<PAGE>   1
                                                                   EXHIBIT 10.34

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                         SECURITIES PURCHASE AGREEMENT

                                    BETWEEN

                          BRIGHAM EXPLORATION COMPANY

                                      AND

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


                                      AND

                              -------------------
                          DATED AS OF AUGUST __, 1998



            $50,000,000 SENIOR SUBORDINATED SECURED NOTES DUE 2003,

            WARRANTS TO PURCHASE __________ SHARES OF COMMON STOCK;

                                      AND

                ACQUISITION OF _________ SHARES OF COMMON STOCK


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                                TABLE OF CONTENTS

<TABLE>
<S>                                                                                                              <C>
ARTICLE I
         DEFINITIONS..............................................................................................1
         Section 1.01      Definitions............................................................................1

ARTICLE II
         ISSUANCE OF SECURITIES; RIGHTS OF PURCHASERS............................................................10
         Section 2.01      Issuance of Securities................................................................10
         Section 2.02      The Closing; Funding Date.............................................................11
         Section 2.03      Delivery..............................................................................11
         Section 2.04      Payment...............................................................................11
         Section 2.05      Tax Matters...........................................................................11
         Section 2.06      Rights of Purchasers..................................................................12

ARTICLE III
         SECURITY FOR THE OBLIGATIONS ...........................................................................12
         Section 3.01      Security..............................................................................12

ARTICLE IV
         REPRESENTATIONS AND WARRANTIES OF THE SELLER............................................................12
         Section 4.01      Corporate Existence...................................................................12
         Section 4.02      Financial Condition...................................................................13
         Section 4.03      Litigation............................................................................13
         Section 4.04      No Breach.............................................................................13
         Section 4.05      Authority.............................................................................14
         Section 4.06      Approvals.............................................................................14
         Section 4.07      Use of Loans..........................................................................14
         Section 4.08      ERISA.................................................................................14
         Section 4.09      Taxes.................................................................................15
         Section 4.10      Titles, etc...........................................................................15
         Section 4.11      No Material Misstatements.............................................................16
         Section 4.12      Investment Company Act................................................................17
         Section 4.13      Public Utility Holding Company Act....................................................17
         Section 4.14      Subsidiaries..........................................................................17
         Section 4.15      Location of Business and Offices......................................................17
         Section 4.16      Defaults..............................................................................17
         Section 4.17      Environmental Matters.................................................................17
         Section 4.18      Compliance with the Law...............................................................18
         Section 4.19      Insurance.............................................................................19
         Section 4.20      Hedging Agreements....................................................................19
         Section 4.21      Restriction on Liens..................................................................20
</TABLE>



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<TABLE>
<S>                                                                                                              <C>
         Section 4.22      Material Agreements...................................................................20
         Section 4.23      Gas Imbalances........................................................................20
         Section 4.24      Capitalization........................................................................20
         Section 4.25      Acquired Shares.......................................................................20
         Section 4.26      Warrant Shares........................................................................21
         Section 4.27      No Restrictions.......................................................................21
         Section 4.28      Certain Fees..........................................................................21

ARTICLE V
         REPRESENTATIONS AND WARRANTIES OF THE PURCHASERS........................................................21
         Section 5.01      Investment............................................................................21
         Section 5.02      Nature of Purchasers..................................................................22
         Section 5.03      Receipt of Information; Authorization.................................................22

ARTICLE VI
         CONDITIONS PRECEDENT TO FUNDING.........................................................................22
         Section 6.01      Conditions Precedent to Obligations of the Purchasers.................................22
         Section 6.02      Conditions Precedent to Obligations of the Seller.....................................25
         Section 6.03      Conditions Precedent to the Obligations of Purchasers and Seller......................26

ARTICLE VII
         AFFIRMATIVE COVENANTS...................................................................................26
         Section 7.01      Warrants..............................................................................26
         Section 7.02      Hart-Scott-Rodino Compliance..........................................................26
         Section 7.03      Board Representation..................................................................27
         Section 7.04      Common Stock; Dividends; Voting Rights................................................27

ARTICLE VIII
         [OMITTED BY THE PARTIES HERETO..........................................................................27

ARTICLE IX
         [OMITTED BY THE PARTIES HERETO].........................................................................27

ARTICLE X
          .......................................................................................................27

ARTICLE XI
         [OMITTED BY THE PARTIES HERETO..........................................................................27

ARTICLE XII
         MISCELLANEOUS...........................................................................................28
         Section 12.01     Interpretation and Survival of Provisions.............................................28
         Section 12.02     Costs, Expenses and Taxes.............................................................28
</TABLE>



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<TABLE>
<S>                                                                                                              <C>
         Section 12.03     No Waiver; Modifications in Writing...................................................29
         Section 12.04     Binding Effect; Assignment............................................................30
         Section 12.05     Replacement Securities................................................................30
         Section 12.06     Communications........................................................................30
         Section 12.07     Governing Law.........................................................................31
         Section 12.08     Arbitration...........................................................................31
         Section 12.09     Execution in Counterparts.............................................................32
</TABLE>

Exhibits:

Exhibit A      -        Form of Warrants


Schedules:

Schedule 4.02  -        Liabilities
Schedule 4.03  -        Litigation
Schedule 4.09  -        Taxes
Schedule 4.10  -        Titles, Etc.
Schedule 4.14  -        Subsidiaries and Addresses
Schedule 4.19  -        Insurance
Schedule 4.20  -        Hedging Agreements
Schedule 4.22  -        Material Agreements
Schedule 4.23  -        Gas Imbalances
Schedule 4.24  -        Voting Agreements; Registration Rights



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                          SECURITIES PURCHASE AGREEMENT

         SECURITIES PURCHASE AGREEMENT, dated as of August __, 1998 (this
"Agreement"), among BRIGHAM EXPLORATION COMPANY, a Delaware corporation, 
__________ ., a _________________ ("___") and _____________________ , a
____________________________ ("_____").

         In consideration of the mutual covenants and agreements set forth
herein and for good and valuable consideration, the receipt of which is hereby
acknowledged, the parties agree as follows:

                                    ARTICLE I
                                   DEFINITIONS

         Section 1.01 Definitions. As used in this Agreement, and unless the
context requires a different meaning, the following terms have the meanings
indicated:

         "Acquired Shares" means ____________ shares of Common Stock acquired by
the Purchasers on the Funding Date in accordance with Section 2.01 and any
additional shares of Common Stock of the Seller issued to the Purchasers after
the Funding Date in accordance with Section 2.01(ii).

         "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 is the sole general partner of a limited partnership, or which owns
directly or indirectly 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" is defined in the Indenture.

         "Average Share Price" means $_____.

         "Basic Documents" means, collectively, this Agreement, the other Loan 
Documents, the Structuring Fee Agreement and the Equity Documents.

         "Board of Directors" means the Board of Directors of the Seller.



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         "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 Opportunities
Shareholders' Agreement dated as of even date herewith between the Purchasers
and the Seller.

         "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.

         "Closing" has the meaning provided therefor in Section 2.02.

         "Closing Date" means the date upon which the Closing occurs as provided
in Section 2.02.

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

         "Collateral" is defined in the Indenture.

         "Collateral Documents" is defined in the Indenture.

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

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

         "Consolidated Subsidiaries" shall mean each Subsidiary of the Seller
(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 Seller in accordance with GAAP.

         "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 past due 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; (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



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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 and fees (other
than past due 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 Seller 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 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.

         "Designee" shall have the meaning set forth in Section 7.03.

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

         "Employee Plan" means any employee benefit plan, program or policy with
respect to which the Seller 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 Seller or any Subsidiary is conducting or at any time has conducted
business, or where any Property of the Seller 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,



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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 Seller 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.

         "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 Seller or any Subsidiary of the Seller
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.

         "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,



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<PAGE>   9

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.

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

         "Financing Agreement" means an agreement between the Seller and
_________________ pursuant to which the Seller grants to _________________ the
right and option to participate during the three years following the Closing
Date for up to 20% on any public or private (e.g. 144A) high yield debt offering
by the Seller with gross proceeds in excess of $50,000,000.

         "Funding Date" means the first Business Day following the date all of
the conditions precedent to funding in Article VI 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 Seller,
the Subsidiaries or any of their Property or any Purchaser.

