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                                                                    EXHIBIT 10.2

                                                                  EXECUTION COPY



                     AMENDED AND RESTATED GUARANTY AGREEMENT



                                       BY


                           BRIGHAM EXPLORATION COMPANY


                                   IN FAVOR OF


                           BANK OF MONTREAL, AS AGENT
                             AND EACH OF THE LENDERS
               PARTY TO THE AMENDED AND RESTATED CREDIT AGREEMENT





                                FEBRUARY 17, 2000






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                                TABLE OF CONTENTS
<TABLE>
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                                                                                                      PAGE


<S>     <C>       <C>      <C>                                                                      <C>
Article I         General Terms.........................................................................2

         Section 1.1        Terms Defined Above.........................................................2

         Section 1.2        Certain Definitions.........................................................2

         Section 1.3        Credit Agreement Definitions................................................3

Article II        The Guaranty..........................................................................3

         Section 2.1        Liabilities Guaranteed......................................................3

         Section 2.2        Nature of Guaranty..........................................................3

         Section 2.3        Agent's Rights..............................................................4

         Section 2.4        Guarantor's Waivers.........................................................4

         Section 2.5        Maturity of Liabilities; Payment............................................5

         Section 2.6        Agent's Expenses............................................................5

         Section 2.7        Liability...................................................................5

         Section 2.8        Events and Circumstances Not Reducing or Discharging
                            Guarantor's Obligations.....................................................5

Article III       Representations, Warranties And Covenants.............................................7

         Section 3.1        By Guarantor................................................................7

         Section 3.2        No Representation by Lenders...............................................11

Article IV        Subordination Of Indebtedness........................................................11

         Section 4.1        Subordination of All Guarantor Claims......................................11

         Section 4.2        Claims in Bankruptcy.......................................................12

         Section 4.3        Payments Held in Trust.....................................................12

         Section 4.4        Liens Subordinate..........................................................12

         Section 4.5        Guarantor's Enforcement Rights.............................................12

Article V         Certain Additional Covenants.........................................................13

         Section 5.1        Affirmative Covenants......................................................13

         Section 5.2        Negative Covenants.........................................................13

Article VI        Miscellaneous........................................................................19

         Section 6.1        Successors and Assigns.....................................................19

         Section 6.2        Notices....................................................................19

         Section 6.3        Business and Financial Information.........................................19

         Section 6.4        Construction...............................................................19

         Section 6.5        Invalidity.................................................................20

         Section 6.6        ENTIRE AGREEMENT...........................................................20
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                     AMENDED AND RESTATED GUARANTY AGREEMENT

         THIS AMENDED AND RESTATED GUARANTY AGREEMENT by BRIGHAM EXPLORATION
COMPANY (hereinafter called "Guarantor"), is in favor of BANK OF MONTREAL, as
agent (the "Agent") for the lenders (the "Lenders") that are or become parties
to the Credit Agreement defined below, and the Lenders (as defined below).

                              W I T N E S S E T H:


         WHEREAS, BRIGHAM OIL & GAS, L.P., a Delaware limited partnership
(hereinafter called "Borrower"), Bank of Montreal, as agent and Societe
Generale, Southwest Agency (the "Prior Lenders") entered into that certain
Credit Agreement dated as of January 26, 1998, as amended (the "Prior Credit
Agreement") pursuant to which the Prior Lenders provided to the Borrower loans
and extensions of credit, which loans and extensions of credit are evidenced by
those certain promissory notes from the Borrower in the aggregate principal
amount of $75,000,000 (the "Prior Notes"); and

         WHEREAS, one of the terms and conditions stated in the Prior Credit
Agreement for the making of the loans described therein was the execution of
that certain Guaranty Agreement dated as of January 26, 1998 in favor of the
Prior Lenders (as amended the "Guaranty Agreement"); and

         WHEREAS, by Partial Assignment of Notes of even date herewith Shell
Capital Inc. ("SCI") has acquired a portion of the Prior Notes (the "Acquired
Notes Interest") and security for the payment of the Acquired Notes Interest and
the performance of the Borrower's obligations under the Prior Credit Agreement;
and

         WHEREAS, the Prior Lenders and SCI together with their successors and
assigns (collectively, the "Lenders") have agreed to provide senior secured debt
in the amount of up to $75,000,000 consisting of a rearrangement of the Prior
Notes and advances to the Borrower, and the Borrower, the Agent and the Lenders
of even date herewith are entering into that certain Amended and Restated Credit
Agreement (the "Credit Agreement") which amends and restates in its entirety the
Prior Credit Agreement and Prior Notes;

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




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                                   ARTICLE I


                                  General Terms

         Section 1.1 Terms Defined Above. As used in this Guaranty Agreement,
the terms "Agent," "Borrower," "Credit Agreement," "Guaranty Agreement,"
"Lenders," "Prior Credit Agreement," "Prior Lenders," "Prior Notes" and
"Acquired Notes Interest" shall have the meanings indicated above.

