Document:

ANCILLARY AGREEMENT

                                    RECITALS:

      A. Reference is made to that certain Amended and Restated Credit Agreement
(the "Senior Credit Agreement") dated as of February 17, 2000, among Brigham Oil
& Gas, L.P. ("Borrower"), Bank of Montreal, a Canadian bank, in its individual
capacity (in its individual capacity, "BMO"), and BMO, in its capacity as agent
(in such capacity, together with its successors in such capacity, the "Senior
Agent"), Societe Generale, Southwest Agency ("Soc-Gen") and Shell Capital Inc.
("SCI"); all capitalized terms used but not defined herein shall have the
meanings assigned to them in the Senior Credit Agreement or in the Equity
Conversion Agreement, as such term is defined in the Senior Credit Agreement.

      B. Borrower and SCI have reached an understanding concerning the reduction
of a portion of the Loans made by the SCI Lenders under the Senior Credit
Agreement, and desire to evidence such understanding by entering into this
Ancillary Agreement.

                                   AGREEMENT:

      1. In the event Borrower does not reduce the outstanding Loans of the SCI
Lenders under the Senior Credit Agreement by at least $15,000,000 on or before
January 31, 2001, Borrower shall permanently forfeit its right to force
conversion of the Tranche One Convertible Amount at $3.90 per share.

      2. Until such time as the Borrower reduces the outstanding Loans of the
SCI Lenders under the Senior Credit Agreement by $15,000,000 the Borrower shall
not have the right to force a conversion of the Tranche One Convertible Amount
pursuant to Section 2.02(a) of the Equity Conversion Agreement.

      3. The Borrower does not have the right to force conversion on any tranche
pursuant to Sections 2.02(a), (b) and (c) of the Equity Conversion Agreement
("Tranche") prior to the release of first quarter 2001 financial information
unless the Guarantor's EBITDA to Interest as of December 31, 2000 is at least
 .9:1.0 and it does not have the right to force conversion on any Tranche after
the release of the first quarter 2001 ratios and prior to the release of second
quarter 2001 financial information unless the Guarantor's EBITDA to Interest as
of the first quarter 2001 is at least 1.1:1.0.

                                 MISCELLANEOUS:

(a) COUNTERPARTS: This Ancillary Agreement is being executed in several
counterparts, all of which are identical; all such counter parts shall be
construed together as the same instrument.

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(b) CHOICE OF LAW: THIS ANCILLARY AGREEMENT SHALL, WITHOUT REGARD TO PRINCIPLES
OF CONFLICTS OF LAW, BE GOVERNED AND CONSTRUED UNDER AND IN ACCORDANCE WITH THE
LAWS OF THE STATE OF TEXAS.

(c) ENTIRETY AND MODIFICATION. This Ancillary Agreement constitutes the entire
agreement between the parties hereto with respect to the subject matter hereof
and supercedes any and all prior agreements and understandings, whether oral or
written, between the parties hereto relating to such subject matter.

      This Ancillary Agreement is executed and delivered on this 31st day of
October, 2000.

                                    SHELL CAPITAL INC.
                                    By: /s/ Robert L. Roberts
                                    Name:   Robert L. Roberts
                                    Title:  Vice President

                                    BRIGHAM OIL & GAS, L.P.

                                    By:   Brigham, Inc., as General Partner

                                    By: /s/ Curtis F. Harrell
                                    Name:   Curtis F. Harrell
                                    Title:  Chief Financial OfficerINTERCREDITOR AND
                             SUBORDINATION AGREEMENT

      THIS INTERCREDITOR AND SUBORDINATION AGREEMENT (this "AGREEMENT") is made
as of October 31, 2000, by and between Shell Capital Inc. as agent (in such
capacity, and together with any successor in such capacity, the "SUBORDINATED
AGENT") for each of the lenders that is signatory to, or which becomes a
signatory to, the Subordinated Credit Agreement (as defined below)
(collectively, the "SUBORDINATED LENDER"), and Bank of Montreal, individually
("BMO") and as agent for the Senior Lenders, as defined below (in such capacity
as agent, and together with any successor in such capacity, the "SENIOR Agent"),
Societe Generale, Southwest Agency ("SOC-GEN"), Shell Capital Inc. ("SCI") (BMO,
Soc-Gen, SCI and any other lender that becomes a signatory to the Senior Credit
Agreement, as defined below, are herein collectively called the "SENIOR
LENDER").