         "Government Requirement" means any law, statute, code, ordinance,
order, determination, rule, regulation, judgment, decree, injunction, franchise,
permit, certificate, license, authorization or other directive or requirement
(in the case of banking regulatory authorities whether or not having the force
of law), including without limitation, Environmental Laws, energy regulations
and occupational, safety and health standards or controls of any Governmental
Authority.

         "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 the Loan Documents.



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         "Guaranty Agreements" means the agreements executed by the Guarantors
in form and substance satisfactory to the Trustee and the Purchasers
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.

         "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 that certain Indenture dated as of August ___, 1998,
executed by Seller.

         "Investment Unit" has the meaning provided therefor in Section 2.05 of
this Agreement.

         "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 Agreement, 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 Agreement, the 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 Seller
or any Subsidiary or Affiliate of the Seller (other than the Equity Documents
and any assignments, participation or similar agreements between any Purchaser
and any other lender or creditor with respect to any Obligations pursuant to
this Agreement) in connection with, or as security for the payment or
performance of, the Notes or this Agreement, as such agreements may be amended,
supplemented or restated from time to time.



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<PAGE>   11

         "Majority Purchasers" means, at any time, the Purchasers holding more
than 50% of the Warrants.

         "Material Adverse Effect" means any material and adverse effect on (i)
the assets, liabilities, financial condition, business, operations or affairs of
the Seller 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 Seller 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.

         "Mortgage" is defined in the Indenture.

         "Mortgaged Property" means the Property owned by the Seller 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.

         "Notes" means the Senior Subordinated Secured Notes issued pursuant to
Section 2.03 of this Agreement and the Indenture, in the aggregate face amount
of $50,000,000, dated as of the date hereof, made by the Seller and initially
payable to the order of the Purchasers in their respective Participations.

         "Noteholders" means, from time to time, the holders of the Notes.

         "Obligations" means any and all amounts, liabilities and obligations
owing from time to time by Seller to the Agent or the Noteholders, pursuant to
any of the Loan 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.

         "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,



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<PAGE>   12



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.

         "Participation" means, for each Purchaser, such Purchaser's
proportionate share of the Obligations and the Warrants. As of the Effective
Date, ECT's Participation shall be 25% and JEDI- II's Participation shall be
75%.

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

         "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 Seller, 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 Seller, 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.

         "Purchasers" means ___ and ______ and/or, to the extent then
applicable, each assignee of ___ or _______ or their respective successors or
assigns pursuant to Section 12.04.

         "Registration Rights Agreement" means the Registration Rights Agreement
dated as of the date hereof, made by the Seller in favor of the Purchasers
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.



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<PAGE>   13

         "Reserve Report" is defined in the Indenture.

         "Responsible Officer" means, as to any Person, the Chief Executive
Officer, the President or any Vice President of such Person and the Chief
Financial Officer of such Person. Unless otherwise specified, all references to
a Responsible Officer herein shall mean a Responsible Officer of the Seller.

         "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.

         "Seller" means Brigham Exploration Company, a Delaware corporation.

         "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 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 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 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).



                                       -9-

<PAGE>   14



         "Structuring Fee Agreement" means the agreement between the Seller and
____________________ dated as of the date hereof.

         "Subordination Agreement" means the Intercreditor Subordination
Agreement dated as of even date herewith, by and among the Trustee, the Senior
Loan Agent, the Senior Lenders, the Agent, the Purchasers, the Seller and
certain Subsidiaries, 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 Seller. Quest Resources L.L.C. and Venture Acquisitions L.P.
shall not be considered Subsidiaries of Seller.

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

         "Trustee" means the Trustee as defined in the Indenture.

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

         "Warrants" means the Warrants issued by the Seller to the Purchasers in
their respective Participations pursuant to Section 2.03, for the purchase of an
aggregate of __________ shares of Common Stock, and any Warrants issued upon the
transfer thereof or in substitution therefor, pursuant to the Warrant
Certificates to be issued to ECT and JEDI-II, forms of which are attached hereto
as Exhibit A.

         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 by the Seller hereunder shall be prepared, in
accordance with GAAP, applied on a basis consistent with the Financial
Statements (except for changes concurred with by the Seller's independent public
accountants).




                                      -10-


<PAGE>   15

                                   ARTICLE II
                  ISSUANCE OF SECURITIES; RIGHTS OF PURCHASERS

         Section 2.01 Issuance of Securities. Subject to the terms and
conditions herein set forth, the Seller agrees that it will issue the Securities
to the Purchasers and the Purchasers agree that they shall each purchase the
Securities from the Seller for an aggregate cash consideration of $50,000,000,
as follows:

                           (i) The Notes and the Warrants will be purchased by
                  the Purchasers in their respective participations and sold for
                  an aggregate cash consideration of $40,000,000.

                           (ii) The Acquired Shares will be purchased by the
                  Purchasers or their respective Affiliates for a total cash
                  consideration of $10,000,000. The number of Acquired Shares to
                  be purchased and sold on the Funding Date shall be determined
                  by dividing the $10,000,000 purchase price by the Average
                  Share Price. If within 180 days following the Funding Date the
                  Seller enters into an agreement to issue or issues new Common
                  Stock for a price per share that is less than the Average
                  Share Price (a "Post Funding Sale Price"), the Seller shall,
                  contemporaneously with the issuance of such new Common Stock,
                  issue and deliver to the Purchasers or their respective
                  Affiliates additional shares of Common Stock (which shall be
                  deemed additional Acquired Shares) such that, after issuance
                  and delivery of such additional Acquired Shares, the total
                  number of Acquired Shares received by the Purchasers or their
                  respective Affiliates multiplied by the Post Funding Date Sale
                  Price, shall aggregate $10,000,000.

         Section 2.02      The Closing; Funding Date.

                  (a) The execution of the Basic Documents and all other
instruments required pursuant to Section 6.01 will take place at a closing (the
"Closing") to be held at the offices of Bracewell & Patterson, L.L.P. on such
date as the Seller and the Purchasers shall agree. The date and time at which
the Closing occurs is the "Closing Date".

                  (b) Delivery of the Securities by the Seller to the
Purchasers, and payment by the Purchasers to the Seller of the consideration
therefor as set forth in Section 2.01, shall occur on the Funding Date.

         Section 2.03 Delivery. Delivery of the Securities pursuant to this
Agreement shall be made on the Funding Date by the Seller delivering to the
Purchasers, against payment of the purchase price therefor, as follows: (i) one
Note executed by the Seller in the face amount of $___________, payable to the
order of ___ and one Note executed by the Seller in the face amount of
$_____________, payable to the order of ______, (ii) one certificate executed by
the Seller representing ____'s Participation in the Warrants and one certificate
executed by the Seller




                                      -11-

<PAGE>   16

 representing ______'s Participation in the Warrants, registered in the names of
____ and ______, respectively (or such other Person as either Purchaser may have
designated in writing to the Seller at least three Business Days prior to the
Funding Date) and (iii) a certificate or certificates of Common Stock executed
by the Seller representing the Purchasers and/or their respective Affiliates
share of the Acquired Shares registered in the name(s) of the Purchasers and/or
their respective Affiliates (or such other Person as either Purchaser may have
designated in writing to the Seller at least three Business Days prior to the
Funding Date).

         Section 2.04 Payment. Payment of the consideration for the Securities
shall be made on the Funding Date by wire transfer of immediately available
funds to such account of the Seller as shall have been designated to ECT at
least two Business Days prior to the Funding Date.

         Section 2.05 Tax Matters. The Seller and the Purchasers agree as
follows: (i) Purchasers' acquisition of the Securities constitutes the purchase
of an "investment unit" (the "Investment Unit") for purposes of Treas. Reg.
ss.1.1273-2(h)(1); (ii) the issue price of the Investment Unit is $50,000,000,
as determined in accordance with Treas. Reg. ss.1.1273-2(a)(1); (iii) the issue
price for the Investment Unit shall be allocated among the Notes, the Warrants,
and the Acquired Shares in accordance with their relative fair market values, as
required by Treas. Reg. ss.1.1273-2(h)(1); and (iv) the parties agree that the
issue price shall be allocated among the Notes, the Warrants, and the Acquired
Shares as follows and the parties shall be bound by such allocation for all
tax-related purposes:

               Notes:                             $_________
               Warrants:                          $_________
               Acquired Shares:                   $10,000,000

         Section 2.06 Rights of Purchasers. The Purchasers shall have such
rights with respect to the registration of the Warrant Shares and the Acquired
Shares under the Securities Act and state securities laws as are set forth in
the Registration Rights Agreement, which shall be executed by the Seller and the
Purchasers at the Closing.