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

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

                  "Guaranty Agreement" shall mean this Amended and Restated
         Guaranty Agreement, as the same may from time to time be amended or
         supplemented.

                  "Indenture" shall mean that certain Indenture dated as of
         August 20, 1998, as from time to time amended, between the Guarantor,
         as issuer of the Subordinated Debt, and Chase Bank of Texas, National
         Association, as trustee.

                  "Liabilities" shall mean:

                  (a)      any and all indebtedness, obligations and liabilities
now or hereafter incurred by the Borrower pursuant to the Credit Agreement,
including without limitation, the unpaid fees and principal of and interest on
the Notes;

                  (b)      payment of and performance of any and all present or
future obligations of Borrower to a Lender according to the terms of any Hedging
Agreement now or hereafter arising between (i) Borrower and Bank of Montreal and
its successors or assigns (a "BMO Hedge Party") and Soc-Gen and its successors
or assigns (a "Soc-Gen Hedge Party") entered into while such BMO Hedge Party or
such Soc-Gen Hedge Party is a Lender; and (ii) Borrower and SCI and its
successors or assigns (with Loans or Commitments of $20 million or more) or any
Affiliate of SCI (SCI and any Affiliate of SCI a "SCI Hedge Party") entered into
while such SCI Hedge Party or Fathom Energy Capital I, L.L.C, is a Lender. For
purposes of this clause (b), the parties intend that any Hedging Agreement
entered into between the Borrower and a Lender or in the case of SCI, a SCI
Hedge Party, while such Person was a party to the Credit Agreement shall
continue to be secured even after the time such Person ceases to be a party to
the Credit Agreement as a Lender.

                  (c) any additional "Indebtedness", as defined in the Credit
Agreement, and




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

                  "Securities Purchase Agreement" shall mean that certain
         Securities Purchase Agreement dated as of August 20, 1998 among the
         Guarantor, Enron Capital & Trade Resources Corp., and Joint Energy
         Development Investments II Limited Partnership regarding $50,000,000
         Senior Subordinated Secured Notes due 2003.

                  "Subordination Agreement" shall mean that certain
         Intercreditor and Subordination Agreement dated August 20, 1998, as
         from time to time amended, among Enron Capital and Trade Resources
         Corp., Joint Energy Development Investments II Limited Partnership, and
         Bank of Montreal.

                  "Subordinated Debt" shall mean the Debt in the principal
         amount not to exceed $40,000,000 (plus interest paid in kind through
         December 31, 2000 pursuant to Section 9.02 of the Indenture or
         otherwise satisfied through payment of the Term ORRI) of Guarantor
         incurred under the Indenture and expressly subordinated to the
         Indebtedness pursuant to the Subordination Agreement.

                  "Subordinated Guarantees" shall mean the Guarantees permitted
         under Section 5.2(a)(7).

                  "Subsidiary Guarantor" shall mean a Subsidiary of the
         Guarantor which is itself a "Guarantor" under the Credit Agreement.

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

                                   ARTICLE II

                                  The Guaranty

         Section 2.1 Liabilities Guaranteed. Guarantor hereby irrevocably and
unconditionally guarantees the prompt payment at maturity of the Liabilities.

         Section 2.2 Nature of Guaranty. This Guaranty Agreement is an absolute,
irrevocable, completed and continuing guaranty of payment and not a guaranty of
collection, and no notice of the Liabilities or any extension of credit already
or hereafter contracted by or extended to Borrower need be given to Guarantor.
This Guaranty Agreement may not be revoked by Guarantor and shall continue to be
effective with respect to debt under the Liabilities arising or created after
any attempted revocation by Guarantor and shall remain in full force and effect
until the Liabilities are paid in full and the Commitments are terminated,
notwithstanding that from time to time prior thereto no Liabilities may be
outstanding. Borrower and the Lenders may modify, alter,




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rearrange, extend for any period and/or renew from time to time, the
Liabilities, and the Lenders may waive any Default or Events of Default without
notice to the Guarantor and in such event Guarantor will remain fully bound
hereunder on the Liabilities. This Guaranty Agreement shall continue to be
effective or be reinstated, as the case may be, if at any time any payment of
the Liabilities is rescinded or must otherwise be returned by any of the Lenders
upon the insolvency, bankruptcy or reorganization of Borrower or otherwise, all
as though such payment had not been made. This Guaranty Agreement may be
enforced by the Agent and any subsequent holder of any of the Liabilities and
shall not be discharged by the assignment or negotiation of all or part of the
Liabilities. Guarantor hereby expressly waives presentment, demand, notice of
non-payment, protest and notice of protest and dishonor, notice of Default or
Event of Default, and also notice of acceptance of this Guaranty Agreement,
acceptance on the part of the Lenders being conclusively presumed by the
Lenders' request for this Guaranty Agreement and delivery of the same to the
Agent.