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

                                    RECITALS

      A. BOG, as the borrower, the Senior Agent and the Senior Lender are
parties to that certain Amended and Restated Credit Agreement dated as of
February 17, 2000 (such agreement, as the same may be from time to time amended,
modified, supplemented, restated, refinanced or replaced, the "SENIOR CREDIT
AGREEMENT"), pursuant to which the Senior Lenders have made certain credit
available to and on behalf of BOG.

      B. BOG has executed one or more Mortgages (as such term is defined in the
Senior Credit Agreement) and associated security agreements and/or financing
statements (such agreements, as the same may have heretofore been or may
hereafter be from time to time amended, supplemented or replaced, the "SENIOR
MORTGAGE") in favor of the Senior Agent to secure, INTER ALIA, the obligations
outstanding under the Senior Credit Agreement.

      C. Parent has executed an Amended and Restated Guaranty Agreement dated as
of February 17, 2000, as amended by a First Amendment to Amended and Restated
Guaranty Agreement of even date herewith (the "PARENT GUARANTY AGREEMENT"), and
BI, BH-I and BH-II have each executed a Guaranty Agreement dated as of January
26, 1998, as each has been amended by a First Amendment to Guaranty Agreement
dated as of February 17, 2000 (such Guaranty Agreements, together with the
Parent Guaranty Agreement, as each of the same may be from time to time further
amended, supplemented or replaced, being referred to herein as the

<PAGE>

"SENIOR GUARANTY AGREEMENTS"), in favor of the Senior Agent and the Senior
Lender to guarantee, INTER ALIA, the obligations of BOG under the Senior Credit
Agreement.

      D. Parent has executed a Security Agreement dated as of January 26, 1998
and a Security Agreement dated as of August 28, 1998, each as amended by an
Amendment to Security Agreement dated as of February 17, 2000 (as the same may
be from time to time further amended, supplemented or replaced, the "SENIOR
PARENT SECURITY AGREEMENT") to secure, INTER ALIA, the obligations of BOG under
the Senior Credit Agreement.

      E. BOG has executed a Security Agreement dated as of January 26, 1998, as
amended by a First Amendment to Security Agreement dated as of March 26, 1999
and a Second Amendment to Security Agreement dated as of February 17, 2000 (as
the same may be from time to time further amended, supplemented or replaced, the
"SENIOR BOG SECURITY AGREEMENT") to secure, INTER ALIA, the obligations of BOG
under the Senior Credit Agreement.

      F. BI has executed a Security Agreement dated as of August 20, 1998, as
amended by a First Amendment to Security Agreement dated as of March 26, 1999,
and a Second Amendment to Security Agreement dated as of February 17, 2000, (the
"SENIOR BI SECURITY AGREEMENT"), BH-I has executed a Security Agreement dated as
of August 20, 1998, as amended by a First Amendment to Security Agreement dated
as of March 26, 1999, and a Second Amendment to Security Agreement dated as of
February 17, 2000, (the "SENIOR BH-I SECURITY AGREEMENT"), and BH-II has
executed a Security Agreement dated as of August 20, 1998, as amended by a First
Amendment to Security Agreement dated as of March 26, 1999, and a Second
Amendment to Security Agreement dated as of February 17, 2000, (the "SENIOR
BH-II SECURITY AGREEMENT") The Senior BI Security Agreement, the Senior BH-I
Security Agreement and the Senior BH-II Security Agreement are herein
collectively called the "SENIOR AFFILIATE SECURITY Agreements". The Senior
Credit Agreement, the Senior Mortgage, the Senior Guaranty Agreements, the
Senior Parent Security Agreement, the Senior BOG Security Agreement, the Senior
Affiliate Security Agreements and any other documents or instruments given in
connection therewith or otherwise in connection with the Senior Credit Agreement
are collectively referred to herein as the "SENIOR LOAN DOCUMENTS".

      G. Of even date herewith, BOG has entered into that certain Subordinated
Credit Agreement with the Subordinated Agent and the Subordinated Lender (the
"SUBORDINATED CREDIT AGREEMENT") pursuant to which the Subordinated Lender will
make loans to BOG, such advances to be evidenced by a promissory note executed
and delivered by BOG in accordance with the Subordinated Credit Agreement (the
"SUBORDINATED NOTE").