                                   ARTICLE III
                          SECURITY FOR THE OBLIGATIONS

         Section 3.01 Security. The Obligations shall be secured by the
Collateral and the Collateral Documents in accordance with the Indenture.




                                      -12-

<PAGE>   17

                                   ARTICLE IV
                  REPRESENTATIONS AND WARRANTIES OF THE SELLER

         The Seller represents and warrants to the Purchasers, for the benefit
of each of the holders of the Notes, the holders of the Warrants and the holders
of the Acquired Shares, which representations and warranties shall survive the
execution of any Basic Document, that as of the date of this Agreement:

         Section 4.01 Corporate Existence. The Seller: (i) is a corporation duly
organized, legally existing and in good standing under the laws of the State of
Delaware; (ii) has all requisite power, and has all material governmental
licenses, authorizations, consents and approvals necessary to own its assets and
carry on its business as now being or as proposed to be conducted; and (iii) is
qualified to do business in all jurisdictions in which the nature of the
business conducted by it makes such qualifications necessary and where failure
so to qualify would have a Material Adverse Effect. Brigham, Inc.: (i) is a
corporation duly organized, legally existing and in good standing under the laws
of the State of Nevada; (ii) has all requisite power, and has all material
governmental licenses, authorizations, consents and approvals necessary to own
its assets and carry on its business as now being or as proposed to be
conducted; and (iii) is qualified to do business in all jurisdictions in which
the nature of the business conducted by it makes such qualifications necessary
and where failure so to qualify would have a Material Adverse Effect. Each of
Brigham Holdings I, LLC and Brigham Holdings II, LLC: (i) is a limited liability
company duly organized, legally existing and in good standing under the laws of
the State of Nevada; (ii) has all requisite power, and has all material
governmental licenses, authorizations, consents and approvals necessary to own
its assets and carry on its business as now being or as proposed to be
conducted; and (iii) is qualified to do business in all jurisdictions in which
the nature of the business conducted by it makes such qualifications necessary
and where failure so to qualify would have a Material Adverse Effect. Brigham
Oil & Gas, L.P.: (i) is a limited partnership duly organized, legally existing
and in good standing under the laws of the State of Delaware; (ii) has all
requisite power, and has all material governmental licenses, authorizations,
consents and approvals necessary to own its assets and carry on its business as
now being or as proposed to be conducted; and (iii) is qualified to do business
in all jurisdictions in which the nature of the business conducted by it makes
such qualifications necessary and where failure so to qualify would have a
Material Adverse Effect.

         Section 4.02 Financial Condition. The audited consolidated balance
sheet of the Seller and its Consolidated Subsidiaries as at December 31, 1997
and the related consolidated statement of income, stockholders' equity and cash
flow of the Seller and its Consolidated Subsidiaries for the fiscal year ended
on said date, with the opinion thereon of Price Waterhouse, heretofore furnished
to the Purchasers and the unaudited consolidated balance sheet of the Seller and
its Consolidated Subsidiaries as at June 30, 1998, and their related
consolidated statements of income, stockholders' equity and cash flow of the
Seller and its Consolidated Subsidiaries for the six-month period ended on such
date heretofore furnished to the Purchasers, are complete and correct and fairly
present the consolidated financial condition of the Seller and its Consolidated
Subsidiaries as at said dates and the results of its operations for the fiscal
year and the six-month period on said dates, all in




                                      -13-

<PAGE>   18

accordance with GAAP, as applied on a consistent basis (subject, in the case of
the interim financial statements, to normal year-end adjustments). Neither the
Seller nor any Consolidated Subsidiary has on the Closing Date any material
Debt, Trade Payables, contingent liabilities, liabilities for taxes, unusual
forward or long-term commitments or unrealized or anticipated losses from any
unfavorable commitments, except as referred to or reflected or provided for in
the Financial Statements or in Schedule 4.02. Since June 30, 1998, there has
been no change or event having a Material Adverse Effect. Since the date of the
Financial Statements, neither the business nor the Properties of the Seller or
any of the Consolidated Subsidiaries, taken as a whole, have been materially and
adversely affected as a result of any fire, explosion, earthquake, flood,
drought, windstorm, accident, strike or other labor disturbance, embargo,
requisition or taking of Property or cancellation of contracts, permits or
concessions by any Governmental Authority, riot, activities of armed forces or
acts of God or of any public enemy.

         Section 4.03 Litigation. Except as disclosed to the Purchasers in
Schedule 4.03, 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 Seller, threatened against or affecting the Seller or
any Subsidiary which both (a) involves the possibility of any judgment or
liability against the Seller or any Subsidiary not fully covered by insurance
(except for normal deductibles), and (b) would be more likely than not to have a
Material Adverse Effect.

         Section 4.04 No Breach. Neither the execution and delivery of the Basic
Documents, 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 Articles of Incorporation or by-laws
of the Seller, the respective charter, by-laws, partnership agreements or
regulations of any Subsidiary or any Governmental Requirement or any material
agreement or instrument to which the Seller or any Subsidiary 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 Seller
or any Subsidiary pursuant to the terms of any such agreement or instrument
other than the Liens created by the Loan Documents.

         Section 4.05 Authority. The Seller and each Subsidiary has all
necessary power and authority to execute, deliver and perform its obligations
under the Basic Documents to which it is a party; and the execution, delivery
and performance by the Seller and each Subsidiary of the Basic Documents to
which it is a party, have been duly authorized by all necessary action on its
part; and the Basic Documents constitute the legal, valid and binding
obligations of the Seller and each Subsidiary, enforceable in accordance with
their terms, except as such enforceability may be limited by bankruptcy,
insolvency, fraudulent transfer and similar laws affecting creditors' rights
generally or by general principles of equity.

         Section 4.06 Approvals. Except for registration of the Securities under
the Securities Act, no authorizations, approvals or consents of, and no filings
or registrations with, any Governmental Authority are necessary for the
execution, delivery or performance by the Seller or any Subsidiary of the Basic
Documents or for the validity or enforceability thereof.




                                      -14-

<PAGE>   19

         Section 4.07 Use of Loans. The purchase price of the Notes, the
Warrants and the Acquired Shares shall be used solely to pay principal and
interest outstanding on the Senior Loan. In no event shall the purchase price of
the Notes, the Warrants or the Acquired Shares be used to finance in whole or in
part any hostile acquisition. The Seller is not engaged principally, or as one
of its important activities, in the business of extending credit for the
purpose, whether immediate, incidental or ultimate, or buying or carrying margin
stock (within the meaning of Regulation G, U or X of the Board of Governors of
the Federal Reserve System) and no part of the purchase price of the Notes, the
Warrants or the Acquired Shares will be used to buy or carry any margin stock.

         Section 4.08      ERISA.

                  (a) The Seller and each ERISA Affiliate have complied in all
material respects with ERISA and, where applicable, the Code regarding such
Plan.

                  (b) Each Plan is, and has been, maintained in substantial
compliance with ERISA and, where applicable, the Code.

                  (c) No act, omission or transaction has occurred which could
result in imposition on the Seller or any ERISA Affiliate (whether directly or
indirectly) of an amount of $100,000 or more as (i) either a civil penalty
assessed pursuant to section 502(c), (i) or (1) of ERISA or a tax imposed
pursuant to Chapter 43 of Subtitle D of the Code or (ii) breach of fiduciary
duty liability damages under section 409 of ERISA.

                  (d) No Plan (other than a defined contribution plan) or any
trust created under any such Plan has been terminated since September 2, 1974.
No liability to the PBGC in excess of $100,000 (other than for the payment of
current premiums which are not past due) by the Seller or any ERISA Affiliate
has been or is expected by the Seller or any ERISA Affiliate to be incurred with
respect to any Plan. No ERISA Event with respect to any Plan has occurred which
could reasonably expected to result in liabilities of $100,000 or more.

                  (e) Full payment when due has been made of all amounts which
the Seller or any ERISA Affiliate is required under the terms of each Plan or
applicable law to have paid as contributions to such Plan, and no accumulated
funding deficiency in an amount of $100,000 or more (as defined in section 302
of ERISA and section 412 of the Code), whether or not waived, exists with
respect to any Plan.