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

         Section 2.4 Guarantor's Waivers.


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

                  (b)      Subrogation. Until the Liabilities have been paid in
full, the Guarantor waives all rights of subrogation or reimbursement against
the Borrower, whether arising by contract or operation of law (including,
without limitation, any such right arising under any federal or state bankruptcy
or insolvency laws) and waives any




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right to enforce any remedy which the Lenders now have or may hereafter have
against the Borrower, and waives any benefit or any right to participate in any
security now or hereafter held by the Agent or any Lender.

         Section 2.5 Maturity of Liabilities; Payment. Guarantor agrees that if
the maturity of any of the Liabilities is accelerated by bankruptcy or
otherwise, such maturity shall also be deemed accelerated for the purpose of
this Guaranty Agreement without demand or notice to Guarantor. Guarantor will,
forthwith upon notice from the Agent, pay to the Agent the amount due and unpaid
by Borrower and guaranteed hereby. The failure of the Agent to give this notice
shall not in any way release Guarantor hereunder.

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

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

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

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

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

                  (c)      Condition of Borrower or Guarantor. The insolvency,
bankruptcy arrangement, adjustment, composition, liquidation, disability,
dissolution, death or lack of power of Borrower or Guarantor or any other Person
at any time liable




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for the payment of all or part of the Liabilities; or any dissolution of
Borrower or Guarantor, or any sale, lease or transfer of any or all of the
assets of Borrower or Guarantor, or any changes in the shareholders, partners,
or members of Borrower or Guarantor; or any reorganization of Borrower or
Guarantor;

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

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

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

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

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


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

                  (j)      Payments Rescinded. Any payment by Borrower to the
Lenders is held to constitute a preference under the bankruptcy laws, or for any
reason the Lenders are required to refund such payment or pay such amount to
Borrower or someone else; or

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

                                  ARTICLE III

                    Representations, Warranties And Covenants

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

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

                  (b)      Corporate Existence. Guarantor is a corporation duly
organized, legally existing and in good standing under the laws of the State of
Delaware and is duly qualified in all jurisdictions wherein the property owned
or the business transacted by it makes such qualification necessary.

                  (c)      Corporate Power and Authorization. Guarantor is duly
authorized and empowered to execute, deliver and perform this Guaranty Agreement
and all corporate action on Guarantor's part requisite for the due execution,
delivery and performance of this Guaranty Agreement has been duly and
effectively taken.

                  (d)      Binding Obligations. This Guaranty Agreement
constitutes valid and binding obligations of Guarantor, enforceable in
accordance with its terms



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(except that enforcement may be subject to any applicable bankruptcy, insolvency
or similar laws generally affecting the enforcement of creditors' rights) or by
general principles of equity.

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

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

                  (g)      Financial Condition. The audited consolidated balance
sheet of the Guarantor and its Consolidated Subsidiaries as at December 31, 1998
and the related consolidated statement of income, stockholders' equity and cash
flow of the Guarantor and its Consolidated Subsidiaries for the fiscal year
ended on said date, with the opinion thereon of Price Waterhouse heretofore
furnished to each of the Lenders and the unaudited consolidated balance sheet of
the Guarantor and its Consolidated Subsidiaries as at September 30, 1999 and
their related consolidated statements of income, stockholders' equity and cash
flow of the Guarantor and its Consolidated Subsidiaries for the nine-month
period ended on such date heretofore furnished to the Agent, are complete and
correct and fairly present the consolidated financial condition of the Guarantor
and its Consolidated Subsidiaries as at said dates and the results of its
operations for the fiscal year and the nine-month period on said dates, all in
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
Guarantor nor any of its Subsidiaries 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 7.02 of the Credit Agreement. Since
December 31, 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 Guarantor and its 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.

                  (h)      Litigation. Except as disclosed to the Lenders in
Schedule 7.03 of the Credit Agreement, at the Closing Date there is no
litigation, legal, administrative or arbitral proceeding, investigation or other
action of any nature pending



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or, to the knowledge of the Guarantor threatened against or affecting the
Guarantor or any of its Subsidiaries which both (a) involves the possibility of
any judgment or liability against the Guarantor or any of its Subsidiaries not
fully covered by insurance (except for normal deductibles), and (b) would be
more likely than not to have a Material Adverse Effect.

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

                  (j)      ERISA.