      H. In connection with the execution and delivery of the Subordinated
Credit Agreement, BOG has executed, or will execute, one or more Mortgages (as
such term is defined in the Subordinated Credit Agreement) and associated
security agreements and/or financing statements (as the same may be from time to
time amended, modified, supplemented or replaced, the "SECOND MORTGAGES") in
favor of the Agent to secure, INTER ALIA, the obligations outstanding under the
Subordinated Loan Documents (as hereinafter defined).

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<PAGE>

      I. In connection with the execution and delivery of the Subordinated
Credit Agreement, Parent, BI, BH-I and BH-II have each executed and delivered a
Subordinated Guaranty Agreement dated of even date herewith (as the same may be
from time to time amended, modified, supplemented or replaced, being referred to
herein as the "SUBORDINATED GUARANTY AGREEMENTS"), in favor of the Subordinated
Agent, for the benefit of the Subordinated Agent and the Subordinated Lender to
guarantee, INTER ALIA, the obligations of the BOG under the Subordinated Loan
Documents.

      J. In connection with the execution and delivery of the Subordinated
Credit Agreement, Parent, Borrower, BI, BH-I and BH-II have each executed and
delivered a Second Security Agreement in favor of the Subordinated Agent dated
of even date herewith (as the same may be from time to time further amended,
modified, supplemented or replaced, the "SECOND SECURITY AGREEMENTS").

      K. The Subordinated Credit Agreement, the Subordinated Note, the Second
Mortgages, the Subordinated Guaranty Agreements, the Second Security Agreements
and those other documents or instruments now or hereafter given in connection
therewith, and including those identified on Exhibit "A" attached hereto, as any
of such documents or instruments may be amended, supplemented or replaced are
collectively referred to herein as the "SUBORDINATED LOAN DOCUMENTS".

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

                                    ARTICLE I
                                   DEFINITIONS

      Section 1.1 TERMS DEFINED ABOVE. As used in this Agreement, the terms
defined above shall have the meanings respectively assigned to them.

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

      "AFFILIATE" of any Person shall mean (i) any Person directly or indirectly
      controlled by, controlling or under common control with such first Person,
      (ii) any director or officer of such first Person or of any Person
      referred to in clause (i) above and (iii) if any Person in clause (i)
      above is an individual, any member of the immediate family (including
      parents, spouse and children) of such individual and any trust whose
      principal beneficiary is such individual or one or more members of such
      immediate family and any Person who is controlled by any such member or
      trust. For purposes of this definition, any Person which owns directly or
      indirectly 20% or more of the securities having ordinary voting power for
      the election of directors or other governing body of a corporation or 20%
      or more of the partnership or other ownership interests of any other
      Person (other than as a

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<PAGE>

      limited partner of such other Person) will be deemed to "CONTROL"
      (including, with its correlative meanings, "CONTROLLED by" and "UNDER
      COMMON CONTROL WITH") such corporation or other Person.

      "HEDGING AGREEMENT" shall mean any commodity, interest rate or currency
      swap, cap, floor, collar, forward agreement or other exchange or
      protection agreements or any option with respect to any such transaction
      permitted by the terms of the Senior Credit Agreement, now or hereafter
      existing between (i) BOG and BMO and its successors or assigns ("BMO HEDGE
      PARTY") and Soc-Gen and its successors and assigns ("SOC-GEN HEDGE PARTY")
      entered into while such BMO Hedge Party or Soc-Gen Hedge Party is a Senior
      Lender; and (ii) BOG and SCI and its successors or assigns (with Loans (as
      defined in the Senior Credit Agreement) or Commitments (as defined in the
      Senior Credit Agreement) 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 Senior
      Lender.

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

      "OIL AND GAS PROPERTIES" shall have the meaning attributed to such term in
      the Senior Credit Agreement.

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

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

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

      "SENIOR INDEBTEDNESS" shall mean the principal balance of all loans
      advanced to or letters of credit issued for the account of BOG pursuant to
      the terms and conditions of the Senior Loan Documents, not to exceed
      $75,000,000 in principal amount plus such additional amounts as are
      permitted under Section 2.6(a)(ii) of this Agreement, and accrued but
      unpaid interest thereon, all fees, expenses, reimbursements obligations,
      liabilities, indemnities or other monetary obligations of BOG, the Parent
      or any Obligor under any Senior Loan Document, and all swap settlement
      amounts or other amounts due and payable under any

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<PAGE>

      Senior Loan Document, and all swap settlement amounts or other amounts due
      and payable under any Hedging Agreements, whether any of the foregoing is
      (i) absolute or contingent, direct or indirect, joint, several or
      independent, (ii) now outstanding or owing or which may hereafter be
      existing or incurred, (iii) due or to become due, or (iv) held or to be
      held by the Senior Agent or any Senior Lender, and all renewals,
      extensions, rearrangements, refundings and modifications thereof permitted
      by the terms hereof.

