SUBORDINATED GUARANTY AGREEMENT


                                       BY


                           BRIGHAM EXPLORATION COMPANY


                                   in favor of


                          SHELL CAPITAL INC., AS AGENT
                             AND EACH OF THE LENDERS
                          PARTY TO THE CREDIT AGREEMENT



                                October 31, 2000




                                TABLE OF CONTENTS
                                -----------------


ARTICLE 1         GENERAL TERMS                                          1
- ---------         -------------
         Section 1.1     Terms Defined Above                             2
         Section 1.2     Certain Definitions                             2
         Section 1.3     Credit Agreement Definitions                    2
ARTICLE 2         THE GUARANTY                                           3
- ---------         ------------
         Section 2.1     Liabilities Guaranteed                          3
         Section 2.2     Nature of Guaranty                              3
         Section 2.3     Agent's Rights                                  3
         Section 2.4     Guarantor's Waivers                             3
         Section 2.5     Maturity of Liabilities; Payment                4
         Section 2.6     Agent's Expenses                                4
         Section 2.7     Liability                                       4
         Section 2.8     Events and Circumstances Not Reducing Or
                         Discharging Guarantor's Obligations             4
ARTICLE 3         REPRESENTATIONS, WARRANTIES AND COVENANTS              6
- ---------         -----------------------------------------
         Section 3.1     By Guarantor                                    6
         Section 3.2     No Representation by Lenders                   10
ARTICLE 4         SUBORDINATION OF INDEBTEDNESS                         11
- ---------         -----------------------------
         Section 4.1     Subordination of All Guarantor Claims          11
         Section 4.2     Claims in Bankruptcy                           11
         Section 4.3     Payments Held in Trust                         11
         Section 4.4     Liens Subordinate                              12
         Section 4.5     Guarantor's Enforcement Rights                 12
ARTICLE 5         CERTAIN ADDITIONAL COVENANTS                          12
- ---------         ----------------------------
         Section 5.1     AFFIRMATIVE COVENANTS                          12
         Financial Statements                                           12
         Section 5.2     NEGATIVE COVENANTS                             13
ARTICLE 6         MISCELLANEOUS                                         18
- ---------         -------------
         Section 6.1     Successors and Assigns                         18
         Section 6.2     Notices                                        18
         Section 6.3     Business and Financial Information             18
         Section 6.4     Construction                                   18
         Section 6.5     Invalidity                                     18
         Section 6.6     Entire Agreement                               19




                         SUBORDINATED GUARANTY AGREEMENT


         THIS SUBORDINATED GUARANTY AGREEMENT (this "GUARANTY AGREEMENT") by
BRIGHAM EXPLORATION COMPANY (hereinafter called "GUARANTOR"), is in favor of
SHELL CAPITAL INC., as agent (the "AGENT") for the lenders (the "LENDERS") that
are or become parties to the Credit Agreement defined below, and the Lenders.

                              W I T N E S S E T H:
                              - - - - - - - - - -

         WHEREAS, on even date herewith, BRIGHAM OIL & GAS, L.P., a Delaware
limited partnership (hereinafter called "BORROWER"), the Agent and the Lenders
have entered into that certain Subordinated Credit Agreement (as the same may be
amended from time to time, the "CREDIT AGREEMENT"); and

         WHEREAS, Borrower has entered into that certain Amended and Restated
Credit Agreement with Bank of Montreal, as agent (the "SENIOR AGENT") and the
Lenders that are or become parties thereto (the "SENIOR LENDER") dated as of
February 17, 2000 (as the same may be amended from time to time, the "SENIOR
CREDIT AGREEMENT"); and

         WHEREAS, pursuant to the terms of the Senior Credit Agreement,
Guarantor has entered into that certain Amended and Restated Guaranty Agreement
in favor of Senior Agent for the Senior Lender dated as of February 17, 2000 (as
the same may be amended from time to time, the "SENIOR GUARANTY AGREEMENT");