                           (1)      The Guarantor, its Subsidiaries and each
                  ERISA Affiliate have complied in all material respects with
                  ERISA and, where applicable, the Code regarding each Plan.

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

                           (3)      No act, omission or transaction has occurred
                  which could result in imposition on the Guarantor, any of its
                  Subsidiaries 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 (l)
                  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.

                           (4)      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 Guarantor, any of its
                  Subsidiaries or any ERISA Affiliate has been or is expected by
                  the Guarantor, any of its Subsidiaries 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.


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<PAGE>   12


                           (5)      Full payment when due has been made of all
                  amounts which the Guarantor, any of its Subsidiaries 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.

                           (6)      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 Guarantor'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.

                           (7)      None of the Guarantor, any of its
                  Subsidiaries 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 Guarantor,
                  any of its Subsidiaries or any ERISA Affiliate in its sole
                  discretion at any time without any material liability.

                           (8)      None of the Guarantor, any of its
                  Subsidiaries 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.

                           (9)      None of the Guarantor, any of its
                  Subsidiaries 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.

                  (k)      Taxes. Except as set out in Schedule 7.09 of the
Credit Agreement, each of the Guarantor and its Subsidiaries 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 Guarantor or any of its
Subsidiaries, 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 Guarantor and its
Subsidiaries in respect of taxes and other governmental charges are, in the
opinion of the Guarantor, adequate. No tax lien has been filed and, to the
knowledge of the Guarantor, no claim is being asserted with respect to any such
tax, fee or other charge,



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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.

                  (l)      Title to Ownership Interest in General Partner and
Limited Partners of Borrower. The Guarantor has good and unencumbered title to
all of the capital stock of the General Partner of the Borrower and, directly or
indirectly, all of the ownership interests in the limited partners of the
Borrower, except for liens and security interests securing the Liabilities or as
permitted under Section 5.2(b)(4).

                  (m)      Investment Company Act. Neither the Guarantor nor any
of its Subsidiaries is an "investment company" or a company "controlled" by an
"investment company," within the meaning of the Investment Company Act of 1940,
as amended.

                  (n)      Public Utility Holding Company Act. Neither the
Guarantor nor any of its Subsidiaries 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.

                  (o)      Subsidiaries. Except as set forth on Schedule 1
hereto or as permitted by Section 9.16 of the Credit Agreement, the Guarantor
has no Subsidiaries.

                  (p)      Compliance with the Law. Neither the Guarantor nor
any of its Subsidiaries 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.

         Section 3.2 No Representation by Lenders. Neither the Lenders nor any
other Person has made any representation, warranty or statement to the Guarantor
in order to induce the Guarantor to execute this Guaranty Agreement.

                                   ARTICLE IV

                          Subordination Of Indebtedness

         Section 4.1 Subordination of All Guarantor Claims. As used herein, the
term "Guarantor Claims" shall mean all debts and liabilities of Borrower or any
Subsidiary of the Borrower to Guarantor, whether such debts and liabilities now
exist or are hereafter incurred or arise, or whether the obligation of Borrower
or such Subsidiary thereon be direct, contingent, primary, secondary, several,
joint and several, or otherwise, and irrespective of whether such debts or
liabilities be evidenced by note, contract, open account, or otherwise, and
irrespective of the person or persons in whose favor such debts or liabilities
may, at their inception, have been, or may hereafter be created, or the manner
in which they have been or may hereafter be acquired by Guarantor. The Guarantor
Claims shall include without limitation all rights and claims of Guarantor




                                       11
<PAGE>   14


against Borrower or any Subsidiary of the Borrower arising as a result of
subrogation or otherwise as a result of Guarantor's payment of all or a portion
of the Liabilities. Until the Liabilities shall be paid and satisfied in full
and Guarantor shall have performed all of its obligations hereunder, Guarantor
shall not receive or collect, directly or indirectly, from Borrower or any
Subsidiary of the Borrower or any other party any amount upon the Guarantor
Claims.

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

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

         Section 4.4 Liens Subordinate. Guarantor agrees that any liens,
security interests, judgment liens, charges or other encumbrances upon
Borrower's or any Subsidiary of the Borrower's assets securing payment of the
Guarantor Claims shall be and remain inferior and subordinate to any liens,
security interests, judgment liens, charges or other encumbrances upon
Borrower's or any Subsidiary of the Borrower's assets securing payment of the
Liabilities, regardless of whether such encumbrances in favor of Guarantor, the
Agent or the Lenders presently exist or are hereafter created or attach.