                  (f) The actuarial present value of the benefit liabilities
under each Plan which is subject to Title IV of ERISA does not, as of the end of
the Seller's most recently ended fiscal year, 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 $100,000 or more.
The term "actuarial present value of the benefit liabilities" shall have the
meaning specified in section 4041 of ERISA.



                                      -15-

<PAGE>   20

                  (g) None of the Seller or any ERISA Affiliate sponsors,
maintains, or contributes to an 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 the Seller or any ERISA Affiliate in its sole discretion at any
time without any material liability.

                  (h) None of the Seller or any ERISA Affiliate sponsors,
maintains or contributes to, or has at any time in the preceding six calendar
years, sponsored, maintained or contributed to, any Multiemployer Plan.

                  (i) None of the Seller or any ERISA Affiliate is required to
provide security under section 401(a)(29) of the Code due to a Plan amendment
that results in an increase in current liability for the Plan.

         Section 4.09 Taxes. Except as set out in Schedule 4.09, the Seller and
each Subsidiary has filed all United States Federal income tax returns and all
other tax returns which are required to be filed by it and has paid all material
taxes due pursuant to such returns or pursuant to any assessment received by the
Seller or any such Subsidiary, except for any taxes which are being contested in
good faith and by proper proceedings and against which adequate reserves are
being maintained. The charges, accruals and reserves on the books of the Seller
and its Subsidiaries in respect of taxes and other governmental charges are, in
the opinion of the Seller, adequate. No tax lien has been filed and, to the
knowledge of the Seller, no claim is being asserted with respect to any such
tax, fee or other charge, except for any taxes, fees or other charges which are
being contested in good faith and by proper proceedings and against which
adequate reserves are being maintained.

         Section 4.10      Titles, etc.

                  (a) Subject to the matters set out in Schedule 4.10, each of
the Seller and the Subsidiaries has good and defensible title to (i) the Oil and
Gas Properties that are both (A) evaluated in the most recently delivered
Reserve Report and (B) described in Part One of Exhibit A to the Mortgage, free
and clear of all Liens except Liens permitted by Section 8.02 of the Indenture,
and (ii) to the best of Seller's knowledge, the balance of Seller's material
(individually or in the aggregate) Oil and Gas Properties (and/or those of the
Subsidiaries) that are described in the Mortgage or that are otherwise evaluated
in the most recently delivered Reserve Report, are free and clear (to the best
of Seller's knowledge) of all Liens except Liens permitted by Section 8.02 of
the Indenture. Except for immaterial divergences, after giving full effect to
the Excepted Liens and the matters set forth in Schedule 4.10, the Seller or its
Subsidiaries own the net interests in production attributable to the Hydrocarbon
Interests that are both (A) evaluated in the most recently delivered Reserve
Report and (B) reflected in the Mortgage, and the ownership of such Hydrocarbon
Interests shall not in any material respect obligate the Seller or its
Subsidiaries to bear the costs and expenses relating to the maintenance,
development and operations of each such Hydrocarbon Interest in an amount in
excess of the working interest of such Hydrocarbon Interest set forth in the
Mortgage (without a corresponding increase in net revenue interest). The Seller
does not believe, based upon




                                      -16-

<PAGE>   21

information in its possession, that its most recently delivered Reserve Report
materially overstates its (or any Subsidiaries) oil and gas reserves, bearing in
mind that reserves are evaluated based upon estimates and assumptions with
respect to which reasonable minds of competent reserve engineers may differ and
that reserve estimates are affected by the oil and gas prices used in the
preparation thereof.

                  (b) All leases and agreements necessary for the conduct of the
business of the Seller and the Subsidiaries are valid and subsisting, in full
force and effect and there exists no default or event or circumstance which with
the giving of notice or the passage of time or both would give rise to a default
under any such lease or leases, which would affect in any material respect the
conduct of the business of the Seller and the Subsidiaries.

                  (c) The Properties presently owned, leased or licensed by the
Seller and the Subsidiaries, including, without limitation, all easements and
rights of way, include all Properties necessary to permit the Seller and the
Subsidiaries to conduct their business in all material respects in the same
manner as its business has been conducted prior to the Closing Date.

                  (d) All of the Properties of the Seller and the Subsidiaries
which are reasonably necessary for the operation of their business are in good
working condition in all material respects and are maintained in accordance with
prudent business standards.

         Section 4.11 No Material Misstatements. Taken as a whole, the written
information, statements, exhibits, certificates, documents and reports furnished
to the Purchasers by the Seller or any Guarantor in connection with the
negotiation of this Agreement do not contain any material misstatement of fact
or omit to state a material fact or any fact necessary to make the statements
contained therein not materially misleading in the light of the circumstances in
which made and with respect to the Seller or any Guarantor. As of the Closing
Date, there is no fact peculiar to the Seller or any Guarantor which has a
Material Adverse Effect or in the future is reasonably likely to have (so far as
the Seller can now foresee) a Material Adverse Effect and which has not been set
forth in this Agreement or the other documents, certificates and statements
furnished to the Purchasers by or on behalf of the Seller or any Guarantor prior
to, or on, the Closing Date in connection with the transactions contemplated
hereby.

         Section 4.12 Investment Company Act. Neither the Seller nor any
Subsidiary is an "investment company" or a company "controlled" by an
"investment company," within the meaning of the Investment Company Act of 1940,
as amended.

         Section 4.13 Public Utility Holding Company Act. Neither the Seller nor
any Subsidiary is a "holding company," or a "subsidiary company" of a "holding
company," or an "affiliate" of a "holding company" or of a "subsidiary company"
of a "holding company," or a "public utility" within the meaning of the Public
Utility Holding Company Act of 1935, as amended.



                                      -17-

<PAGE>   22

         Section 4.14 Subsidiaries. Except as set forth on Schedule 4.14, the
Seller has no Subsidiaries or any direct or indirect ownership interest in any
other Persons. Schedule 4.14 sets forth the ownership interest of the Seller
(direct or indirect) in and to all such Persons.

         Section 4.15 Location of Business and Offices. As of the Closing Date,
the Seller's principal place of business and chief executive offices are located
at the address stated in Section 12.06. The principal place of business and
chief executive office of each Subsidiary are located at the addresses stated on
Schedule 4.14.

         Section 4.16 Defaults. Neither the Seller nor any Subsidiary is in
default nor has any event or circumstance occurred which, but for the expiration
of any applicable grace period or the giving of notice, or both, would
constitute a default under any material agreement or instrument to which the
Seller or any Subsidiary is a party or by which the Seller or any Subsidiary is
bound which default would have a Material Adverse Effect. No Default hereunder
has occurred and is continuing. No "Event of Default" under the Senior Loan
Documents has occurred and is continuing nor has Seller or any of its
Subsidiaries received any notice of a "Default" under the Senior Loan Documents
that has triggered a cure period.

         Section 4.17 Environmental Matters. Except as provided in Schedule 4.17
or for matters which are more likely than not to not to have a Material Adverse
Effect (or with respect to (c), (d) and (e) below, where the failure to take
such actions is more likely than not to not have a Material Adverse Effect):

                  (a) Neither any Property of the Seller or any of its
Subsidiaries nor the operations conducted thereon violate any order or
requirement of any court or Governmental Authority or any Environmental Laws;

                  (b) Without limitation of clause (a) above, no Property of the
Seller or any of its Subsidiaries nor the operations currently conducted thereon
or, to the best knowledge of the Seller, by any prior owner or operator of such
Property or operation, are in violation of or subject to any existing, pending
or threatened action, suit, investigation, inquiry or proceeding by or before
any court or Governmental Authority or to any remedial obligations under
Environmental Laws;

                  (c) All notices, permits, licenses or similar authorizations,
if any, required to be obtained or filed by the Seller or any of its
Subsidiaries in connection with the operation or use of any and all Property of
the Seller and each of its Subsidiaries, including without limitation present,
or to the best of Seller's knowledge, past treatment, storage, disposal or
release of a hazardous substance or solid waste into the environment, have been
duly obtained or filed, and the Seller and each Subsidiary thereof are in
compliance with the terms and conditions of all such notices, permits, licenses
and similar authorizations;

