obligations so satisfied shall be
revived and continue as if such payment or proceeds had not been received by
Secured Party or the Noteholders, and Secured Party's and the Noteholders'
security interests, rights, powers and remedies hereunder shall continue in
full force and effect.  In such event, this Agreement shall be automatically
reinstated if it shall theretofore have been terminated pursuant to Section
7.08.

         Section 7.08     Termination.  The grant of a security interest
hereunder and all of Secured Party's and the Noteholders' rights, powers and
remedies in connection therewith shall remain in full force and effect until
Secured Party has retransferred and delivered all Collateral in its possession
to Debtor, and executed a written release or termination statement and
reassigned to Debtor without recourse or warranty any remaining Collateral and
all rights conveyed hereby.  Upon the complete





                                      -15-
<PAGE>   132
payment of the Obligations and the compliance by Debtor with all covenants and
agreements hereof, Secured Party, at the written request and expense of Debtor,
will release, reassign and transfer the Collateral to Debtor and declare this
Agreement to be of no further force or effect.  Notwithstanding the foregoing,
the reimbursement and indemnification provisions of Section 4.08 and the
provisions of subsection 7.07(b) shall survive the termination of this
Agreement.

         Section 7.08     Subordination Agreement.  This Agreement and the
rights and remedies of the Agent and the Noteholders hereunder are subject to
this Agreement and the terms and conditions of that certain Subordination
Agreement dated as of August __, 1998, made by the Agent, the Noteholders and
the Bank of Montreal.

         Section 7.09     Counterparts, Effectiveness.  This Agreement may be
executed in two or more counterparts.  Each counterpart is deemed an original,
but all such counterparts taken together constitute one and the same
instrument.  This Agreement becomes effective upon the execution hereof by
Debtor and delivery of the same to Secured Party or the Noteholders, and it is
not necessary for Secured Party or any Noteholder to execute any acceptance
hereof or otherwise signify or express its acceptance hereof.

DEBTOR:                                 BRIGHAM OIL & GAS, L.P.

                                        By: Brigham, Inc., its General Partner



                                        By:
                                           ----------------------------
                                        Name:   Craig M. Fleming
                                        Title:  Chief Financial Officer





                                      -16-
<PAGE>   133
                              FINANCING STATEMENT


         This Financing Statement is presented to a filing officer for filing
pursuant to the Uniform Commercial Code.


1.       The name and address of the Debtor is:

                 Brigham Oil & Gas, L.P.
                 6300 Bridge Point Parkway
                 Building 2, Suite 500
                 Austin, Texas 78730

2.       The name and address of the Secured Party is:

                 Chase Manhattan Bank
                 600 Travis
                 Suite 1150
                 Houston, Texas 77002

3.       This Financing Statement covers the following Collateral:

                 (a)      All of Debtor's accounts, inventory, equipment,
         chattel paper, documents, instruments and general intangibles.

                 (b)      (i) Any related or additional property from time to
         time delivered to or deposited with Secured Party by or for the
         account of Debtor; (ii) all certificates of title or other documents
         evidencing ownership or possession of or otherwise relating to any
         property referred to in this paragraph 3; (iii) all property used or
         usable in connection with any property referred to in this paragraph
         3; (iv) all policies of insurance (whether or not required by Secured
         Party) covering any property referred to in this paragraph 3; (v) all
         goods which were at any time included in the Collateral and which are
         returned to or for the account of Debtor following their sale, lease
         or other disposition; (vi) all proceeds, products, replacements,
         additions to, substitutions for, accessions of, and property necessary
         for the operation of any of the property referred to in this paragraph
         3, including, without limitation, insurance payable as a result of
         loss or damage to any of the property referred to in this paragraph 3,
         refunds of unearned premiums of any such insurance policy and claims
         against third parties; and (vii) all books and records related to any
         of the property referred to in this paragraph 3, including, without
         limitation, any and all books of account, customer lists and





                                      -1-
<PAGE>   134
         other records relating in any way to the accounts, chattel paper,
         instruments or inventory referred to in this paragraph 3.

                 (c)      All general intangibles related to any property
         referred to in this paragraph 3, including, without limitation, all
         (i) bonds, guaranties, purchase or sales agreements and other
         contractual rights, rights to performance, and claims for damages,
         refunds (including tax refunds) or other monies due or to become due;
         (ii) orders, franchises, permits, certificates, licenses, consents,
         exemptions, variances, authorizations or other approvals by any
         governmental agency or court; (iii) consulting, engineering and
         technological information and specifications, design data, patent
         rights, trade secrets, literary rights, copyrights, trademarks,
         labels, trade names and other intellectual property; (iv) business
         records, computer tapes and computer software; (v) goodwill; and (vi)
         all other intangible personal property, whether similar or dissimilar
         to the foregoing.

DEBTOR:                                 BRIGHAM OIL & GAS, L.P.

                                        By: Brigham, Inc., its General Partner



                                        By:
                                           -------------------------------
                                        Name:  Craig M. Fleming 
                                        Title: Chief Financial Officer





                                      -2-
<PAGE>   135
                                 SCHEDULE 3.06

                                     STATES


Texas
Oklahoma
New Mexico
Kansas





                                      -3-
<PAGE>   136
                                   EXHIBIT F

WHEN RECORDED RETURN TO:
Chase Manhattan Bank
600 Travis
Suite 1150
Houston, Texas  77002


               MORTGAGE, DEED OF TRUST, ASSIGNMENT OF PRODUCTION,
                   SECURITY AGREEMENT AND FINANCING STATEMENT



                                      FROM


                            BRIGHAM OIL & GAS, L.P.


                                       TO


                          ______________, AS MORTGAGEE



                               FOR THE BENEFIT OF


          _________________________________________________________
                                    AS AGENT


A POWER OF SALE HAS BEEN GRANTED IN THIS INSTRUMENT.  IN CERTAIN STATES, A
POWER OF SALE MAY ALLOW THE TRUSTEE OR THE AGENT TO TAKE THE MORTGAGED PROPERTY
AND SELL IT WITHOUT GOING TO COURT IN A FORECLOSURE ACTION UPON DEFAULT BY THE
GRANTOR UNDER THIS INSTRUMENT.

THIS INSTRUMENT CONTAINS AFTER-ACQUIRED PROPERTY PROVISIONS.

THIS INSTRUMENT SECURES PAYMENT OF FUTURE ADVANCES.

THIS INSTRUMENT COVERS PROCEEDS OF MORTGAGED PROPERTY.

THIS IS DEEMED TO BE A LINE OF CREDIT MORTGAGE UNDER THE PROVISIONS OF SECTION
48-7-4 N.M.S.A.
<PAGE>   137
                               TABLE OF CONTENTS

<TABLE>
<S>                                                                                                                    <C>
ARTICLE I

         Grant of Lien and Indebtedness Secured
         Section 1.01     Grant of Liens  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         Section 1.02     Grant of Security Interest  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
         Section 1.03     Indebtedness Secured  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
         Section 1.04     Fixture Filing, Etc.  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
         Section 1.05     Defined Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

ARTICLE II

         Assignment of Production
         Section 2.01     Assignment  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
         Section 2.02     Rights Under Texas Act  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
         Section 2.03     No Modification of Payment Obligations  . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

ARTICLE III

         Representations and Warranties and Covenants
         Section 3.01     Title . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
         Section 3.02     Defend Title  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
         Section 3.03     Not a Foreign Person  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
         Section 3.04     Power to Create Lien and Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
         Section 3.05     Revenue and Cost Bearing Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
         Section 3.06     Rentals Paid; Leases in Effect  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
         Section 3.07     Operation by Third Parties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
         Section 3.08     Abandon, Sales  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
         Section 3.09     Failure to Perform  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

ARTICLE IV

         Rights and Remedies
         Section 4.01     Event of Default  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
         Section 4.02     Foreclosure and Sale  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
         Section 4.03     Substitute Trustees and Agents  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
</TABLE>
<PAGE>   138
<TABLE>
<S>                       <C>                                                                                          <C>
         Section 4.04     Judicial Foreclosure; Receivership  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 4.05     Foreclosure for Installments  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 4.06     Separate Sales  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 4.07     Occupancy After Foreclosure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12
         Section 4.08     Remedies Cumulative, Concurrent and Nonexclusive  . . . . . . . . . . . . . . . . . . . . .  12
         Section 4.09     No Release of Obligations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12
         Section 4.10     Release of and Resort to Collateral . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13
         Section 4.11     Waiver of Redemption, Notice and Marshalling of Assets, Etc . . . . . . . . . . . . . . . .  13
         Section 4.12     Discontinuance of Proceedings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13
         Section 4.13     Application of Proceeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13
         Section 4.14     Resignation of Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14
         Section 4.15     INDEMNITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14
         Section 4.16     Power of Sale in Oklahoma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  15

ARTICLE V

         The Trustee
         Section 5.01     Duties, Rights, and Powers of Trustee . . . . . . . . . . . . . . . . . . . . . . . . . . .  15
         Section 5.02     Successor Trustee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  16
         Section 5.03     Retention of Moneys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  16