         Section 4.5 Guarantor's Enforcement Rights. Without the prior written
consent of the Lenders, Guarantor shall not (a) exercise or enforce any
creditor's right it may have against the Borrower or any Subsidiary of the
Borrower, or (b) foreclose, repossess, sequester or otherwise take steps or
institute any action or proceeding (judicial or otherwise, including without
limitation the commencement of or joinder in any liquidation, bankruptcy,
rearrangement, debtor's relief or insolvency proceeding) to enforce any lien,
mortgages, deeds of trust, security interest, collateral rights, judgments


                                       12
<PAGE>   15

or other encumbrances on assets of Borrower or any Subsidiary of the Borrower
held by Guarantor.

                                    ARTICLE V

                          Certain Additional Covenants

         Section 5.1 Affirmative Covenants.

         Financial Statements. The Guarantor shall cause the Borrower to deliver
as and when required, the financial statements and other information called for
in Section 8.01 of the Credit Agreement and Guarantor shall:

                  (i)      Notice of Default. Promptly after the Guarantor knows
         that any default in any covenant herein has occurred, the Guarantor
         will give notice of such default to the Agent, describing the same in
         reasonable detail and the action the Guarantor proposes to take with
         respect thereto.

                  (ii)     Payment of Trade Payables. The Guarantor will pay and
         cause all of its Subsidiaries to pay all of their respective Trade
         Payables now or hereafter incurred within 60 days of the invoice or
         billing date, unless subject to legal offset or unless being contested
         in good faith by appropriate proceedings and reserves adequate under
         GAAP shall have been established therefor.

         Section 5.2 Negative Covenants. The Guarantor covenants and agrees
that, so long as any of the Commitments are in effect and until payment in full
of the Liabilities hereunder, all interest thereon and all other amounts payable
by the Guarantor hereunder, without the prior written consent of the Lenders:

                  (a)      Debt. The Guarantor will not and will not permit any
of its Subsidiaries to incur, create, assume or suffer to exist any Debt,
except:

                           (1)      the Notes or other Indebtedness arising
                  under the Loan Documents or any guaranty of or suretyship
                  arrangement for the Notes or other Indebtedness arising under
                  the Loan Documents;

                           (2)      Debt existing on the Closing Date which is
                  reflected in the Financial Statements or is disclosed in
                  Schedule 9.01 to the Credit Agreement, and any renewals or
                  extensions (but not increases) thereof;

                           (3)      Debt permitted under the Credit Agreement;

                           (4)      Debt owing to the Borrower, the Guarantor or
                  a Subsidiary Guarantor which (other than Debt owing to the
                  Borrower) is subordinated to the Indebtedness as provided in
                  the


                                       13
<PAGE>   16


                  Guaranty Agreement of the Guarantor or such Subsidiary
                  Guarantor;

                           (5)      Debt of the Guarantor or any of its
                  Subsidiaries which is not described in Sections 5.2(a)(1)
                  through (4) above and which together with all Debt of the
                  Borrower allowed under Section 9.01(h) of the Credit
                  Agreement, does not exceed $1,000,000 at any one time
                  outstanding;

                           (6)      the Subordinated Debt; and

                           (7)      Guarantees by Subsidiaries of the Guarantor
                  (which also are obligated upon or otherwise guarantee the
                  Liabilities pursuant to documents in form and substance
                  satisfactory to the Agent) which guarantee the Subordinated
                  Debt permitted under Section 5.2(a)(6) above, which Guarantees
                  are subordinated consistent with the Subordination Agreement
                  and otherwise are in form and substance satisfactory to the
                  Agent consistent with the Subordination Agreement.

                  (b)      Liens. The Guarantor will not and will not permit any
of its Subsidiaries to create, incur, assume or permit to exist any Lien on any
of its Properties (now owned or hereafter acquired), except:

                           (1)      Liens securing the payment of any
                  Indebtedness;

                           (2)      Excepted Liens;

                           (3)      Liens incurred by the Borrower and the
                  Borrower's Subsidiaries as permitted under the Credit
                  Agreement;

                           (4)      Liens securing the Subordinated Debt or the
                  Subordinated Guarantees on Properties upon which prior Liens
                  have been granted to secure the Liabilities pursuant to
                  documents in form and substance satisfactory to the Agent,
                  provided that such Liens (i) are subordinated to the Liens in
                  favor of the Lenders and otherwise are in form and substance
                  satisfactory to the Agent consistent with the Subordination
                  Agreement and (ii) do not directly or indirectly secure any
                  Hedging Agreements; and

                           (5)      the Term ORRI.