                  (d) All hazardous substances, solid waste, and oil and gas
exploration and production wastes, if any, generated at any and all Property of
the Seller and each of its Subsidiaries



                                      -18-
<PAGE>   23

have in the past, during Seller's or its Subsidiaries' tenure of ownership and
to the best of Seller's knowledge, prior thereto, been transported, treated and
disposed of in accordance with Environmental Laws and so as not to pose an
imminent and substantial endangerment to public health or welfare or the
environment, and, to the best knowledge of the Seller, all such transport
carriers and treatment and disposal facilities have been and are operating in
compliance with Environmental Laws and so as not to pose an imminent and
substantial endangerment to public health or welfare or the environment, and are
not the subject of any existing, pending or threatened action, investigation or
inquiry by any Governmental Authority in connection with any Environmental Laws;

                  (e) The Seller has taken all steps reasonably necessary to
determine and has determined that no hazardous substances, solid waste, or oil
and gas exploration and production wastes, have been disposed of or otherwise
released and there has been no threatened release of any hazardous substances on
or to any Property of the Seller or any of its Subsidiaries except in compliance
with Environmental Laws and so as not to pose an imminent and substantial
endangerment to public health or welfare or the environment;

                  (f) To the extent applicable, all Property of the Seller and
each of its Subsidiaries currently satisfies all design, operation, and
equipment requirements imposed by the OPA or scheduled as of the Closing Date to
be imposed by OPA during the term of this Agreement, and the Seller does not
have any reason to believe that such Property, to the extent subject to OPA,
will not be able to maintain compliance with the OPA requirements during the
term of this Agreement; and

                  (g) Neither the Seller nor any of its Subsidiaries has any
known contingent liability in connection with any release or threatened release
of any oil, hazardous substance or solid waste into the environment.

         Section 4.18 Compliance with the Law. Neither the Seller nor any
Subsidiary has violated any Governmental Requirement or failed to obtain any
license, permit, franchise or other governmental authorization necessary for the
ownership of any of its Properties or the conduct of its business, which
violation or failure would have (in the event such violation or failure were
asserted by any Person through appropriate action) a Material Adverse Effect.
Except for such acts or failures to act as would not have a Material Adverse
Effect, the Oil and Gas Properties (and properties unitized therewith) of the
Seller and its subsidiaries have been maintained, operated and developed in a
good and workmanlike manner and in conformity with all applicable laws and all
rules, regulations and orders of all duly constituted authorities having
jurisdiction and in conformity with the provisions of all leases, subleases or
other contracts comprising a part of the Hydrocarbon Interests and other
contracts and agreements forming a part of such Oil and Gas Properties;
specifically in this connection, but subject to the Material Adverse Effect
qualification set forth above, (i) after the Closing Date, no such Oil and Gas
Property is subject to having allowable production reduced below the full and
regular allowable (including the maximum permissible tolerance) because of any
overproduction (whether or not the same was permissible at the time) prior to
the Closing Date and (ii) none of the wells comprising a part of such Oil and
Gas Properties (or



                                      -19-

<PAGE>   24

properties unitized therewith) are deviated from the vertical more than the
maximum permitted by applicable laws, regulations, rules and orders, and such
wells are, in fact, bottomed under and are producing from, and the well bores
are wholly within, such Oil and Gas Properties (or in the case of wells located
on properties unitized therewith, such unitized properties).

         Section 4.19 Insurance. Schedule 4.19 attached hereto contains an
accurate and complete description of all material policies of fire, liability,
workmen's compensation and other forms of insurance owned or held by the Seller
and each Subsidiary as of the Closing Date. All such policies are in full force
and effect, all premiums with respect thereto covering all periods up to and
including the Closing Date have been paid, and no notice of cancellation or
termination has been received with respect to any such policy. Such policies are
sufficient for compliance with all requirements of law and of all agreements to
which the Seller or any Subsidiary is a party; are valid, outstanding and
enforceable policies; provide adequate insurance coverage in at lease such
amounts and against at least such risks (but including in any event public
liability) as are usually insured against in the same general area by companies
engaged in the same or a similar business for the assets and operations of the
Seller and each Subsidiary; will remain in full force and effect through the
respective dates set forth on Schedule 4.19 without the payment of additional
premiums; and will not in any way be affected by, or terminate or lapse by
reason of, the transactions contemplated by this Agreement. Schedule 4.19
identifies all material risks, if any, which the Seller, the Subsidiaries and
their respective board of directors or officers have designated as being self
insured. Neither the Seller nor any Subsidiary has been refused any insurance
with respect to its assets or operations, nor has its coverage been limited
below usual and customary policy limits, by an insurance carrier to which it has
applied for any such insurance or with which is has carried insurance during the
last three years.

         Section 4.20 Hedging Agreements. Schedule 4.20 sets forth, as of the
Closing Date, a true and complete list of all Hedging Agreements (including
commodity price swap agreements, forward agreements or contracts of sale which
provide for prepayment for deferred shipment or delivery of oil, gas or other
commodities) of the Seller and each Subsidiary, the material terms thereof
(including the type, term, effective date, termination date and notional amounts
of volumes), the net mark to market value thereof, all credit support agreements
relating thereto (including any margin required or supplied), and the
counterparty to each such agreement.

         Section 4.21 Restriction on Liens. Neither the Seller nor any
Subsidiary is a party to any agreement or arrangement (other than the Loan
Documents and the Senior Loan Documents), or subject to any order, judgment,
writ or decree, which either restricts or purports to restrict ability to grant
Liens to other Persons on or in respect of their respective assets or
Properties.

         Section 4.22 Material Agreements. Set forth on Schedule 4.22 hereto is
a complete and correct list of all material agreements, leases, indentures,
purchase agreements, obligations in respect of letters of credit, guarantees,
joint venture agreements, and other instruments in effect or to be in effect as
of the Closing Date (other than the Senior Loan Documents and Hedging
Agreements) providing for, evidencing, securing or otherwise relating to any
material Debt of the Seller or any Subsidiary, and all obligations of the Seller
or any Subsidiary to issuers of surety or appeal bonds



                                      -20-

<PAGE>   25

(excluding operator's bonds, plugging and abandonment bonds, and similar surety
obligations obtained in the ordinary course of business) issued for account of
the Seller or any such Subsidiary, and such list correctly set forth the names
of the debtor or lessee and creditor or lessor with respect to the Debt or lease
obligations outstanding or to be outstanding and the property subject to any
Lien securing such Debt or lease obligations.

         Section 4.23 Gas Imbalances. As of the Closing Date, except as set
forth in the most recent Reserve Report furnished to the Purchasers or on
Schedule 4.23, on a net basis there are no gas imbalances, take or pay or other
prepayments with respect to the Seller's or any Subsidiary's Hydrocarbon
Interests which would require the Seller or such Subsidiary to deliver five
percent (5%) or more of the monthly production from the Seller's and its
Subsidiaries' Hydrocarbons produced on a monthly basis from the Hydrocarbon
Interests, at some future time without then or thereafter receiving full payment
therefor.

         Section 4.24 Capitalization. The authorized Capital Stock of the Seller
consists of: (a) 30,000,000 shares of Common Stock, par value $.01 per share and
(b) 10,000,000 shares of Preferred Stock, par value $.01 per share, of which
there are issued and outstanding 12,253,574 shares of Common Stock and no other
shares of Capital Stock. All outstanding shares of Common Stock are validly
issued, fully paid and nonassessable and were issued free of preemptive rights.
Except as set forth on Schedule 4.24, the Seller is not a party to any voting
trust or other agreement with respect to the voting of its Capital Stock. Except
for the Warrants, there are no (i) outstanding securities convertible or
exchangeable into Capital Stock of the Seller or (ii) warrants, contracts,
commitments, agreements, understandings, or arrangements of any kind to which
the Seller is a party relating to the repurchase or issuance of any Capital
Stock. Except as set forth on Schedule 4.24 and except as contemplated in the
Equity Documents, the Seller is not a party to or bound by any agreement with
respect to any of its securities which grants registration rights to any Person.

         Section 4.25 Acquired Shares. When issued and delivered against payment
therefor in accordance with the terms of this Agreement, the Acquired Shares
will be duly and validly issued, fully paid, nonassessable, free of preemptive
rights and free from all taxes payable by the Seller and Liens (except any Liens
created or suffered to be created by the Purchasers) and will not be subject to
any restriction on the voting or transfer thereof created by the Seller other
than in the Equity Documents and the applicable provisions of federal and state
securities laws.