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

                                   ARTICLE II
                                  SUBORDINATION

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

      Section 2.2 PAYMENT SUBORDINATION UPON DEFAULT.

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

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

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

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

                        (B) the payment of the Subordinated Indebtedness would
                  result in a default or event of default under the Senior Loan
                  Documents or any

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<PAGE>

                  other default has occurred and is continuing with respect to
                  the Senior Indebtedness that permits, or with the giving of
                  notice or passage of time or both (unless cured or waived)
                  would permit, the Senior Agent or the Senior Lender to
                  accelerate its maturity and the Subordinated Agent receives a
                  notice of the default (a "PAYMENT BLOCKAGE NOTICE") from the
                  Parent, BOG, and Obligor, the Senior Agent or any Senior
                  Lender with regard to the foregoing.

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

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

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

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

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

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

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

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<PAGE>

                  Indebtedness in full, after giving effect to any concurrent
                  payment, distribution or provision thereof to or for the
                  Senior Agent and the Senior Lender.

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

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

      Section 2.3 PAYMENTS RECEIVED OR MADE IN VIOLATION OF THIS AGREEMENT.

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

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

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

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            Section 2.4 LIENS SUBORDINATE.

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

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

      Section 2.5 AGREEMENT NOT TO PURSUE ACTION.

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

                                      -8-
<PAGE>

the running of any applicable statute of limitations, or (C) or similar actions
necessary to preserve the legal rights of the Subordinated Lender and/or the
Subordinated Agent.

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

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

      Section 2.6. RIGHTS OF THE SENIOR AGENT AND THE SENIOR LENDER. The Senior
Agent and the Senior Lender may, at any time, and from time to time, without the
consent of or notice to the Subordinated Agent or any Subordinated Lender,
without incurring responsibility to the Subordinated Agent and/or any
Subordinated Lender, without impairing or releasing any of the Senior Agent or
the Senior Lender's rights or any of the obligations of the Subordinated Agent
and the Subordinated Lender under this Agreement:

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

                  (i)   To increase rate of interest; or

                  (ii) To increase the principal amount of the Senior
            Indebtedness (excluding obligations of any kind under any Hedging
            Agreements) above $75,000,000, unless such increase does not violate
            the terms of or create a default under the Subordinated Credit
            Agreement; or

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

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

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

                                      -9-
<PAGE>

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

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

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

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

      Section 2.7 SUBORDINATION MAY NOT BE IMPAIRED BY THE PARENT, BOG OR ANY
OBLIGORS. No right of any present or future Senior Agent or Senior Lender to
enforce the subordination as provided in this Agreement will at any time or in
any way be prejudiced or impaired by any act or failure to act on the part of
the Parent, BOG or any Obligor or by any act or failure to act, in good faith,
by the Senior Agent or any Senior Lender, or by any noncompliance by the Parent,
BOG or any Obligor with the terms of any Subordinated Loan Document, regardless
of any knowledge thereof that the Senior Agent or any Senior Lender may have or
otherwise be charged with. The provisions of this Section 2.7 are intended to be
for the benefit of, and shall be enforceable directly by, the Senior Agent or
the Senior Lender.

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

                                   ARTICLE III
                    REPRESENTATIONS, WARRANTIES AND COVENANT

      Section 3.1.  REPRESENTATIONS  OF  SUBORDINATED  AGENT  AND SUBORDINATED
LENDER.  The  Subordinated Agent and  each Subordinated Lender represent and
warrant that:

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

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

                                      -10-
<PAGE>

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

      Section 3.2.  REPRESENTATIONS OF SENIOR AGENT. The Senior Agent represents
and warrants that:

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

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

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

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

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

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

            (c) not amend, supplement or otherwise modify the terms of the
Subordinated Indebtedness, (including, without limitation, the Subordinated Loan
Documents) without the express written consent of the Senior Agent, which
consent will not be unreasonably withheld, which has the effect of (i)
increasing the outstanding principal amount of the Subordinated Indebtedness
above $20,000,000, provided that the foregoing shall not affect the BOG's right
to make payment in kind of accrued interest or the Subordinated Lender's ability
to accept payment in kind as provided in the Subordinated Loan Documents,
thereby increasing the principal amount of the Subordinated Indebtedness and
(ii) increasing the rate of interest or any fees charged on the Subordinated
Indebtedness.