                  (c)      Investments, Loans and Advances. The Guarantor will
not and will not permit any of its Subsidiaries to remain outstanding any loans
or advances to or investments in any Person, except that the foregoing
restriction shall not apply to:

                           (1)      investments, loans or advances by the
                  Guarantor or a Subsidiary Guarantor (other than a Subsidiary
                  of the Borrower)



                                       14
<PAGE>   17



                  in or to the Borrower, the Guarantor or a Subsidiary
                  Guarantor; and

                           (2)      any other investments, loans and advances by
                  the Borrower or a Subsidiary of the Borrower as permitted
                  under Section 9.03 of the Credit Agreement.

                  (d)      Dividends, Distributions and Redemptions. The
Guarantor will not declare or pay any dividend, purchase, redeem or otherwise
acquire for value any of its stock now or hereafter outstanding, return any
capital to its stockholders or make any distribution of its assets to its
stockholders.

                  (e)      Sales and Leasebacks. The Guarantor will not and will
not permit any of its Subsidiaries to enter into any arrangement, directly or
indirectly, with any Person whereby such Person shall sell or transfer any of
its Property, whether now owned or hereafter acquired, and whereby such Person
shall then or thereafter rent or lease as lessee such Property or any part
thereof or other Property which such Person intends to use for substantially the
same purpose or purposes as the Property sold or transferred.

                  (f)      Nature of Business. The Guarantor will not allow any
material change to be made in the character of its business as presently
conducted.

                  (g)      Limitation on Leases. The Guarantor will not and will
not permit any of its Subsidiaries to create, incur, assume or suffer to exist
any obligation for the payment of rent or hire of Property of any kind
whatsoever (real or personal including capital leases but excluding leases of
Hydrocarbon Interests and the equipment used thereon), under leases or lease
agreements which would cause the aggregate amount of all payments made by the
Guarantor and its Subsidiaries pursuant to all such leases or lease agreements
to exceed $2,000,000 in any period of twelve consecutive calendar months during
the life of such leases.

                  (h)      Mergers, Etc. The Guarantor will not and will not
permit any of its Subsidiaries to merge into or with or consolidate with any
other Person or sell, lease or otherwise dispose of (whether in one transaction
or in a series of transactions) all or substantially all of its Property or
assets to any other Person unless the Guarantor, the Borrower or any Subsidiary
Guarantor whose Guaranty Agreement is in full force and effect is the surviving
entity and no Default exists or will be created thereby.

                  (i)      ERISA Compliance. The Guarantor will not and will not
permit any of its Subsidiaries to at any time:

                           (1)      Engage in, or permit any ERISA Affiliate to
                  engage in, any transaction in connection with which the
                  Guarantor, any of its Subsidiaries or any ERISA Affiliate
                  could be subjected to either a civil penalty assessed pursuant
                  to section 502(c), (i) or (l) of ERISA or a tax imposed by
                  Chapter 43 of Subtitle D of the Code in excess of $100,000;



                                       15
<PAGE>   18

                           (2)      Terminate, or permit any ERISA Affiliate to
                  terminate, any Plan in a manner, or take any other action with
                  respect to any Plan, which could reasonably be expected to
                  result in any liability of the Guarantor, any of its
                  Subsidiaries or any ERISA Affiliate to the PBGC in excess of
                  $100,000;

                           (3)      Fail to make, or permit any ERISA Affiliate
                  to fail to make, full payment when due of all amounts which
                  under the provisions of any Plan, agreement relating thereto
                  or applicable law, the Guarantor, any of its Subsidiaries or
                  any ERISA Affiliate is required to pay as contributions
                  thereto;

                           (4)      Permit to exist, or allow any ERISA
                  Affiliate to permit to exist, any accumulated funding
                  deficiency in excess of $100,000 within the meaning of Section
                  302 of ERISA or section 412 of the Code, whether or not
                  waived, with respect to any Plan;

                           (5)      Permit, or allow any ERISA Affiliate to
                  permit, the actuarial present value of the benefit liabilities
                  under any Plan maintained by the Guarantor, any of its
                  Subsidiaries or any ERISA Affiliate which is regulated under
                  Title IV of ERISA to exceed the current value of the assets
                  (computed on a plan termination basis in accordance with Title
                  IV of ERISA) of such Plan allocable to such benefit
                  liabilities by an amount in excess of $100,000. The term
                  "actuarial present value of the benefit liabilities" shall
                  have the meaning specified in section 4041 of ERISA;

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

                           (7)      Acquire, or permit any ERISA Affiliate to
                  acquire, an interest in any Person that causes such Person to
                  become an ERISA Affiliate with respect to the Borrower or any
                  ERISA Affiliate if such Person sponsors, maintains or
                  contributes to, or at any time in the six-year period
                  preceding such acquisition has sponsored, maintained, or
                  contributed to, (a) any Multiemployer Plan, or (b) any other
                  Plan that is subject to Title IV of ERISA under which the
                  actuarial present value of the benefit liabilities under such
                  Plan exceeds 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;

                           (8)      Incur, or permit any ERISA Affiliate to
                  incur, a liability to or on account of a Plan under sections
                  515, 4062, 4063, 4064, 4201 or 4204 of ERISA which in the
                  aggregate for all such liability exceeds $100,000;


                                       16
<PAGE>   19

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

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

                  (j)      Sale or Discount of Receivables. The Guarantor will
not and will not permit any of its Subsidiaries to discount or sell (with or
without recourse) any of its notes receivable or accounts receivable.