ARTICLE VI

         Miscellaneous
         Section 6.01     Instrument Construed as Mortgage, Etc.  . . . . . . . . . . . . . . . . . . . . . . . . . .  16
         Section 6.02     Release of Mortgage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  17
         Section 6.03     Severability  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  17
         Section 6.04     Successors and Assigns of Parties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  17
         Section 6.05     Satisfaction of Prior Encumbrance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  17
         Section 6.06     Subrogation of Trustee  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  17
         Section 6.07     Nature of Covenants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  17
         Section 6.08     Notices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  17
         Section 6.09     Counterparts  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  18
         SECTION 6.10     EXCULPATION PROVISIONS  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  18
         Section 6.11     Subordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  18

         Exhibit A        -       Mortgaged Property
</TABLE>





                                       ii
<PAGE>   139
                     MORTGAGE, DEED OF TRUST, ASSIGNMENT OF
             PRODUCTION, SECURITY AGREEMENT AND FINANCING STATEMENT


         This MORTGAGE, DEED OF TRUST, ASSIGNMENT OF PRODUCTION, SECURITY
AGREEMENT AND FINANCING STATEMENT (this "Mortgage") is entered into as of the
effective time and date hereinafter stated (the "Effective Date") by BRIGHAM OIL
& GAS, L.P., a Delaware limited partnership, whose address for notice is 6300
Bridge Point Parkway, Building 2, Suite 500, Austin, Texas  78730 ("Mortgagor"),
to ___________, whose address is _________, ("Mortgagee"), for the benefit of
___________________________________________________________, whose address for
notice is ________________, as Agent (as defined below), and for the benefit of
the Noteholders (as defined below).

                                R E C I T A L S:

         A.      Brigham Exploration Company, a Delaware corporation
("Borrower") has executed (i) a Securities Purchase Agreement dated as of August
__, 1998 (such agreement, as same may from time to time be modified, extended,
renewed, replaced, restated, amended or supplemented, being herein called the
"Securities Purchase Agreement") among the Mortgagor, the purchasers named
therein ("Noteholders"), and _______________________________________, as agent
for the Noteholders ("Agent") and (ii) the Indenture dated as of August __, 1998
("Indenture," and together with the Securities Purchase Agreement, collectively
referred to herein as the "Securities Purchase Documents").

         B.      The proceeds of the indebtedness evidenced by the Securities
Purchase Documents and the Notes (as defined in the Securities Purchase
Documents) issued in connection therewith are being used by the Borrower to
repay indebtedness owing under (i) the Credit Agreement dated as of January 28,
1998 (such agreement, as the same may from time to time be modified, extended,
renewed, restated, amended or supplemented, being herein called the "Credit
Agreement") among the Mortgagor, the lenders party thereto ("Senior Lenders"),
and Bank of Montreal, as agent for the Lenders ("Senior Loan Agent") and (ii)
the promissory note in the original principal amount of $75,000,000 (such note,
as the same may from time to time be modified, extended, renewed, restated,
amended, replaced or supplemented, being herein called the "BMO Note") issued
by the Mortgagor payable to the order of Bank of Montreal.

         C.      The BMO Note and all other obligations now or hereafter
existing or to exist under the Credit Agreement is secured in part by those
certain deeds of trust, mortgages, and other documents more particularly
described on Schedule 1 attached hereto and made a part hereof (such
instruments, together with any others as may now exist or hereafter be executed
pursuant to the Credit Agreement, as any of the same may from time to time be
amended, renewed, restated, modified or supplemented, being referred to herein
collectively as the "Senior Mortgages").
<PAGE>   140
         D.      In connection with the execution and delivery of the
Securities Purchase Documents, the Agent, the Noteholders and the Senior Loan
Agent have executed the Subordination Agreement dated as of August __, 1998
("Subordination Agreement") in order to evidence the relative priorities and
rights of the Senior Loan Agent and the Senior Lenders to the rights and
obligations of the Agent, the Noteholders and the Borrower under the Securities
Purchase Documents.

         E.      The Mortgagor will derive substantial benefit, both directly
and indirectly, from the making of the loans under the Securities Purchase
Documents and has agreed to execute and deliver to the Mortgagee for the
benefit of the Agent and the Noteholders the Guaranty Agreement dated as of
August __, 1998 ("Guaranty").

         F.      Therefore, in order to secure both the obligations of the
Borrower under the Securities Purchase Documents and under the Notes and the
obligations of the Mortgagor under the Guaranty, and to otherwise comply with
the terms and conditions of the Securities Purchase Documents and for other
good and valuable consideration, the receipt and sufficiency of which are
hereby acknowledged, Mortgagor hereby agrees with Mortgagee as follows:


                                   ARTICLE I

                     Grant of Lien and Indebtedness Secured

         Section 1.01     Grant of Liens.  To secure payment of the
Indebtedness (as hereinafter defined) and the performance of the covenants and
obligations herein contained, Mortgagor does by these presents hereby, subject
to the reservations and restrictions set forth herein below and further subject
to the priority of the Liens created or evidenced by the Senior Mortgage(s) and
any Security Agreement or financing statement associated therewith, (i) GRANT,
BARGAIN, SELL, ASSIGN, SET OVER, TRANSFER and CONVEY unto_______, as Trustee,
whose address for notice hereunder is __________________("Trustee") and the
Trustee's successors and substitutes in trust hereunder with power of sale, for
the use and benefit of the Mortgagee on behalf of the Agent and the
Noteholders, all of the following described real and personal property, rights,
titles, interests and estates which are located in (or cover properties located
in) the State of Texas or which are located within (or cover properties located
within) the offshore area over which the United States of America asserts
jurisdiction and to which the laws of such state are applicable with respect to
this Mortgage and/or the liens or security interests created hereby (the "Deed
of Trust Mortgaged Property") and (ii) GRANT, MORTGAGE, PLEDGE, HYPOTHECATE AND
GRANT A POWER OF SALE to Mortgagee, for its benefit and the benefit of the
Agent and the Noteholders, with respect to, all of the following described real
and personal property, rights, titles, interests and estates which were not
granted to Trustee in clause (i) above (the "Other





                                       2
<PAGE>   141
Mortgaged Property") (the Deed of Trust Property and the Other Mortgaged
Property herein collectively called the "Mortgaged Property"):

         (a)     All rights, titles, interests and estates now owned or
hereafter acquired by Mortgagor in and to the oil and gas leases and/or oil,
gas and other mineral leases and other interests and estates and the lands and
premises covered or affected thereby which are described on Exhibit A attached
to the Senior Mortgages listed in Schedule 1 (the "Senior Mortgages Exhibit A")
and Exhibit A (including Part I and Part II thereof) hereto (the "Additional
Exhibit A") (collectively called the "Hydrocarbon Property") or which
Hydrocarbon Property is otherwise referred to herein, and specifically, but
without limitation, the undivided interests of Mortgagor which are more
particularly described on the Senior Mortgages Exhibit A and the Additional
Exhibit A (the Senior Mortgages Exhibit A and the Additional Exhibit A are
herein collectively referred to as "Exhibit A").

         (b)     All rights, titles, interests and estates now owned or
hereafter acquired by Mortgagor in and to (i) the properties now or hereafter
pooled or unitized with the Hydrocarbon Property; (ii) all presently existing
or future unitization, communitization, pooling agreements and declarations of
pooled units and the units created thereby (including, without limitation, all
units created under orders, regulations, rules or other official acts of any
Federal, State or other governmental body or agency having jurisdiction and any
units created solely among working interest owners pursuant to operating
agreements or otherwise) which may affect all or any portion of the Hydrocarbon
Property including, without limitation, those units which may be described or
referred to on attached Exhibit A; (iii) all operating agreements, production
sales or other contracts, farmout agreements, farm-in agreements, area of
mutual interest agreements, equipment leases and other agreements described or
referred to in this Mortgage or which relate to any of the Hydrocarbon Property
or interests in the Hydrocarbon Property described or referred to herein or on
Exhibit A or to the production, sale, purchase, exchange, processing, handling,
storage, transporting or marketing of the Hydrocarbons (hereinafter defined)
from or attributable to such Hydrocarbon Property or interests; and (iv)
subject to applicable restrictions on disclosure and/or transfer, all
geological, geophysical, engineering, accounting, title, legal, and other
technical or business data concerning the Mortgaged Property, the Hydrocarbons,
or any other item of Property which are in the possession of Mortgagor or in
which Mortgagor can otherwise grant a security interest, and all books, files,
records, magnetic media, computer records, and other forms of recording or
obtaining access to such data.

         (c)     All rights, titles, interests and estates now owned or
hereafter acquired by Mortgagor in and to all oil, gas, casinghead gas,
condensate, distillate, liquid hydrocarbons, gaseous hydrocarbons and all
products refined therefrom and all other minerals (collectively called the
"Hydrocarbons") in and under and which may be produced and saved from or
attributable to the Hydrocarbon Property, the lands pooled or unitized
therewith and Mortgagor's interests therein, including all oil in tanks and all
rents, issues, profits, proceeds, products, revenues and other income from or
attributable to the Hydrocarbon Property, the lands pooled or unitized
therewith and Mortgagor's interests therein which are subjected or required to
be subjected to the liens and security interests of this Mortgage.