         Section 4.26 Warrant Shares. When issued and delivered against payment
therefor in accordance with the terms of the Warrants, the Warrant Shares
issuable upon exercise of the Warrants will be duly and validly issued, fully
paid, nonassessable, free of preemptive rights and free from all taxes payable
by the Seller and Liens (except any Liens created or suffered to be created by
the Purchasers) and will not be subject to any restriction on the voting or
transfer thereof created by the Seller other than in the Equity Documents and
the applicable provisions of federal and state securities laws. The Seller has
duly and validly reserved the Warrant Shares, as of the Closing Date, for
issuance upon conversion of the Warrants.



                                      -21-

<PAGE>   26

         Section 4.27 No Restrictions. The Seller currently is not, and in the
future will not, be subject to any agreements that purport to impose
restrictions or limitations on the Purchasers, as affiliates of the Seller or
otherwise, without the prior written consent and authorization of each of the
Purchasers.

         Section 4.28 Certain Fees. Except for the fees payable to ECT
Securities Corp. and JEDI-II pursuant to the Structuring Fee Agreement, no fees
or commissions will be payable by the Seller to brokers, finders, investment
bankers, or Purchasers with respect to the issuance and sale of any of the
Securities or the consummation of the transaction contemplated by this
Agreement. The Seller agrees that it will indemnify and hold harmless the
Purchasers from and against any and all claims, demands, or liabilities for
broker's, finders, placement, or other similar fees or commissions incurred by
the Seller or alleged to have been incurred by the Seller in connection with the
issuance or sale of the Securities or the consummation of the transaction
contemplated by this Agreement.

                                    ARTICLE V
                REPRESENTATIONS AND WARRANTIES OF THE PURCHASERS

         The Purchasers each represent and warrant to the Seller, which
representations and warranties shall survive the execution of any Basic
Document, that as of the date of this Agreement:

         Section 5.01 Investment. Each Purchaser represents and warrants to, and
covenants and agrees with, the Seller that the Securities are being acquired for
its own account and with no intention of distributing or reselling the Notes,
the Warrants, the Warrant Shares or the Acquired Shares in any transaction which
would be in violation of the securities laws of the United States of America or
any State, without prejudice, however, to Purchasers' right at all times to sell
or otherwise dispose of all or any part of the Notes, the Warrants, the Warrant
Shares or the Acquired Shares under a registration statement under the
Securities Act and applicable state securities laws or under an exemption from
such registration available thereunder (including, without limitation, if
available, Rule 144A promulgated thereunder). If either Purchaser should in the
future decide to dispose of any of the Notes, the Warrants, the Warrant Shares
or the Acquired Shares, the Purchasers understand and agree (i) that it may do
so only (A) in compliance with the Securities Act and applicable state
securities law, as then in effect, and (B) in the manner contemplated by any
registration statement pursuant to which such securities are being offered, and
(ii) that stop-transfer instructions to that effect will be in effect with
respect to such securities. The Purchasers agree to the imprinting, so long as
appropriate, of a legend on each Note and on each certificate representing
Warrants, Warrant Shares or the Acquired Shares, to the effect as set forth
above.

         Section 5.02 Nature of Purchasers. Each Purchaser represents and
warrants to, and covenants and agrees with, the Seller that, (i) it is an
"accredited investor" within the meaning of paragraphs (a)(3) or (8) of Rule 501
under the Securities Act and (ii) by reason of its business and financial
experience it has such knowledge, sophistication and experience in business and
financial




                                      -22-

<PAGE>   27

matters so as to be capable of evaluating the merits and risks of the
prospective investment in the Securities, is able to bear the economic risk of
such investment and, at the present time, would be able to afford a complete
loss of such investment.

         Section 5.03 Receipt of Information; Authorization. Each Purchaser
acknowledges that it has been furnished all information that it deems necessary
or desirable to the making of an informed investment decision concerning the
Securities. Each Purchaser acknowledges that it has had an opportunity to ask
questions of and receive satisfactory answers from designated representatives of
the Seller concerning the terms and conditions pursuant to which the purchase of
the Securities are made. Each Purchaser acknowledges that it has been afforded
an opportunity to examine such documents and other information which it has
requested for the purpose of verifying the information provided to it and for
the purpose of answering any questions it may have concerning the business
affairs and financial condition of the Seller. Each Purchaser represents that it
alone or with its advisors has knowledge and experience in the business of the
Seller and the Seller so as to be capable of evaluating the merits and risks of
an investment in the Seller based upon the information furnished to it, its
knowledge of the business and affairs of the Seller, the records, files, and
plans of the Seller (which have been made available to it), such additional
information as it has requested and has received from the Seller, and the
independent inquiries and investigations undertaken by it. Each Purchaser
represents and warrants that the purchase of the Securities by it has been duly
and properly authorized and this Agreement and each Basic Document to which the
Purchasers are a signatory has been duly executed and delivered by it or on its
behalf.

                                   ARTICLE VI
                         CONDITIONS PRECEDENT TO FUNDING

         Section 6.01 Conditions Precedent to Obligations of the Purchasers. The
obligation of the Purchasers to acquire the Securities on the Funding Date is
subject to each of the following:

                  (a) The accuracy as of the Closing Date of each and every
representation and warranty of the Seller, each Guarantor, and the Senior Loan
Agent made in this Agreement or any other Basic Document, or in any certificate
delivered to the Purchasers pursuant to or in connection with this Agreement,
and receipt by the Purchasers of a Certificate executed by a duly Responsible
Officer, dated as of the Funding Date, certifying that each of the
representations and warranties of the Seller and each Guarantor made in this
Agreement or any other Basic Document are true and correct as of the Funding
Date, and that the Seller and each Guarantor has performed to date all of its
respective covenants and agreements under the Basic Documents.

                  (b) The absence as of the Closing Date and the Funding Date of
a Default or Event of Default hereunder or an "Event of Default" under the
Senior Credit Agreement or any "Default"under the Senior Loan Documents that has
triggered a cure period.

                  (c) The performance by the Seller of its respective
obligations to be performed hereunder on or before the Funding Date.




                                      -23-


<PAGE>   28



                  (d) The satisfaction of each of the following conditions as of
or prior to the Closing Date:

                           (i) The Purchasers (or the Trustee, where
         appropriate) shall have received the following, each in form and
         substance satisfactory to the Purchasers and in sufficient
         counterparts:

                                    (A) Duly executed counterparts of this
                  Agreement and the Indenture signed by all the parties hereto
                  and thereto.

                                    (B) The duly executed Financing Agreement,
                  Structuring Fee Agreement, Guaranty Agreements, Subordination
                  Agreement and Registration Rights Agreement, dated as of the
                  Closing Date in form and substance satisfactory to Purchasers.

                                    (C) Duly executed counterparts of the
                  Collateral Documents (including without limitation UCC-1
                  Financing Statements).

                                    (D) Certificates of good standing as to the
                  Seller and each Guarantor issued by the Secretary of State of
                  their respective states of incorporation or formation.

                                    (E) The duly executed certificate of the
                  Secretary of the Seller setting forth (i) resolutions of its
                  directors in form and substance satisfactory to the Purchasers
                  with respect to the authorization of this Agreement and the
                  other Basic Documents to which it is a party and the
                  transactions contemplated hereby and thereby; (ii) the names
                  and true signatures of the officers authorized to sign such
                  instruments; and (iii) copies of the articles or certificate
                  of incorporation and the bylaws of the Seller.

                                    (F) The duly executed certificate of the
                  Secretary of each Guarantor which is a corporation setting
                  forth (i) resolutions of its directors in form and substance
                  satisfactory to the Purchasers with respect to the
                  authorization of the Guaranty Agreements executed by such
                  Guarantors and the transactions contemplated hereby and
                  thereby; (ii) the names and true signatures of the officers
                  authorized to sign such instruments; and (iii) copies of the
                  articles or certificate of incorporation and the bylaws of
                  each Guarantor.

                                    (G) The duly executed certificate of all the
                  partners of each Guarantor that is a Partnership and each
                  member of each Guarantor that is a limited liability company,
                  setting forth (i) the authorization of the Guaranty Agreements
                  and the transactions contemplated hereby and thereby; (ii) the
                  names and title of all




                                      -24-

<PAGE>   29

                  persons authorized to sign such instruments; and (iii) copies
                  of the applicable partnership agreement or other regulating
                  documents of each such Guarantor.