                  (k)      Capital Expenditures. The Guarantor will not and will
not permit Borrower to exceed the capital expenditure limitations provided in
Section 9.22 of the Credit Agreement.

                  (l)      Environmental Matters. The Guarantor will not and
will not permit any of its Subsidiaries to cause or permit any of its Property
to be in violation of, or do anything or permit anything to be done which will
subject any such Property to any remedial obligations under any Environmental
Laws, assuming disclosure to the applicable Governmental Authority of all
relevant facts, conditions and circumstances, if any, pertaining to such
Property where such violations or remedial obligations would have a Material
Adverse Effect.

                  (m)      Transactions with Affiliates. The Guarantor will not
and will not permit any of its Subsidiaries to enter into any transaction,
including, without limitation, any purchase, sale, lease or exchange of Property
or the rendering of any service, with any Affiliate unless such transactions are
otherwise not in violation of the Credit Agreement, are in the ordinary course
of its business and are upon fair and reasonable terms no less favorable to it
(or, if the Borrower is involved, no less favorable to the Borrower) than it
would obtain in a comparable arm's length transaction with a Person not an
Affiliate.

                  (n)      Subsidiaries. The Guarantor will not and will not
permit any of its Subsidiaries to, create any additional Subsidiaries except for
the Subsidiaries of the Borrower as permitted by the Credit Agreement.

                  (o)      Negative Pledge Agreements. The Guarantor will not
and will not permit any of its Subsidiaries to create, incur, assume or suffer
to exist any contract, agreement or understanding (other than the Loan
Documents, the Indenture and the documents described in Section 4.01(a) through
(d) of the Indenture, and any other



                                       17
<PAGE>   20


documents establishing Liens permitted under Sections 5.2(b)(4) and (5)) which
in any way prohibits or restricts the granting, conveying, creation or
imposition of any Lien on any of its Property or which requires the consent of
or notice to other Persons in connection therewith.

                  (p)      Capital Stock of General Partner of Borrower. The
Guarantor will not permit any of the capital stock of the General Partner of the
Borrower or any ownership interest in any limited partner of the Borrower to be
owned or controlled by any Person other than the Guarantor or Brigham Inc.

                  (q)      Current Ratio. The Guarantor will not permit its
ratio of (i) consolidated current assets of the Guarantor and its Consolidated
Subsidiaries to (ii) their consolidated current liabilities (excluding the
Indebtedness) to be less than (A) .75 to 1.0 for the quarters ended December 31,
1999 and March 31, 2000 or (B) 1.0 to 1.0 at any time thereafter.

                  (r)      Interest Coverage Ratio. The Guarantor will not
permit its Interest Coverage Ratio as of the end of any fiscal quarter of the
Guarantor (calculated quarterly at the end of each fiscal quarter) to be less
than the ratio set forth below for such period. Interest Coverage Ratio shall
mean the ratio of (i) EBITDA to (ii) the sum of all required payments of
interest (whether paid in cash or in kind) during such period on borrowed money
(excluding any payments made on account of the Term ORRI):

                  (i)      not less than .75 to 1.0 for the twelve (12) month
         period ending September 30, 2000;

                  (ii)     not less than .90 to 1.0 for the twelve (12) month
         period ending December 31, 2000;

                  (iii)    not less than 1.1 to 1.0 for the twelve (12) month
         period ending March 31, 2001;

                  (iv)     not less than 1.3 to 1.0 for the twelve (12) month
         period ending June 30, 2001;

                  (v)      not less than 1.5 to 1.0 for the twelve (12) month
         period ending September 30, 2001;

                  (vi)     thereafter, not less than 1.7 to 1.0 for the twelve
         (12) month period ending December 31, 2001, and each twelve (12) month
         period ending at the end of each fiscal quarter of Guarantor;

                  (s)      Securities Purchase Agreement, Indenture and Equity
Conversion Agreement. The Guarantor will not agree to any amendment or
modification to the Securities Purchase Agreement, the Indenture or the Equity
Conversion Agreement without the express written consent of the Majority
Lenders; provided that a waiver of a default under the Equity Conversion
Agreement shall not constitute a modification or amendment or require the
consent of any BMO/Soc-Gen Lender.