                                       3
<PAGE>   142
         (d)     All tenements, hereditaments, appurtenances and properties in
anywise appertaining, belonging, affixed or incidental to the Hydrocarbon
Property, rights, titles, interests and estates described or referred to in
paragraphs (a) and (b) above, which are now owned or which may hereafter be
acquired by Mortgagor, including, without limitation, any and all property,
real or personal, now owned or hereafter acquired and situated upon, used, held
for use, or useful in connection with the operating, working or development of
any of such Hydrocarbon Property or the lands pooled or unitized therewith
(excluding drilling rigs, trucks, automotive equipment or other personal
property which may be taken to the premises for the purpose of drilling a well
or for other similar temporary uses) and including any and all oil wells, gas
wells, injection wells or other wells, buildings, structures, field separators,
liquid extraction plants, plant compressors, pumps, pumping units, pipelines,
sales and flow lines, gathering systems, field gathering systems, salt water
disposal facilities, tanks and tank batteries, fixtures, valves, fittings,
machinery and parts, engines, boilers, meters, apparatus, equipment,
appliances, tools, implements, cables, wires, towers, casing, tubing and rods,
surface leases, rights-of-way, easements, servitudes, licenses and other
surface and subsurface rights together with all additions, substitutions,
replacements, accessions and attachments to any and all of the foregoing
properties.

         (e)     Any property that may from time to time hereafter, by delivery
or by writing of any kind, be subjected to the lien and security interest
hereof by Mortgagor or by anyone on Mortgagor's behalf; and the Trustee is
hereby authorized to receive the same at any time as additional security
hereunder.

         (f)     All of the rights, titles and interests of every nature
whatsoever now owned or hereafter acquired by Mortgagor in and to the
Hydrocarbon Property rights, titles, interests and estates and every part and
parcel thereof, including, without limitation, the Hydrocarbon Property rights,
titles, interests and estates as the same may be enlarged by the discharge of
any payments out of production or by the removal of any charges or Permitted
Encumbrances (as hereinafter defined in Section 3.01) to which any of the
Hydrocarbon Property rights, titles, interests or estates are subject, or
otherwise; all rights of Mortgagor to liens and security interests securing
payment of proceeds from the sale of production from the Mortgaged Property,
including, but not limited to, those liens and security interests provided in
Tex. Bus. & Com. Code Ann. Section 9.319 (Tex. UCC) (Vernon Supp. 1989)
("Section 9.319 Tex. UCC"), as amended from time to time; together with any and
all renewals and extensions of any of the Hydrocarbon Property rights, titles,
interests or estates; all contracts and agreements supplemental to or
amendatory of or in substitution for the contracts and agreements described or
mentioned above; and any and all additional interests of any kind hereafter
acquired by Mortgagor in and to the Hydrocarbon Property rights, titles,
interests or estates.

         (g)     All accounts, contract rights, inventory, general intangibles,
insurance contracts and insurance proceeds constituting a part of, relating to
or arising out of those portions of the Mortgaged Property which are described
in paragraphs (a) through (f) above and all proceeds and products of all such
portions of the Mortgaged Property and payments in lieu of production (such as
"take or





                                       4
<PAGE>   143
pay" payments), whether such proceeds or payments are goods, money, documents,
instruments, chattel paper, securities, accounts, general intangibles,
fixtures, real property, or other assets.

         Notwithstanding any provision hereof to the contrary, this Mortgage
does not cover, and there is expressly excepted and excluded from the definition
of Mortgaged Property, any properties, rights and interests as may now or
hereafter be beneficially or equitable owned by (or contractually owing to) a
third party under any one or more of the agreements or other arrangements now or
hereafter described in Schedule 4.10 of the Securities Purchase Agreements (the
"Participating Third Parties"), but only to the extent any such exception and
exclusion does not cause the undivided interests specified in Exhibit A to be
reduced or otherwise adversely affected.  Without limitation of the generality
of the foregoing, any undivided interest (a) with respect to which Mortgagor
holds legal title (whether of record or not), and (b) that is in excess of the
undivided interests in such Mortgaged Property as are specified in the Exhibit A
shall be excluded from the definition of Mortgaged Property to the extent a
Participating Third Party now or hereafter has an interest therein and, to that
extent, shall otherwise be free and clear of this Mortgage (and any security
agreement and/or financing statement associated herewith).

         TO HAVE AND TO HOLD the Mortgaged Property unto the Trustee and to his
successors and assigns forever to secure the payment of the Indebtedness
(hereinafter defined) and to secure the performance of the covenants,
agreements, and obligations of the Mortgagor herein contained.

         Section 1.02     Grant of Security Interest.  To further secure the
Indebtedness, Mortgagor hereby grants to Mortgagee, subject to the reservations
and restrictions set forth herein below and further subject to the priority of
the Liens created or evidenced by the Senior Mortgage(s) and any security
agreement or financing statement executed in association therewith and to the
terms of the Subordinated Agreement (as defined in the Securities Purchase
Documents), a security interest in and to the Mortgaged Property (whether now
or hereafter acquired by operation of law or otherwise) insofar as the
Mortgaged Property consists of equipment, accounts, contract rights, general
intangibles (subject in the case of geological and geophysical data (including
without limitation raw data and interpretations) contract rights and general
intangibles to any existing restrictions on disclosure and/or transfer),
insurance contracts, insurance proceeds, inventory, Hydrocarbons, fixtures and
any and all other personal property of any kind or character defined in and
subject to the provisions of the Uniform Commercial Code presently in effect in
the jurisdiction in which the Mortgaged Property is situated ("Applicable
UCC"), including the proceeds and products from any and all of such personal
property.  Upon the happening of any of the Events of Default, but subject to
Liens created or evidenced by the Senior Mortgage(s) and the terms of the
Subordination Agreement, Mortgagee is and shall be entitled to all of the
rights, powers and remedies afforded a secured party by the Applicable UCC with
reference to the personal property and fixtures in which Mortgagee has been
granted a security interest herein, or the Trustee or Mortgagee may proceed as
to both the real and personal property covered hereby in accordance with the
rights and remedies granted under this Mortgage in respect of the real property
covered hereby.  Such rights, powers and





                                       5
<PAGE>   144
remedies shall be cumulative and in addition to those granted to the Trustee or
Mortgagee under any other provision of this Mortgage or under any other
Collateral Document (as defined in the Securities Purchase Documents).  Written
notice mailed to Mortgagor as provided herein at least five (5) days prior to
the date of public sale of any part of the Mortgaged Property which is personal
property subject to the provisions of the Applicable UCC, or prior to the date
after which private sale of any such part of the Mortgaged Property will be
made, shall constitute reasonable notice.

         Section 1.03     Indebtedness Secured.  This Mortgage is executed and
delivered by Mortgagor to secure and enforce the following (the
"Indebtedness"):

         (a)     Payment of and performance of (i) any and all indebtedness,
obligations and liabilities of Borrower owing to the Agent and the Noteholders
pursuant to the Securities Purchase Documents, whether now existing or
hereafter arising, and (ii) any and all indebtedness, obligations and
liabilities of Mortgagor owing to the Agent and the Noteholders pursuant to the
Guaranty, which Guaranty guarantees the payment of all amounts owing by the
Borrower under, or in connection with, the Securities Purchase Documents,
including, without limitation, all obligations of the Borrower under the
promissory notes which are or may be executed by the Borrower payable to the
order of the Noteholders and being in the original face amount of $50,000,000
with final maturity on or before ____________, 2003 and all other notes given
in substitution therefor or in modification, renewal or extension thereof, in
whole or in part (such notes, as from time to time supplemented, amended or
modified and all other notes given in substitution therefor or in modification,
renewal or extension thereof, in whole or in part, being hereafter called the
"Note").

         (b)     Any sums which may be advanced or paid by Mortgagee under the
terms hereof or of the Securities Purchase Documents on account of the failure
of Mortgagor to comply with the covenants of Mortgagor contained herein or in
the Securities Purchase Documents, and all other indebtedness of Mortgagor
arising pursuant to the provisions of this Mortgage.

         Section 1.04     Fixture Filing, Etc.  Without in any manner limiting
the generality of any of the other provisions of this Mortgage: (a) some
portions of the goods described or to which reference is made herein are or are
to become fixtures on the land described or to which reference is made herein
or on attached Exhibit A; (b) the security interests created hereby under
applicable provisions of the Applicable UCC will attach to Hydrocarbons
(minerals including oil and gas) or the accounts resulting from the sale
thereof at the wellhead or minehead located on the land described or to which
reference is made herein; (c) this Mortgage is to be filed of record in the
real estate records as a financing statement, and (d) Mortgagor is the record
owner of the real estate or interests in the real estate comprised of the
Mortgaged Property.

         Section 1.05     Defined Terms.  Any capitalized term used in this
Mortgage and not defined in this Mortgage shall have the meaning assigned to
such term in the Securities Purchase Documents.