                                    (H) Evidence that the insurance required
                  hereunder and under the other Basic Documents has been
                  obtained and is in full force and effect.

                                    (I) Copies of the Senior Loan Documents.

                                    (J) Any other document which the Purchasers
                  may reasonably request, including opinions addressed to
                  Purchasers, dated as of the Closing Date, from the counsel for
                  the Seller and each of the Guarantors acceptable to each of
                  the Purchasers addressing the existence and good standing of
                  the Seller, the authorization of the Basic Documents, the
                  enforceability of the Basic Documents, the absence of
                  conflicts with law, other material agreements, and court
                  orders, the absence of litigation, and such other matters as
                  the Purchasers may reasonably request.

                           (ii) The Seller shall have executed (but not
         delivered) the Notes, Warrants and Acquired Shares, each in form and
         substance satisfactory to the Purchasers.

                           (iii) The Seller shall have received consents to the
         Basic Documents by the Senior Lenders; and the Senior Loan Documents
         shall have been amended in form and substance reasonably satisfactory
         to Purchasers to permit the transactions contemplated by the Loan
         Documents, including the payment of dividends or other distributions by
         Subsidiaries to the Seller in order for the Seller to meet its debt
         service obligations to the Purchasers under the Notes.

                           (iv) The Purchasers shall have completed a due
         diligence review of the Seller and the Subsidiaries to the satisfaction
         of the Purchasers in their sole discretion.

                           (v) The Purchasers shall have received the latest
         internally prepared consolidated financial statements of the Seller and
         its Subsidiaries which shall be at least through June 30, 1998. Since
         June 30, 1998, there shall have occurred no event which could have a
         Material Adverse Effect.

                           (vi) The Board of Directors of each of the Seller,
          the Guarantors, the Purchasers and ________ must have approved the 
          transactions contemplated under this Agreement and the other Basic 
          Documents.

                           (vii) All other consents, including without
         limitation any required shareholder approval, and waivers necessary to
         complete the transactions under this Agreement and the other Basic
         Documents shall have been obtained by the Seller, the Guarantors and
         the Purchasers.



                                      -25-


<PAGE>   30

                  (e) The Warrants Shares and the Acquired Shares shall have
been approved for listing on NASDAQ and the registration statement on Form S-1
registering the Notes, the Warrants, and the Acquired Shares shall have been
declared effective by the Commission and no stop order with respect thereto
shall have been issued.

                  (f) The Seller shall have delivered to the Purchasers the
executed Notes, Warrants and Acquired Shares.

                  (g) The Mortgages shall have been filed in two counties of
Purchasers' choice.

                  (h) The Seller shall have paid to ECT Securities Corp. and
JEDI-II all payments required under the terms of the Structuring Fee Agreement.

                  (i) If requested in writing by either of the Purchasers, a
Designee of the Purchasers shall have been appointed to the Board of Directors
of the Seller pursuant to Section 7.03.

                  (j) The Seller shall have duly and validly reserved the
Warrant Shares for issuance upon conversion of the Warrants.

                  (k) The issuance of the Securities by the Seller shall not as
of the Funding Date be enjoined (temporarily or permanently) under the laws of
any jurisdiction to which the Seller is subject.

                  (l) Each of the Basic Documents shall have been executed and
delivered by all the respective parties thereto and shall be in full force and
effect.

         Section 6.02 Conditions Precedent to Obligations of the Seller. The
obligations of the Seller to issue and sell Securities hereunder is subject, on
the Funding Date, to the prior or simultaneous satisfaction or waiver of the
following conditions:

                  (a) The representations and warranties made by the Purchasers
herein shall be true and correct in all respects on and as of the Funding Date
with the same effect as though such representations and warranties had been made
on and as of the Funding Date.

                  (b) The Purchasers shall have accepted delivery of and made
payment for the Securities.

                  (c) The issuance of the Securities by the Seller shall not as
of the Funding Date be enjoined (temporarily or permanently) under the laws of
any jurisdiction to which the Seller is subject.

                  (d) Each of the Basic Documents shall have been executed and
delivered by all the respective parties thereto and shall be in full force and
effect.




                                      -26-

<PAGE>   31

         Section 6.03 Conditions Precedent to the Obligations of Purchasers and
Seller. The obligations of the Purchasers and Seller hereunder are contingent
upon the Funding Date occurring on or before 5:00 p.m., Houston, Texas time on
September 1, 1998.

                                   ARTICLE VII
                              AFFIRMATIVE COVENANTS

         Unless the prior written consent to the contrary is obtained from (i)
the holders of the majority of the Warrants (as to Sections 7.01 and 7.02) and
(ii) ECT (as to Sections 7.03 and 7.04) the Seller will, for the benefit of each
of the holders of the Warrants or Warrant Shares and the holders of the Acquired
Shares, 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 (x) the term of the Warrants, as to Sections 7.01 and
7.02, (y) ______ and ______ and/or their Affiliates beneficially own 5% or more
of the outstanding Common Stock of the Seller (including the Warrant Shares
represented by the Warrants, whether exercised or not), as to Section 7.03 and
(z) any part of the Obligations is outstanding, as to Section 7.04.

         Section 7.01 Warrants. Seller shall at all times during the term of the
Warrants maintain a sufficient number of shares of Common Stock of the Seller to
be issued as Warrant Shares upon the exercise of all or part of the Warrants.
Seller shall (i) notify the holders of the Warrants promptly after the exercise
of any of the Warrants by a holder or holders thereof, of the exercise thereof,
(ii) provide to the holders of the Warrants such information or materials in
connection therewith as may be reasonably requested by the the holders of the
Warrants, and (iii) otherwise provide to all the holders of the Warrants copies
of all notices provided to or from the Seller in connection with the Warrants.

         Section 7.02 Hart-Scott-Rodino Compliance. As soon as practicable after
the receipt from any holder of the Warrants or any Seller (the "Notice Giver")
of notice of the exercise of a number of Warrants sufficient to require a filing
under the Hart-Scott-Rodino Antitrust Improvements Act of 1976 and the rules,
regulations and formal interpretations thereunder, as amended from time to time
(the "HSR Act"), but in any event no later than the 10th Business Day after
receipt of such notice, the Seller will (i) prepare and file with the Antitrust
Division of the Department of Justice (the "DOJ") and the Federal Trade
Commission (the "FTC") the Notification and Report Form (accompanied by all
documentary attachments contemplated thereby) required by the HSR Act, (ii) upon
the request of any holder of the Warrants (the "Notice Giver"), request early
termination of the waiting period imposed by the HSR Act, (iii) coordinate and
cooperate with the Notice Giver in responding to formal and informal requests
for additional information and documentary material from the DOJ and the FTC in
connection with such filing, and (iv) use its best efforts to take, or cause to
be taken, all reasonable action and to do, or cause to be done, all things
reasonably necessary and appropriate to permit the issuance to the Notice Giver
of the shares of common stock issuance upon the exercise of the warrants with
respect to which any filing is required under the HSR Act, and (v) reimburse the
holders of the Warrants for the entire amount of any filing fee or any other
costs and expenses incurred by holders of the Warrants in connection therewith
(including legal fees), or as required to be paid under the HSR Act.



                                      -27-

<PAGE>   32

         Section 7.03 Board Representation. ___ or its designated Affiliate (the
"Acting Party") shall have the right (a) to designate one member of the Board
of Directors of the Seller or (b) (i) to receive (and Seller covenants and
agrees to deliver to the Acting Party) prior notice of any proposed board
action and to receive (and Seller covenants and agrees to deliver to the Acting
Party) reasonable notice of and a right to attend any meeting of the Seller's
Board of Directors, (ii) to receive (and Seller covenants and agrees to deliver
to the Acting Party), promptly after they are produced, all management reports
and accounts relating to the Seller that are provided to Seller's Board of
Directors or any committee of the Board of Directors and (iii) upon reasonable
notice, to have reasonable access to the books and records of the Seller,
including statutory books, minute books and customer lists. In the event the
Acting Party elects to designate a person to serve as a member of the Board of
Directors of the Seller (the "Designee"), the Seller shall (x) expand as
required the number of directors constituting the entire board, (y) fill the
vacancy created by such expansion with such Designee and (z) submit the name of
such Designee to the stockholders of the Seller (together with a recommendation
of his or her election) at each meeting of stockholders at which directors are
elected, until requested otherwise by the Acting Party. Any Designee shall
agree to resign at the request of the Seller, at any time after the expiration
of the rights of the ___ and any Acting Party pursuant to this Section 7.03.
The rights of ___ under this Section 7.03 shall not be assignable other than to
an Affiliate of ___.