                                       18
<PAGE>   21

                  (t)      Payments on Subordinated Debt.


                           (i)      No prepayments of principal will be made on
the Subordinated Debt unless all of the Subordinated Debt is prepaid by (a)
converting all of the Subordinated Debt into common stock and/or preferred stock
with cashless dividends of Guarantor or (b) applying the proceeds from a sale of
Guarantor's common stock and/or preferred stock with cashless dividends or (c)
refinancing the Subordinated Debt through the issuance of debt and/or common
stock and/or preferred stock with cashless dividends of Guarantor on refinancing
terms reasonably acceptable to the Majority Lenders; and

                           (ii)     No payment of interest will be made in cash
on the Subordinated Debt on or before August 20, 2000 and from and after August
20, 2000, (a) no payment of interest will be made in cash on the Subordinated
Debt if on or before November 20, 2000 Guarantor has earned the right to pay
interest in kind for such quarterly payment and (b) no payment of interest will
be made in cash on the Subordinated Debt (i) if an Event of Default under
Section 10.01(a) of the Credit Agreement has occurred, or (ii) if a Borrowing
Base deficiency is in existence under the Credit Agreement.

                                   ARTICLE VI

                                  Miscellaneous

         Section 6.1 Successors and Assigns. This Guaranty Agreement is and
shall be, in every particular, available to the successors and assigns of the
Lenders and is and shall always be fully binding upon the legal representatives,
heirs, successors and assigns of Guarantor, notwithstanding that some or all of
the monies, the repayment of which this Guaranty Agreement applies, may be
actually advanced after any bankruptcy, receivership, reorganization, death,
disability or other event affecting Guarantor.

         Section 6.2 Notices. Any notice or demand to Guarantor under or in
connection with this Guaranty Agreement may be given and shall conclusively be
deemed and considered to have been given and received in accordance with Section
12.02 of the Credit Agreement, addressed to Guarantor at the address on the
signature page hereof or at such other address provided to the Agent in writing.

         Section 6.3 Business and Financial Information. Subject to any
applicable confidentiality agreements, the Guarantor will promptly furnish to
the Agent and the Lenders from time to time upon request such information
regarding the business and affairs and financial condition of the Guarantor and
its subsidiaries as the Agent and the Lenders may reasonably request.

         Section 6.4 Construction. This Guaranty Agreement is a contract made
under and shall be construed in accordance with and governed by the laws of the
State of Texas.


                                       19
<PAGE>   22


         Section 6.5 Invalidity. In the event that any one or more of the
provisions contained in this Guaranty Agreement shall, for any reason, be held
invalid, illegal or unenforceable in any respect, such invalidity, illegality or
unenforceability shall not affect any other provision of this Guaranty
Agreement.

         Section 6.6 ENTIRE AGREEMENT. THIS WRITTEN GUARANTY AGREEMENT EMBODIES
THE ENTIRE AGREEMENT AND UNDERSTANDING BETWEEN THE LENDERS AND THE GUARANTOR AND
SUPERSEDES ALL OTHER AGREEMENTS AND UNDERSTANDINGS BETWEEN SUCH PARTIES RELATING
TO THE SUBJECT MATTER HEREOF AND THEREOF. THIS WRITTEN GUARANTY AGREEMENT
REPRESENTS THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED
BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL AGREEMENTS OF THE
PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.




                                       20
<PAGE>   23





         WITNESS THE EXECUTION HEREOF, as of this the 17th day of February,
2000.

                                              BRIGHAM EXPLORATION COMPANY



                                              By:
                                                 -------------------------------
                                              Name:    Curtis F. Harrell
                                              Title:   Chief Financial Officer

                                              Address for Notices:

                                              6300 Bridge Point Parkway
                                              Building 2, Suite 500
                                              Austin, Texas  78730
                                              Telecopier No.: (512) 427-3400
                                              Telephone No.: (512) 427-3300
                                              Attention:  Curtis F. Harrell


                                        S
<PAGE>   24




                                   SCHEDULE I

                       SUBSIDIARIES OF BRIGHAM EXPLORATION

                  Brigham Exploration has the following Subsidiaries:

         1.       Brigham, Inc., a Nevada corporation, all of whose shares are
                  owned by Brigham Exploration.

         2.       Brigham Holdings I, LLC, a Nevada limited liability company,
                  whose only member is Brigham Exploration.

         3.       Brigham Holdings II, LLC, a Nevada limited liability company,
                  whose only member is Brigham, Inc.

         4.       Borrower, a Delaware limited partnership, whose only General
                  Partner is Brigham, Inc., and whose only limited partners are
                  Brigham Holdings I, LLC and Brigham Holdings II, LLC.



                                     SCH I-1