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<PAGE>   145
                                   ARTICLE II

                            Assignment of Production

         Section 2.01     Assignment.  Subject to the priority of the Liens
created or evidenced by the Senior Mortgages and any security agreement or
financing statement executed in connection therewith, and to the terms of the
Subordination Agreement and the Permitted Encumbrances, Mortgagor has
absolutely and unconditionally assigned, transferred, and conveyed, and does
hereby absolutely and unconditionally assign, transfer and convey unto
Mortgagee, its successors and assigns, all of the Hydrocarbons and all products
obtained or processed therefrom, and the revenues and proceeds now and
hereafter attributable to the Hydrocarbons and said products and all payments
in lieu of the Hydrocarbons such as "take or pay" payments or settlements.
Subject to the terms of the Subordination Agreement and the Securities Purchase
Documents, the Hydrocarbons and products are to be delivered into pipe lines
connected with the Mortgaged Property, or to the purchaser thereof, to the
credit of Mortgagee, free and clear of all taxes, charges, costs, and expenses,
and all such revenues and proceeds shall be paid directly to Mortgagee, at its
head quarters in _________________ with no duty or obligation of any party
paying the same to inquire into the rights of Mortgagee to receive the same,
what application is made thereof, or as to any other matter.  Mortgagor agrees
to perform all such acts, and to execute all such further assignments,
transfers and division orders, and other instruments as may be required or
desired by Mortgagee or any party in order to have said proceeds and revenues
so paid to Mortgagee.  Subject to the Liens created or evidenced by the Senior
Mortgage(s) and the terms of the Subordination Agreement and the Securities
Purchase Documents, Mortgagee is fully authorized to receive and receipt for
said revenues and proceeds; to endorse and cash any and all checks and drafts
payable to the order of Mortgagor or Mortgagee for the account of Mortgagor
received from or in connection with said revenues or proceeds and to hold the
proceeds thereof in a bank account as additional collateral securing the
Indebtedness; and to execute transfer and division orders in the name of
Mortgagor, or otherwise, with warranties binding Mortgagor.  All proceeds
received by the Mortgagee pursuant to this assignment shall be applied as
provided in the Securities Purchase Documents and in the other Loan Documents.
Mortgagee shall not be liable for any delay, neglect, or failure to effect
collection of any proceeds or to take any other action in connection therewith
or hereunder; but Mortgagee shall have the right, at its election, in the name
of Mortgagor or otherwise, to prosecute and defend any and all actions or legal
proceedings deemed advisable by Mortgagee in order to collect such funds and to
protect the interests of Mortgagee, and/or Mortgagor, with all costs, expenses
and attorneys' fees incurred in connection therewith being paid by Mortgagor.
Mortgagor hereby appoints Mortgagee as its attorney-in-fact to pursue any and
all rights of Mortgagor to liens on and security interests in the Hydrocarbons
securing payment of proceeds of runs attributable to the Hydrocarbons.  In
addition to the rights granted to Trustee and/or Mortgagee in Section 1.01 (f)
of this Mortgage, Mortgagor hereby further transfers and assigns to Mortgagee
any and all such liens, security interests, financing statements or similar
interests of Mortgagor attributable to its interest in the Hydrocarbons and
proceeds of runs therefrom arising under or created by said statutory
provision, judicial decision or otherwise.  The power of attorney granted to
Mortgagee in this Section 2.01,





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<PAGE>   146
being coupled with an interest, shall be irrevocable so long as the
Indebtedness or any part thereof remains unpaid.

         Section 2.02     Rights Under Texas Act.  Subject to the priority of
the Liens created or evidenced by the Senior Mortgages and any security
agreement or financing statement executed in connection therewith, and to the
terms of the Subordination Agreement, the Securities Purchase Documents and the
Permitted Encumbrances, Mortgagor hereby grants, sells, assigns, sets over and
mortgages unto Mortgagee during the term hereof, all of Mortgagor's rights and
interests pursuant to the provisions of Section 9.319 Tex. UCC, hereby vesting
in Mortgagee all of Mortgagor's rights as an interest owner to the continuing
security interest in and lien upon the Mortgaged Property.

         Section 2.03     No Modification of Payment Obligations.  Nothing
herein contained shall modify or otherwise alter the obligation of Mortgagor to
make prompt payment of all principal and interest owing on the Indebtedness
when and as the same become due regardless of whether the proceeds of the
Hydrocarbons are sufficient to pay the same and the rights provided in
accordance with the foregoing assignment provision shall be cumulative of all
other security of any and every character now or hereafter existing to secure
payment of the Indebtedness.


                                  ARTICLE III

                  Representations and Warranties and Covenants

         Mortgagor hereby represents and warrants as follows:

         Section 3.01     Title.  To the extent of the undivided interests
specified on the attached Additional Exhibit A and the Senior Mortgages Exhibit
A, Mortgagor has good and indefeasible title to and is possessed of the
Mortgaged Property, subject to the Permitted Encumbrances.  The Mortgaged
Property is free of any and all Liens except for Excepted Liens and Liens, if
any, described in the Senior Mortgages, or on Exhibit A (collectively, the
"Permitted Encumbrances").

         Notwithstanding and provision hereof to the contrary, the covenants,
representation and warranties contained in this Mortgage, to the extent
pertaining to any Mortgaged Property described in Part II of Additional Exhibit
A, are limited to the wellbores (and any production therefrom) of the wells
specifically listed in such Part II of Additional Exhibit A.

         Section 3.02     Defend Title.  This Mortgage is, and always will be
kept, a direct first or, to the extent the Senior Mortgage is in place, second
lien and security interest upon the Mortgaged Property subject only to the
Permitted Encumbrances and, except as provided in the Securities Purchase
Documents, Mortgagor will not create or suffer to be created or permit to exist
any lien, security interest or charge prior or junior to or on a parity with
the lien and security interest of this





                                       8
<PAGE>   147
Mortgage upon the Mortgaged Property or any part thereof or upon the rents,
issues, revenues, profits and other income therefrom.  Mortgagor will warrant
and defend the title to the Mortgaged Property against the claims and demands
of all other persons whomsoever and will maintain and preserve the lien created
hereby so long as any of the Indebtedness secured hereby remains unpaid.
Should an adverse claim be made against or a cloud develop upon the title to
any part of the Mortgaged Property, Mortgagor agrees it will immediately defend
against such adverse claim or take appropriate action to remove such cloud at
Mortgagor's cost and expense, and Mortgagor further agrees that the Trustee
and/or Mortgagee may, subject to the terms of the Subordination Agreement, take
such other action as they deem advisable to protect and preserve their
interests in the Mortgaged Property, and in such event Mortgagor will indemnify
the Trustee and Mortgagee against any and all cost, attorney's fees and other
expenses which they may incur in defending against any such adverse claim or
taking action to remove any such cloud.

         Section 3.03     Not a Foreign Person.  Mortgagor is not a "foreign
person" within the meaning of the Internal Revenue Code of 1986, as amended
(hereinafter called the "Code"), Sections 1445 and 7701 (i.e. Mortgagor is not
a non-resident alien, foreign corporation, foreign partnership, foreign trust
or foreign estate as those terms are defined in the Code and any regulations
promulgated thereunder).

         Section 3.04     Power to Create Lien and Security.  The Mortgagor
has, in all material respects, full power and lawful authority to grant,
bargain, sell, assign, transfer, mortgage, and convey a security interest in
all of the Mortgaged Property in the manner and form herein provided and
without obtaining the authorization, approval, consent or waiver of any lessor,
sublessor, Governmental Authority or other party or parties whomsoever.

         Section 3.05     Revenue and Cost Bearing Interest.  Mortgagor's
ownership of the Hydrocarbon Property and the undivided interests therein as
specified on the Senior Mortgages Exhibit A and the Additional Exhibit A does,
after giving full effect to all Permitted Encumbrances, afford Mortgagor not
less than those net interests (expressed as a fraction, percentage or decimal)
in the production from or which is allocated to such Hydrocarbon Property
specified as net revenue interest (NRI) on the Senior Mortgages Exhibit A and
the Additional Exhibit A and causes Mortgagor to bear not more than that
portion (expressed as a fraction, percentage or decimal), specified as net
revenue interest (NRI) on the Senior Mortgages Exhibit A and the Additional
Exhibit A, of the costs of drilling, developing and operating the wells
identified on the Senior Mortgages Exhibit A and the Additional Exhibit A.

         Section 3.06     Rentals Paid; Leases in Effect.  All rentals and
royalties due and payable in accordance with the terms of any leases or
subleases comprising any material part of the Hydrocarbon Property have been
duly paid or provided for and all leases or subleases comprising any material
part of the Hydrocarbon Property are in full force and effect.





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<PAGE>   148
         Section 3.07     Operation by Third Parties.  All or portions of the
Mortgaged Property may be comprised of interests in the Hydrocarbon Property
which are other than working interests or which may be operated by a party or
parties other than Mortgagor and with respect to all or any such interests and
properties as may be comprised of interests other than working interests or
which may be operated by parties other than Mortgagor, Mortgagor's covenants as
expressed in this Article III are modified to require that Mortgagor use its
best efforts to obtain compliance with such covenants by the working interest
owners or the operator or operators of such leases or properties.

         Section 3.08     Abandon, Sales.  The Mortgagor will not sell, lease,
assign, transfer or otherwise dispose or abandon any of the Mortgaged Property
except as permitted by the Securities Purchase Documents.