         WHEREAS, one of the terms and conditions stated in the Credit Agreement
for the making of the loans described therein is the execution and delivery to
the Agent for the benefit of the Lenders of this Guaranty Agreement;

         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 as follows:


                                    ARTICLE I

                                  GENERAL TERMS

         Section 1.1 TERMS DEFINED ABOVE. As used in this Guaranty Agreement,
the terms "Borrower", "Credit Agreement", "Guarantor", "Lenders", "Senior
Agent", "Senior Credit


                                       1


Agreement", "Senior Guaranty Agreement" and "SeniorLender" 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 Guaranty Agreement, as the same
         may from time to time be amended or supplemented.

         "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;

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

                  (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.

         "SUBORDINATION AGREEMENT" shall mean that certain Intercreditor and
         Subordination Agreement of even date herewith among the Senior Agent,
         Senior Lender, Agent, Lender Guarantor, each of the Subsidiary
         Guarantors and Borrower.

         "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.


                                       2


                                   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, 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


                                       3


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 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


                                       4


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 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;


                                       5


         (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;

         (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:


                                       6


         (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 (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, 1999 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 June 30, 2000 and their related
         consolidated statements of income, stockholders' equity and cash flow
         of the Guarantor and its Consolidated Subsidiaries for the six-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
         six-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


                                       7


         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, 1999, 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 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


                                       8


         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.

                  (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


                                       9


         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, 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.

         (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.


                                       10


                                   ARTICLE IV

                                  SUBORDINATION

         Section 4.1  SUBORDINATION.

         (a) 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 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.

         (b) SUBORDINATION OF THIS GUARANTY AGREEMENT. The payment and
         performance of this Guaranty Agreement is subordinated pursuant to the
         terms and provisions of the Subordination Agreement.

         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


                                       11


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 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:

         (a) 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.

         (b) 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 date of invoice, unless
         subject to legal offset or unless being contested in good faith by


                                       12


         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 Majority
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 Guaranty Agreement of the
         Guarantor or such Subsidiary Guarantor;

                  (5) Debt of the Guarantor not described in Sections 5.2 (1)
         through (4) above 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; and

                  (6) The Senior Indebtedness and any other Debt arising under
         or otherwise in relation to the Senior Loan Documents.

         (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 created, incurred, assumed or permitted to
                           exist by the Borrower and the Borrower's Subsidiaries
                           as permitted under the Credit Agreement; and


                                       13


                  (4)      Liens securing the payment of the Senior
                           Indebtedness.

         (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) 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; provided that Guarantor may pay dividends on its
         preferred equity securities so long as they are paid in kind and not in
         cash.

         (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


                                       14


         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;

                  (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


                                       15


         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;

                  (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 9.20 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.


                                       16


         (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 and the Senior Loan Documents) 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 (including, without limitation, any unused and available
         Aggregate Commitments) to (ii) their consolidated current liabilities
         (excluding the Indebtedness) to be less than 1.0 to 1.0 at any time.

         (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:

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

                  (ii)     not less than .80 to 1.0 for the twelve (12) month
                           period ending December 31, 2000;

                  (iii)    not less than .90 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;


                                       17



                  (vi)     not less than 1.7 to 1.0 for the twelve (12) month
                           period ending December 31, 2001;

                  (vii)    not less than 2.0 to 1.0 for the twelve (12) month
                           period ending March 31, 2002;

                  (viii)   not less than 2.25 to 1.0 for the twelve (12) month
                           period ending June 30, 2002; and

                  (ix)     thereafter, not less than 2.50 to 1.0 for the twelve
                           (12) month period ending September 30, 2002, and each
                           twelve (12) month period ending at the end of each
                           fiscal quarter of Guarantor.



                                   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.

         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


                                       18


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.


         WITNESS THE EXECUTION HEREOF, as of this the 31st day of October, 2000.

                                     BRIGHAM EXPLORATION COMPANY




                                     By:  /s/ Curtis F. Harrell
                                     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:


                                       19


                                   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.


                                       20