         Section 7.04 Common Stock; Dividends; Voting Rights. The declaration of
dividends by the Seller shall be solely at the discretion of the Board of
Directors of the Seller. Except for holders of Common Stock, no other class of
Capital Stock of the Seller shall have any voting rights whatsoever, either
separately or in conjunction with the Common Stock.


                                  ARTICLE VIII
                         [OMITTED BY THE PARTIES HERETO]


                                   ARTICLE IX
                         [OMITTED BY THE PARTIES HERETO]


                                    ARTICLE X
                         [OMITTED BY THE PARTIES HERETO]


                                   ARTICLE XI
                         [OMITTED BY THE PARTIES HERETO]



                                      -28-

<PAGE>   33

                                   ARTICLE XII
                                  MISCELLANEOUS

         Section 12.01 Interpretation and Survival of Provisions. Article,
Section, Schedule, and Exhibit references are to this Agreement, 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 Seller has an obligation under the
Basic Documents, the expense of complying with that obligation shall be an
expense of the Seller unless otherwise specified. Whenever any determination,
consent, or approval is to be made or given by the Purchasers, any holder of the
Warrants or the Acquired Shares, such action shall be in such Person's sole
discretion unless otherwise specified in this Agreement. 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 Agreement, 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 Seller or the
Purchasers or (b) acceptance of any of the Securities and payment therefor and
repayment or repurchase thereof. All indemnification obligations of the Seller
and the provisions of Section 12.02 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 Agreement.

         Section 12.02     Costs, Expenses and Taxes.

                  (a)       Intentionally Deleted.

                  (b) The Seller agrees to indemnify the Purchasers, 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 by third parties, 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 Seller of the
proceeds of any sale of the Securities, (ii) the operations of the business of
the Seller 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 Seller or any
Subsidiary to comply with any



                                      -29-

<PAGE>   34
Governmental Requirement, or (vi) any other aspect of this Agreement 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 Purchasers or any Purchaser's shareholders
against any Purchaser or by reason of the gross negligence or wilful misconduct
of any Indemnitee).

                  (c) The Seller agrees to pay and hold the Purchasers harmless
from and against any and all present and future stamp and other similar taxes
with respect to this Agreement and the Equity Documents and save the Purchasers
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 Purchasers
for the full amount of taxes paid by the Purchasers in respect of payments made
or to be made under this Agreement, any other Equity 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) In the case of any indemnification hereunder, the
Purchaser or other Person indemnified hereunder shall give notice to the Seller
within a reasonable period of time of any such claim or demand being made
against the Purchaser or other indemnified Person and the Seller, at its sole
cost and expense, shall provide a defense of such claim, provided, however,
that, (i) if the Seller 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 Seller 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 Seller or
such Subsidiary or if the interests of the indemnified party reasonably may be
deemed to conflict with the interest of the Seller 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 Seller as incurred.

                  (e) 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 12.02.

                  (f) This Section 12.02 shall not apply to actions, suits,
proceedings, investigations, demands, losses, liabilities, claims, damages,
deficiencies, interest, judgements, 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



                                      -30-


<PAGE>   35

acquired possession of such Property (whether through foreclosure or deed in
lieu of foreclosure, as mortgagee in possession or otherwise).

                  (g) The Seller's obligations under this Section 12.02 shall
survive any termination of this Agreement and the payment of the Obligations.

         Section 12.03 No Waiver; Modifications in Writing.

                  (a) No failure or delay on the part of the Seller or the
Purchasers 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 Seller or the
Purchasers at law or in equity or otherwise.

                  (b) Except as otherwise provided herein, no amendment, waiver,
consent, modification, or termination of any provision of this Agreement, shall
be effective unless signed by the Seller and the holders of more than 50% of the
outstanding principal balance of the Notes and the holders of more than 50% of
the Warrants. Any amendment, supplement or modification of or to any provision
of this Agreement or any other Equity Document, any waiver of any provision of
this Agreement or any other Equity Document, and any consent to any departure by
the Seller from the terms of any provision of this Agreement or any other Equity
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 Agreement, no notice to or demand on the Seller in any case shall entitle
the Seller to any other or further notice or demand in similar or other
circumstances.

         Section 12.04 Binding Effect; Assignment. This Agreement shall be
binding upon the Seller and the Purchasers, and their respective successors and
permitted assigns. Except as expressly provided in this Agreement, this
Agreement shall not be construed so as to confer any right or benefit upon any
Person other than the parties to this Agreement, and their respective successors
and permitted assigns. Subject to applicable federal and state securities laws
the rights and obligations of the Purchasers under this Agreement with respect
to the Warrants and the Equity Documents may be sold, assigned or pledged by any
Purchaser, in whole or in part, in accordance with the provisions of the
Warrants, and upon any such assignment, the holders of the Warrants shall
succeed to all of the selling Purchaser's rights and obligations under this
Agreement with respect to the Warrants and the Equity Documents to the extent
assigned and the selling Purchaser shall be automatically released from any
obligations thereunder with respect to the Warrants and the Equity Documents to
the extent assigned. Subject to applicable federal and state securities laws the
Acquired Shares may be sold, assigned or pledged subject only to the
Registration Rights Agreement and upon any such assignment the holders of the
Acquired Shares shall succeed to the Purchaser's rights and obligations under
the Registration Rights Agreement. Upon request of any Purchaser in connection
with any transfer of the Warrants or Acquired Shares, the Seller shall execute
and deliver any amendment to




                                      -31-

<PAGE>   36

this Agreement, the Warrants, and the other Equity Documents reasonably
requested by the Purchaser to reflect the transfer and delineate the rights of
the transferor and the transferee.

         Section 12.05 Replacement Securities. Upon receipt of evidence
satisfactory to the Seller of the loss, theft, destruction, or mutilation of any
Warrants, Warrant Shares or Acquired Shares and, in the case of any such loss,
theft, or destruction, upon delivery of any unsecured letter of indemnity
reasonably satisfactory to the Seller or, in the case of any such mutilation,
upon surrender or cancellation thereof, the Seller will issue a new Warrants,
Warrant Shares or Acquired Shares, as applicable.

         Section 12.06 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 Purchasers:


         and


         If to the Seller:

         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 Seller or any Purchaser 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



                                      -32-

<PAGE>   37

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.

         Section 12.07 Governing Law. This Agreement 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 12.08     Arbitration.

                  (a) Binding Arbitration. Subject to the provisions of
subparagraph (e), on the request of either the Seller or any Purchaser, 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 Agreement (a "Dispute") shall be resolved by binding
arbitration in accordance with the terms hereof. Either the Seller or any
Purchaser 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 Seller and the Purchasers each agree to keep all
Disputes and arbitration proceedings strictly confidential except for disclosure
of information required by applicable law.



                                      -33-

<PAGE>   38

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

         Section 12.09 Execution in Counterparts. This Agreement 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.

                  IN WITNESS WHEREOF, the parties hereto execute this Agreement,
effective as of the date first above written.

                                          BRIGHAM EXPLORATION COMPANY,
                                          a Delaware corporation



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




                                      -34-

<PAGE>   39

                                  SCHEDULE 4.02

                                   LIABILITIES


                                      None




<PAGE>   40

                                  SCHEDULE 4.03

                                   LITIGATION


                                      None





<PAGE>   41

                                  SCHEDULE 4.09

                                      TAXES


                                      None





<PAGE>   42



                                  SCHEDULE 4.20

                               HEDGING AGREEMENTS


                                      None







<PAGE>   43



                                  SCHEDULE 4.22

                               MATERIAL AGREEMENTS


                                      None








<PAGE>   44



                                  SCHEDULE 4.23

                                 GAS IMBALANCES


                                      None







<PAGE>   45


                                  SCHEDULE 4.24

                     VOTING AGREEMENTS; REGISTRATION RIGHTS