         Section 3.09     Failure to Perform.  Subject to the priority of the
Liens created or evidenced by the Senior Mortgages and any security agreement
or financing statement executed in connection therewith, and to the terms of
the Subordination Agreement, the Mortgagor agrees that if the Mortgagor, after
receipt from Mortgagee of written notice and demand,  fails to perform any act
or to take any action which the Mortgagor is required to perform or take
hereunder or pay any money which the Mortgagor is required to pay hereunder,
each of the Mortgagee and the Trustee in the Mortgagor's name or its or their
own name may, but shall not be obligated to, perform or cause to perform such
act or take such action or pay such money, and any expenses so incurred by
either of them and any money so paid by either of them shall be a demand
obligation owing by the Mortgagor to the Mortgagee or the Trustee, as the case
may be, and each of the Mortgagee and the Trustee, upon making such payment,
shall be subrogated to all of the rights of the Person receiving such payment.
Each amount due and owing by Mortgagor to each of the Mortgagee and the Trustee
pursuant to this Mortgage shall bear interest from the date of such expenditure
or payment or other occurrence which gives rise to such amount being owed to
such Person until paid at the [Post-Default Rate], and all such amounts
together with such interest thereon shall be a part of the Indebtedness
described in Section 1.03 hereof.

                                   ARTICLE IV

                              Rights and Remedies

         Section 4.01     Event of Default.  An "Event of Default" under the
Securities Purchase Documents shall be an Event of Default under this Mortgage.

         Section 4.02     Foreclosure and Sale.  Subject to the priority of the
Liens created or evidenced by the Senior Mortgages and any security agreement
or financing statement executed in connection therewith, and to the terms of
the Subordination Agreement and the Securities Purchase Documents, if an Event
of Default shall occur and be continuing, Mortgagee shall have the right and
option to proceed with foreclosure by directing the Trustee, or his successors
or substitutes in trust, to proceed with foreclosure and to sell, to the extent
permitted by law, all or any portion of the Mortgaged





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<PAGE>   149
Property at one or more sales, as an entirety or in parcels, at such place or
places in otherwise such manner and upon such notice as may be required by law,
or, in the absence of any such requirement, as the Mortgagee may deem
appropriate, and to make conveyance to the purchaser or purchasers.  Where the
Mortgaged Property is situated in more than one county, notice as above
provided shall be posted and filed in all such counties (if such notices are
required by law), and all such Mortgaged Property may be sold in any such
county and any such notice shall designate the county where such Mortgaged
Property is to be sold.  Subject to the priority of the Liens created or
evidenced by the Senior Mortgages and any security agreement or financing
statement executed in connection therewith, and to the terms of the
Subordination Agreement and the Securities Purchase Documents, nothing
contained in this Section 4.02 shall be construed so as to limit in any way the
Trustee's rights to sell the Mortgaged Property, or any portion thereof, by
private sale if, and to the extent that, such private sale is permitted under
the laws of the applicable jurisdiction or by public or private sale after
entry of a judgment by any court of competent jurisdiction so ordering.
Mortgagor hereby irrevocably appoints the Trustee to be the attorney of
Mortgagor and in the name and on behalf of Mortgagor to execute and deliver any
deeds, transfers, conveyances, assignments, assurances and notices which
Mortgagor ought to execute and deliver and do and perform any and all such acts
and things which Mortgagor ought to do and perform under the covenants herein
contained and generally, to use the name of Mortgagor in the exercise of all or
any of the powers hereby conferred on the Trustee.  At any such sale: (i)
whether made under the power herein contained or any other legal enactment, or
by virtue of any judicial proceedings or any other legal right, remedy or
recourse, it shall not be necessary for Trustee to have physically present, or
to have constructive possession of, the Mortgaged Property (Mortgagor hereby
covenanting and agreeing to deliver to Trustee any portion of the Mortgaged
Property not actually or constructively possessed by Trustee immediately upon
demand by Trustee) and the title to and right of possession of any such
property shall pass to the purchaser thereof as completely as if the same had
been actually present and delivered to purchaser at such sale, (ii) each
instrument of conveyance executed by Trustee shall contain a general warranty
of title, binding upon Mortgagor and its successors and assigns, (iii) each and
every recital contained in any instrument of conveyance made by Trustee shall
conclusively establish the truth and accuracy of the matters recited therein,
including, without limitation, nonpayment of the Indebtedness, advertisement
and conduct of such sale in the manner provided herein and otherwise by law and
appointment of any successor Trustee hereunder, (iv) any and all prerequisites
to the validity thereof shall be conclusively presumed to have been performed,
(v) the receipt of Trustee or of such other party or officer making the sale
shall be a sufficient discharge to the purchaser or purchasers for its purchase
money and no such purchaser or purchasers, or its assigns or personal
representatives, shall thereafter be obligated to see to the application of
such purchase money, or be in any way answerable for any loss, misapplication
or nonapplication thereof, (vi) to the fullest extent permitted by law,
Mortgagor shall be completely and irrevocably divested of all of its right,
title, interest, claim and demand whatsoever, either at law or in equity, in
and to the property sold and such sale shall be a perpetual bar both at law and
in equity against Mortgagor, and against any and all other persons claiming or
to claim the property sold or any part thereof, by, through or under Mortgagor,
and (vii) to the extent and under such circumstances as are permitted by law,
Mortgagee may be a purchaser at any such sale, and shall have the right, after
paying or accounting for all costs





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<PAGE>   150
of said sale or sales, to credit the amount of the bid upon the amount of the
Indebtedness (in the order of priority set forth in Section 4.13 hereof) in
lieu of cash payment.

         Section 4.03     Substitute Trustees and Agents.  The Trustee or his
successor or substitute may appoint or delegate any one or more persons as
agent to perform any act or acts necessary or incident to any sale held by
Trustee, including the posting of notices and the conduct of sale, but in the
name and on behalf of Trustee, his successor or substitute.  If Trustee or his
successor or substitute shall have given notice of sale hereunder, any
successor or substitute trustee thereafter appointed may complete the sale and
the conveyance of the property pursuant thereto as if such notice had been
given by the successor or substitute trustee conducting the sale.

         Section 4.04     Judicial Foreclosure; Receivership.  Subject to the
priority of the Liens created or evidenced by the Senior Mortgages and any
security agreement or financing statement executed in connection therewith, and
to the terms of the Subordination Agreement and the Securities Purchase
Documents:  if any of the Indebtedness shall become due and payable and shall
not be promptly paid, the Trustee or Mortgagee shall have the right and power
to proceed by a suit or suits in equity or at law, whether for the specific
performance of any covenant or agreement herein contained or in aid of the
execution of any power herein granted, or for any foreclosure hereunder or for
the sale of the Mortgaged Property under the judgment or decree of any court or
courts of competent jurisdiction, or for the appointment of a receiver pending
any foreclosure hereunder or the sale of the Mortgaged Property under the order
of a court or courts of competent jurisdiction or under executory or other
legal process, or for the enforcement of any other appropriate legal or
equitable remedy.  Any money advanced by the Trustee and/or Mortgagee in
connection with any such receivership shall be a demand obligation (which
obligation Mortgagor hereby expressly promises to pay) owing by Mortgagor to
the Trustee and/or Mortgagee and shall bear interest from the date of making
such advance by the Trustee and/or Mortgagee until paid at the Post Default
Rate.

         Section 4.05     Foreclosure for Installments.  Subject to the
priority of the Liens created or evidenced by the Senior Mortgages and any
security agreement or financing statement executed in connection therewith, and
to the terms of the Subordination Agreement and the Securities Purchase
Documents:  Mortgagee shall also have the option to proceed with foreclosure in
satisfaction of any installments of the Indebtedness which have not been paid
when due either through the courts or by directing the Trustee or his
successors in trust to proceed with foreclosure in satisfaction of the matured
but unpaid portion of the Indebtedness as if under a full foreclosure,
conducting the sale as herein provided and without declaring the entire
principal balance and accrued interest due; such sale may be made subject to
the unmatured portion of the Indebtedness, and any such sale shall not in any
manner affect the unmatured portion of the Indebtedness, but as to such
unmatured portion of the Indebtedness this Mortgage shall remain in full force
and effect just as though no sale had been made hereunder.  It is further
agreed that several sales may be made hereunder without exhausting the right of
sale for any unmatured part of the Indebtedness, it being the purpose hereof to
provide for a foreclosure and sale of the security for any matured portion of
the Indebtedness without





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<PAGE>   151
exhausting the power to foreclose and sell the Mortgaged Property for any
subsequently maturing portion of the Indebtedness.

         Section 4.06     Separate Sales  The Mortgaged Property may be sold in
one or more parcels and in such manner and order as Mortgagee, in its sole
discretion, may elect, it being expressly understood and agreed that the right
of sale arising out of any Event of Default shall not be exhausted by any one
or more sales.

         Section 4.07     Occupancy After Foreclosure.  In the event there is a
foreclosure sale hereunder and at the time of such sale Mortgagor or
Mortgagor's heirs, devisees, representatives, successors or assigns or any
other person claiming any interest in the Mortgaged Property by, through or
under Mortgagor, are occupying or using the Mortgaged Property or any part
thereof, each and all shall immediately become the tenant of the purchaser at
such sale, which tenancy shall be a tenancy from day to day, terminable at the
will of either the landlord or tenant, or at a reasonable rental per day based
upon the value of the property occupied, such rental to be due daily to the
purchaser; to the extent permitted by applicable law, the purchaser at such
sale shall, notwithstanding any language herein apparently to the contrary,
have the sole option to demand immediate possession following the sale or to
permit the occupants to remain as tenants at will.  In the event the tenant
fails to surrender possession of said property upon demand, the purchaser shall
be entitled to institute and maintain a summary action for possession of the
Mortgaged Property (such as an action for forcible entry and detainer) in any
court having jurisdiction.

         Section 4.08     Remedies Cumulative, Concurrent and Nonexclusive.
Every right, power and remedy herein given to the Trustee or Mortgagee shall
subject to the Liens created or evidenced by the Senior Mortgage(s) and to the
terms of the Subordination Agreement, be cumulative and in addition to every
other right, power and remedy herein specifically given or now or hereafter
existing in equity, at law or by statute (including specifically those granted
by the Applicable UCC in effect and applicable to the Mortgaged Property or any
portion thereof) and each and every right, power and remedy whether
specifically herein given or otherwise existing may, subject to the priority of
the Liens created or evidenced by the Senior Mortgages and any security
agreement or financing statement executed in connection therewith, and to the
terms of the Subordination Agreement, be exercised from time to time and so
often and in such order as may be deemed expedient by the Trustee or Mortgagee,
and the exercise, or the beginning of the exercise, of any such right, power or
remedy shall not be deemed a waiver of the right to exercise, at the same time
or thereafter any other right, power or remedy.  No delay or omission by the
Trustee or Mortgagee in the exercise of any right, power or remedy shall impair
any such right, power or remedy or operate as a waiver thereof or of any other
right, power or remedy then or thereafter existing.

         Section 4.09     No Release of Obligations.  Neither Mortgagor, any
guarantor nor any other person hereafter obligated for payment of all or any
part of the Indebtedness shall be relieved of such obligation by reason of (a)
the failure of Trustee to comply with any request of Mortgagor, or any
guarantor or any other person so obligated to foreclose the lien of this
Mortgage or to enforce any





                                       13
<PAGE>   152
provision hereunder or under the Securities Purchase Documents; (b) the
release, regardless of consideration, of the Mortgaged Property or any portion
thereof or interest therein or the addition of any other property to the
Mortgaged Property; (c) any agreement or stipulation between any subsequent
owner of the Mortgaged Property and Mortgagee extending, renewing, rearranging
or in any other way modifying the terms of this Mortgage without first having
obtained the consent of, given notice to or paid any consideration to
Mortgagor, any guarantor or such other person, and in such event Mortgagor,
guarantor and all such other persons shall continue to be liable to make
payment according to the terms of any such extension or modification agreement
unless expressly released and discharged in writing by Mortgagee; or (d) by any
other act or occurrence save and except the complete payment of the
Indebtedness and the complete fulfillment of all obligations hereunder or under
the Securities Purchase Documents.

         Section 4.10     Release of and Resort to Collateral.  Mortgagee may
release, regardless of consideration, any part of the Mortgaged Property
without, as to the remainder, in any way impairing, affecting, subordinating or
releasing the lien or security interest created in or evidenced by this
Mortgage or its stature as, subject to the Liens created or evidenced by the
Senior Mortgage(s) and the terms of the Subordination Agreement, a first and
prior lien and security interest in and to the Mortgaged Property, and without
in any way releasing or diminishing the liability of any person or entity
liable for the repayment of the Indebtedness.  For payment of the Indebtedness,
Mortgagee may resort to any other security therefor held by Mortgagee or
Trustee in such order and manner as Mortgagee may elect.

         Section 4.11     Waiver of Redemption, Notice and Marshalling of
Assets, Etc.  To the fullest extent permitted by law, Mortgagor hereby
irrevocably and unconditionally waives and releases (a) all benefits that might
accrue to Mortgagor by virtue of any present or future moratorium law or other
law exempting the Mortgaged Property from attachment, levy or sale on execution
or providing for any appraisement, valuation, stay of execution, exemption from
civil process, redemption or extension of time for payment and (b) any right to
a marshalling of assets or a sale in inverse order of alienation.  If any law
referred to in this Mortgage and now in force, of which Mortgagor or its
successor or successors might take advantage despite the provisions hereof,
shall hereafter be repealed or cease to be in force, such law shall thereafter
be deemed not to constitute any part of the contract herein contained or to
preclude the operation or application of the provisions hereof.  Provided,
however, that if the laws of any state do not permit the redemption period to
be waived, the redemption period is specifically reduced to the minimum amount
of time allowable by statute, and specifically for any property located in the
State of New Mexico, the redemption period hereunder shall be reduced to one
month.

         Section 4.12     Discontinuance of Proceedings  In case Mortgagee
shall have proceeded to invoke any right, remedy or recourse permitted
hereunder or under the Securities Purchase Documents and shall thereafter elect
to discontinue or abandon same for any reason, Mortgagee shall have the
unqualified right so to do and, in such an event, Mortgagor and Mortgagee shall
be restored to their former positions with respect to the Indebtedness, this
Mortgage, the Securities Purchase





                                       14
<PAGE>   153
Documents, the Mortgaged Property and otherwise, and the rights, remedies,
recourses and powers of Mortgagee shall continue as if same had never been
invoked.

         Section 4.13     Application of Proceeds.  Subject to the priority of
the Liens created or evidenced by the Senior Mortgages and any security
agreement or financing statement executed in connection therewith, and to the
terms of the Subordination Agreement the proceeds of any sale of the Mortgaged
Property or any part thereof and all other monies received by the Trustee or
Mortgagee in any proceedings for the enforcement hereof or otherwise, whose
application has not elsewhere herein been specifically provided for, shall be
applied:

         (a)     first, to the payment of all reasonable expenses incurred by
the Agent or any Noteholder incident to the enforcement of this Mortgage, the
Securities Purchase Documents or any of the Indebtedness (including, without
limiting the generality of the foregoing, expenses of any entry or taking of
possession, of any sale, of advertisement thereof, and of conveyances, and
court costs, compensation of agents and employees, legal fees and a reasonable
commission to the Trustee acting), and to the payment of all other charges,
reasonable expenses, liabilities and advances incurred or made by the Trustee
or Mortgagee under this Mortgage or in executing any trust or power hereunder;

         (b)     second to payment of the Indebtedness in such order and manner
as Mortgagee may elect; and

         (c)     third, to Mortgagor; or as otherwise required by any 
Governmental Requirement.

         Section 4.14     Resignation of Operator.  In addition to all rights
and remedies under this Mortgage, at law and in equity, if any Event of Default
shall occur and Trustee or the Mortgagee shall exercise any possessory remedies
under this Mortgage with respect to any portion of the Hydrocarbon Property (or
Mortgagor shall transfer any Mortgaged Property "in lieu of" foreclosure), the
Mortgagee or the Trustee shall have the right to request that any operator of
any Hydrocarbon Property which is either Mortgagor or any Affiliate of
Mortgagor to resign as operator under the joint operating agreement applicable
thereto, and no later than 60 days after receipt by Mortgagor of any such
request, Mortgagor shall resign (or cause such other party to resign) as
operator of such Hydrocarbon Property.

         Section 4.15     INDEMNITY.  IN CONNECTION WITH ANY ACTION TAKEN BY
THE TRUSTEE AND/OR MORTGAGEE PURSUANT TO THIS MORTGAGE, THE TRUSTEE AND/OR
MORTGAGEE AND THEIR OFFICERS, DIRECTORS, EMPLOYEES, REPRESENTATIVES, AGENTS,
ATTORNEYS, ACCOUNTANTS AND EXPERTS ("INDEMNIFIED PARTIES") SHALL NOT BE LIABLE
FOR ANY LOSS SUSTAINED BY MORTGAGOR RESULTING FROM AN ASSERTION THAT MORTGAGEE
HAS RECEIVED FUNDS FROM THE PRODUCTION OF HYDROCARBONS CLAIMED BY THIRD PERSONS
OR ANY ACT OR OMISSION OF ANY INDEMNIFIED PARTY IN ADMINISTERING, MANAGING,
OPERATING OR CONTROLLING THE MORTGAGED PROPERTY INCLUDING SUCH LOSS WHICH MAY
RESULT FROM





                                       15
<PAGE>   154
THE ORDINARY NEGLIGENCE OF AN INDEMNIFIED PARTY UNLESS SUCH LOSS IS CAUSED BY
THE GROSS NEGLIGENCE, WILLFUL MISCONDUCT OR BAD FAITH OF AN INDEMNIFIED PARTY,
NOR SHALL THE TRUSTEE AND/OR MORTGAGEE BE OBLIGATED TO PERFORM OR DISCHARGE ANY
OBLIGATION, DUTY OR LIABILITY OF MORTGAGOR. MORTGAGOR SHALL AND DOES HEREBY
AGREE TO INDEMNIFY EACH INDEMNIFIED PARTY FOR, AND TO HOLD EACH INDEMNIFIED
PARTY HARMLESS FROM, ANY AND ALL LIABILITY, LOSS OR DAMAGE WHICH MAY OR MIGHT
BE INCURRED BY ANY INDEMNIFIED PARTY BY REASON OF THIS MORTGAGE OR THE EXERCISE
OF RIGHTS OR REMEDIES HEREUNDER; SHOULD THE TRUSTEE AND/OR MORTGAGEE MAKE ANY
EXPENDITURE ON ACCOUNT OF ANY SUCH LIABILITY, LOSS OR DAMAGE, THE AMOUNT
THEREOF, INCLUDING COSTS, EXPENSES AND REASONABLE ATTORNEYS' FEES, SHALL BE A
DEMAND OBLIGATION (WHICH OBLIGATION MORTGAGOR HEREBY EXPRESSLY PROMISES TO PAY)
OWING BY MORTGAGOR TO THE TRUSTEE AND/OR MORTGAGEE AND SHALL BEAR INTEREST FROM
THE DATE EXPENDED UNTIL PAID AT THE POST-DEFAULT RATE, SHALL BE A PART OF THE
INDEBTEDNESS AND SHALL BE SECURED BY THIS MORTGAGE AND ANY OTHER SECURITY
INSTRUMENT.  MORTGAGOR HEREBY ASSENTS TO, RATIFIES AND CONFIRMS ANY AND ALL
ACTIONS OF THE TRUSTEE AND/OR MORTGAGEE WITH RESPECT TO THE MORTGAGED PROPERTY
TAKEN UNDER, AND IN COMPLIANCE WITH THE TERMS OF, THIS MORTGAGE.  THE
LIABILITIES OF THE MORTGAGOR AS SET FORTH IN THIS SECTION 4.15 SHALL SURVIVE
THE TERMINATION OF THIS MORTGAGE.

         Section 4.16     Power of Sale in Oklahoma.  Any sale of any part of
the Mortgaged Property located in the State of Oklahoma shall be made in
conformity to the laws thereof, and it is agreed that the appraisement of any
such properties is expressly waived or not waived at the option of the Agent,
and any such option may be exercised prior to the time judgment is rendered in
any foreclosure hereon. A POWER OF SALE HAS BEEN GRANTED IN THIS MORTGAGE. A
POWER OF SALE MAY ALLOW THE MORTGAGEE TO TAKE THE MORTGAGED PROPERTY AND SELL
IT WITHOUT GOING TO COURT IN A FORECLOSURE ACTION UPON DEFAULT BY GRANTOR UNDER
THIS MORTGAGE.  The parties hereto are cognizant of and acknowledge the
Oklahoma Power of Sale Mortgage Foreclosure Act which went into effect November
1, 1986.  Notwithstanding any provision Article IV to the contrary, it is the
intent of the parties that the provisions herein relating to the power of sale
which are applicable to the Mortgaged Property located in the State of Oklahoma
are subject to the provisions of the Oklahoma Power of Sale Mortgage
Foreclosure Act.  In addition, it is the intent of the parties that the power
of sale granted herein may be exercised by the Mortgagee pursuant to the terms
and provisions of the Oklahoma Power of Sale Mortgage Foreclosure Act.





                                       16
<PAGE>   155
                                   ARTICLE V

                                  The Trustee

         Section 5.01     Duties, Rights, and Powers of Trustee.  It shall be
no part of the duty of the Trustee to see to any recording, filing or
registration of this Mortgage or any other instrument in addition or
supplemental thereto, or to give any notice thereof, or to see to the payment
of or be under any duty in respect of any tax or assessment or other
governmental charge which may be levied or assessed on the Mortgaged Property,
or any part thereof, or against Mortgagor, or to see to the performance or
observance by Mortgagor of any of the covenants and agreements contained
herein.  The Trustee shall not be responsible for the execution, acknowledgment
or validity of this Mortgage or of any instrument in addition or supplemental
hereto or for the sufficiency of the security purported to be created hereby,
and makes no representation in respect thereof or in respect of the rights of
Mortgagee.  The Trustee shall have the right to advise with counsel upon any
matters arising hereunder and shall be fully protected in relying as to legal
matters on the advice of counsel.  The Trustee shall not incur any personal
liability hereunder except for Trustee's own gross negligence, bad faith and/or
willful misconduct; and the Trustee shall have the right to rely on any
instrument, document or signature authorizing or supporting any action taken or
proposed to be taken by him hereunder, believed by him in good faith to be
genuine.

         Section 5.02     Successor Trustee.  The Trustee may resign by written
notice addressed to Mortgagee or be removed at any time with or without cause
by an instrument in writing duly executed on behalf of Mortgagee.  In case of
the death, resignation or removal of the Trustee, a successor trustee may be
appointed by Mortgagee by instrument of substitution complying with any
applicable requirements of law, or, in the absence of any such requirement,
without other formality than appointment and designation in writing.  Written
notice of such appointment and designation shall be given by Mortgagee to
Mortgagor, but the validity of any such appointment shall not be impaired or
affected by failure to give such notice or by any defect therein.  Such
appointment and designation shall be full evidence of the right and authority
to make the same and of all the facts therein recited, and, upon the making of
any such appointment and designation, this Mortgage shall vest in the successor
trustee all the estate and title in and to all of the Mortgaged Property, and
the successor trustee shall thereupon succeed to all of the rights, powers,
privileges, immunities and duties hereby conferred upon the Trustee named
herein, and one such appointment and designation shall not exhaust the right to
appoint and designate a successor trustee hereunder but such right may be
exercised repeatedly as long as any Indebtedness remains unpaid hereunder.  To
facilitate the administration of the duties hereunder, Mortgagee may appoint
multiple trustees to serve in such capacity or in such jurisdictions as
Mortgagee may designate.

         Section 5.03     Retention of Moneys.  All moneys received by Trustee
shall, until used or applied as herein provided, be held in trust for the
purposes for which they were received, but need not be segregated in any manner
from any other moneys (except to the extent required by law), and Trustee shall
be under no liability for interest on any moneys received by him hereunder.





                                       17
<PAGE>   156
                                   ARTICLE VI

                                 Miscellaneous

         Section 6.01     Instrument Construed as Mortgage, Etc.  With respect
to any portions of the Mortgaged Property located in any state or other
jurisdiction the laws of which do not provide for the use or enforcement of a
deed of trust or the office, rights and authority of the Trustee as herein
provided, the general language of conveyance hereof to the Trustee is intended
and the same shall be construed as words of mortgage unto and in favor of
Mortgagee and the rights and authority granted to the Trustee herein may be
enforced and asserted by Mortgagee in accordance with the laws of the
jurisdiction in which such portion of the Mortgaged Property is located and the
same may be foreclosed at the option of Mortgagee as to any or all such
portions of the Mortgaged Property in any manner permitted by the laws of the
jurisdiction in which such portions of the Mortgaged Property is situated.
This Mortgage may be construed as a mortgage, deed of trust, chattel mortgage,
conveyance, assignment, security agreement, pledge, financing statement,
hypothecation or contract, or any one or more of them, in order fully to
effectuate the lien hereof and the purposes and agreements herein set forth.

         Section 6.02     Release of Mortgage.  If all Indebtedness secured
hereby shall be paid and the Securities Purchase Documents terminated,
Mortgagee shall forthwith cause satisfaction and discharge of this Mortgage to
be entered upon the record at the expense of Mortgagor and shall execute and
deliver or cause to be executed and delivered such instruments of satisfaction
and reassignment as may be appropriate.  Otherwise, this Mortgage shall remain
and continue in full force and effect.

         Section 6.03     Severability.  If any provision hereof is invalid or
unenforceable in any jurisdiction, the other provisions hereof shall remain in
full force and effect in such jurisdiction and the remaining provisions hereof
shall be liberally construed in favor of the Trustee and Mortgagee in order to
effectuate the provisions hereof, and the invalidity or unenforceability of any
provision hereof in any jurisdiction shall not affect the validity or
enforceability of any such provision in any other jurisdiction.

         Section 6.04     Successors and Assigns of Parties.  The term
"Mortgagee" as used herein shall mean and include any legal owner, holder,
assignee or pledgee of any of the Indebtedness secured hereby (including,
without limitation, the Agent and the Noteholders).  The terms used to
designate Trustee, Mortgagee and Mortgagor shall be deemed to include the
respective heirs, legal representatives, successors and assigns of such
parties.

         Section 6.05     Satisfaction of Prior Encumbrance.  To the extent
that proceeds of the Securities Purchase Documents are used to pay indebtedness
secured by any outstanding lien, security interest, charge or prior encumbrance
against the Mortgaged Property, including the Senior





                                       18
<PAGE>   157
Mortgages but subject to the Subordination Agreement, such proceeds have been
advanced by Mortgagee at Mortgagor's request, and Mortgagee shall be subrogated
to any and all rights, security interests and liens owned by any owner or
holder of such outstanding liens, security interests, charges or encumbrances,
irrespective of whether said liens, security interests, charges or encumbrances
are released, and it is expressly understood that, in consideration of the
payment of such other indebtedness by Mortgagee, Mortgagor hereby waives and
releases all demands and causes of action for offsets and payments to, upon and
in connection with the said indebtedness.

         Section 6.06     Subrogation of Trustee.  This Mortgage is made with
full substitution and subrogation of the Trustee and his successors in this
trust and his and their assigns in and to all covenants and warranties by
others heretofore given or made in respect of the Mortgaged Property or any
part thereof.

         Section 6.07     Nature of Covenants.  The covenants and agreements
herein contained shall constitute covenants running with the land and interests
covered or affected hereby and shall be binding upon the heirs, legal
representatives, successors and assigns of the parties hereto.

         Section 6.08     Notices.  All notices, requests, consents, demands
and other communications required or permitted hereunder shall be in writing
and shall be deemed sufficiently given or furnished if delivered by registered
or certified United States mail, postage prepaid, or by personal service
(including express or courier service) at the addresses specified in the first
paragraph of this Mortgage (unless changed by similar notice in writing given
by the particular party whose address is to be changed). Any such notice or
communication shall be deemed to have been given either at the time of personal
delivery or, in the case of delivery at the address and in the manner provided
herein, upon receipt; provided that, service of notice as required by the laws
of any state in which portions of the Mortgaged Property may be situated shall
for all purposes be deemed appropriate and sufficient with the giving of such
notice.

         Section 6.09     Counterparts.  This Mortgage is being executed in
several counterparts, all of which are identical, except that to facilitate
recordation, if the Mortgaged Property is situated in more than one county,
descriptions of only those portions of the Mortgaged Property located in the
county in which a particular counterpart is recorded shall be attached as the
Additional Exhibit A thereto.  Attached to certain of those counterparts to be
recorded in the state of Oklahoma will be Exhibit A-1 which will contain the
descriptions of those portions of the Mortgaged Property located in Oklahoma
described in the Senior Mortgages Exhibit A. A complete Additional Exhibit A
will be attached to that certain counterpart to be attached to a Financing
Statement and filed with the Secretary of State of Texas in the Uniform
Commercial Code Records.  Each of such counterparts shall for all purposes be
deemed to be an original and all such counterparts shall together constitute
but one and the same instrument.

         SECTION 6.10     EXCULPATION PROVISIONS.  EACH OF THE PARTIES HERETO
SPECIFICALLY AGREES THAT IT HAS A DUTY TO READ THIS MORTGAGE; AND AGREES THAT
IT IS CHARGED WITH





                                       19
<PAGE>   158
NOTICE AND KNOWLEDGE OF THE TERMS OF THIS MORTGAGE; THAT IT HAS IN FACT READ
THIS MORTGAGE AND IS FULLY INFORMED AND HAS FULL NOTICE AND KNOWLEDGE OF THE
TERMS, CONDITIONS AND EFFECTS OF THIS MORTGAGE; THAT IT HAS BEEN REPRESENTED BY
INDEPENDENT LEGAL COUNSEL OF ITS CHOICE THROUGHOUT THE NEGOTIATIONS PRECEDING
ITS EXECUTION OF THIS MORTGAGE; AND HAS RECEIVED THE ADVICE OF ITS ATTORNEY IN
ENTERING INTO THIS MORTGAGE; AND THAT IT RECOGNIZES THAT CERTAIN OF THE TERMS
OF THIS MORTGAGE RESULT IN ONE PARTY ASSUMING THE LIABILITY INHERENT IN SOME
ASPECTS OF THE TRANSACTION AND RELIEVING THE OTHER PARTY OF ITS RESPONSIBILITY
FOR SUCH LIABILITY.  EACH PARTY HERETO AGREES AND COVENANTS THAT IT WILL NOT
CONTEST THE VALIDITY OR ENFORCEABILITY OF ANY EXCULPATORY PROVISION OF THIS
MORTGAGE ON THE BASIS THAT THE PARTY HAD NO NOTICE OR KNOWLEDGE OF SUCH
PROVISION OR THAT THE PROVISION IS NOT "CONSPICUOUS."

         Section 6.11     Subordination.  The rights and remedies of the
Mortgagee, the Agent and the Noteholders under this Mortgage are subject to the
terms and conditions of the Subordination Agreement.

         WITNESS THE EXECUTION HEREOF, this ________ day of ___________, 1998,
to be effective as of ________________, 1998 (the "Effective Date").

                                        MORTGAGOR:

                                        BRIGHAM OIL & GAS, L.P.
                                        By:  Brigham, Inc., its General Partner



                                        By:
                                           --------------------------------
                                        Name:  Craig M. Fleming
                                        Title:  Chief Financial Officer

                                        MORTGAGEE:


                                        -----------------------------------


                                        By:
                                           --------------------------------
                                        Name:
                                             ------------------------------
                                        Title:
                                              -----------------------------





                                       20
<PAGE>   159
STATE OF TEXAS            )
                          )
COUNTY OF HARRIS          )


                                   NEW MEXICO

         The foregoing instrument was acknowledged before me on ______________,
1998 by Craig M. Fleming, Chief Financial Officer of BRIGHAM, INC., a Nevada
corporation, as general partner of BRIGHAM OIL & GAS, L.P., a Delaware limited
partnership, on behalf of such corporation, as general partner of the limited
partnership.

                                    OKLAHOMA

         This instrument was acknowledged before me on _____________, 1998 by
Craig M. Fleming, Chief Financial Officer of BRIGHAM, INC., a Nevada
corporation, as general partner of BRIGHAM OIL & GAS, L.P., a Delaware limited
partnership, on behalf of the corporation, as general partner of the limited
partnership.

                                     TEXAS

         This instrument was acknowledged before me on ___________, 1998 by
Craig M. Fleming, Chief Financial Officer of BRIGHAM, INC., a Nevada
corporation, as general partner of BRIGHAM OIL & GAS, L.P., a Delaware limited
partnership, on behalf of such corporation, as general partner of the limited
partnership.



                                                -------------------------------
                                                Notary Public in and for the
                                                State of Texas

                                                Notarial Seal:





                                       21
<PAGE>   160
STATE OF TEXAS            )
                          )
COUNTY OF HARRIS          )


                                   NEW MEXICO

         The foregoing instrument was acknowledged before me on ___________,
1998 by __________________, ________________ of __________________, a
________________, on behalf of such _______________.


                                    OKLAHOMA

         This instrument was acknowledged before me on ___________, 1998 by
__________________, _______________ of __________________, a ____________, on
behalf of the __________________.


                                     TEXAS

         This instrument was acknowledged before me on ___________, 1998 by
__________________, _______________ of __________________, a ____________, on
behalf of the __________________.



                                                -------------------------------
                                                Notary Public in and for the
                                                State of Texas

                                                Notarial Seal:






                                       22
<PAGE>   161
                              FINANCING STATEMENT


         This Financing Statement is presented to a Filing Officer for filing
pursuant to the Uniform Commercial Code.

1.       The name and address of the Debtor is:

                 BRIGHAM OIL & GAS, L.P.
                 6300 Bridge Point Parkway
                 Building 2, Suite 500
                 Austin, Texas  78730

2.       The name and address of Secured Party is:

                 ----------------------------

                 ----------------------------

                 ----------------------------

                 ----------------------------

3.       This Financing Statement covers the following Collateral:

         All of Debtor's rights, titles and interests in and to the accounts,
         equipment, goods, fixtures, general intangibles, inventory and any and
         all other personal property of any kind or character described in and
         covered by the Mortgage, Deed of Trust, Assignment of Production,
         Security Agreement and Financing Statement from Debtor to the Trustee
         named therein and Secured Party, a copy of which instrument is
         attached hereto as Exhibit "A" and made a part hereof for all
         purposes, and the proceeds and products of such personal property.

                                        DEBTOR:

                                        BRIGHAM OIL & GAS, L.P.

                                        By: Brigham, Inc., its General Partner



                                        By:
                                           -----------------------------
                                        Name: Craig M. Fleming 
                                        Title: Chief Financial Officer





                                       23
<PAGE>   162

                                   EXHIBIT G

                                Re: $50,000,000
                          Brigham Exploration Company
                   Senior Subordinated Secured Notes due 2003
                                 (the "Notes")

                           ACCEPTANCE OF APPOINTMENT

     FOR GOOD AND VALUABLE CONSIDERATION, the receipt of which is hereby
acknowledged, First Union National Bank, a national banking association (the
"Successor Trustee"), does hereby accept its appointment upon the terms
specified in Section 12.13 of the Indenture securing the referenced Notes, and
does hereby irrevocably agree (subject to its rights of resignation described
below) to assume the responsibilities, rights, powers and obligations of the
Trustee for the Notes immediately upon its receipt of notice from any person of
the resignation of Chase Bank of Texas, National Association as Trustee,
pursuant to Section 12.13 of the Indenture. Promptly upon receipt of such
notice, the Successor Trustee will notify the resigning Trustee, the Agent and
the Noteholders of its assumption of the duties of Trustee.

     The Successor Trustee hereby reserves the right to resign, and does hereby
acknowledge that it may be removed, in the same manner as is provided for the
resignation and removal of the Trustee pursuant to Section 12.08 of the
Indenture; provided that no such resignation or removal shall become effective
until a successor to the Successor Trustee shall have been appointed and shall
have accepted its appointment in the manner described in Section 12.08 of the
Indenture.

     IN WITNESS WHEREOF, the Successor Trustee has caused this Acceptance of
Appointment to be executed by its duly authorized officer as of the ____ day of
August, 1998.


                                                     FIRST UNION NATIONAL BANK

                                                     By: 
                                                         ----------------------

                                                     Name:
                                                           --------------------
     
                                                     Title: 
                                                            -------------------

Address of Successor Trustee:

225 Water Street, 3rd Floor
Jacksonville, Florida 32202-0122
Telephone: (904) 361-3174
Telecopy: (904) 361-7735