                                      -11-
<PAGE>

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

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

                                   ARTICLE IV
                                  MISCELLANEOUS

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

      Section 4.2 ASSIGNMENT BY THE SENIOR AGENT AND THE SENIOR LENDER. This
Agreement may be assigned by the Senior Agent and the Senior Lender in
connection with any assignment or transfer of the Senior Indebtedness or any
replacement or refinancing of the Senior Loan.

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

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

or at such other address as shall be designated by the Senior Agent in a notice
to each other party. Except as otherwise provided in this Agreement, all such
communications shall be deemed to have been duly given when transmitted by
telecopier or personally delivered or, in the case of a mailed notice, five (5)
days after the date deposited in the mails, postage prepaid, in each case given
or addressed as aforesaid.

      Section 4.4 AMENDMENTS AND WAIVERS. The Senior Agent's, Subordinated
Agent's, any Senior Lender's or Subordinated Lender's acceptance of partial or
delinquent payments or any forbearance, failure or delay by any of the foregoing
in exercising any right, power or

                                      -12-
<PAGE>

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

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

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

      Section 4.7 GOVERNING  LAW.  THIS  AGREEMENT  SHALL BE GOVNERNED  BY, AND
CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF TEXAS.

      Section 4.8 ENTIRE AGREEMENT. THIS WRITTEN AGREEMENT EMBODIES THE ENTIRE
AGREEMENT AND UNDERSTANDING BETWEEN THE SENIOR AGENT AND THE SENIOR LENDER, THE
SUBORDINATED AGENT AND THE SUBORDINATED LENDER AND SUPERSEDES ALL OTHER
AGREEMENTS AND UNDERSTANDINGS BETWEEN SUCH PARTIES RELATING TO THE SUBJECT
MATTER HEREOF AND THEREOF. THIS WRITTEN AGREEMENT REPRESENTS THE

                                      -13-
<PAGE>

FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF
PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE
NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.

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

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

      Section 4.11 SUBROGATION. Subject to the terms of Section 4.6, after all
Senior Indebtedness is paid in full and until the Subordinated Indebtedness has
been paid in full, the Subordinated Lender shall be subrogated to the rights of
the Senior Agent and the Senior Lender to receive distributions and payments
applicable to the Senior Indebtedness to the extent that distributions and
payments otherwise payable to the Subordinated Lender have been applied to the
payment of Senior Indebtedness. A payment or distribution made under this
Agreement to the Senior Agent and/or the Senior Lender that otherwise would have
been made to the Subordinated Lender is not, as between Parent, BOG or any
Obligor and the Subordinated Agent and Subordinated Lender, a payment on the
Subordinated Indebtedness.

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

                              SENIOR AGENT AND SENIOR LENDERS:

                              BANK OF MONTREAL,
                              both as Senior Agent and a Senior Lender

                              By:       /s/ Thomas E. McGraw
                              Name:     Thomas E. McGraw
                              Title:    Director

                                      -14-
<PAGE>

                              SOCIETE GENERALE, SOUTHWEST AGENCY,
                              as a Senior Lender

                              By:       /s/ Mark A. Cox
                              Name:     Mark A. Cox
                              Title:    Director

                              SHELL CAPITAL INC.,
                              as a Senior Lender

                              By:       /s/ Robert L. Roberts
                              Name:     Robert L. Roberts
                              Title:    Vice President

                              SUBORDINATED AGENT AND
                              SUBORDINATED LENDER:

                              SHELL CAPITAL INC.
                              both as a Subordinated Agent and a Subordinated
                              Lender

                              By:       /s/ Robert L. Roberts
                              Name:     Robert L. Roberts
                              Title:    Vice President

                              Address for the Subordinated Agent
                              and Subordinated Lender:

                              910 Louisiana Street, Suite 5000
                              Houston, Texas 77002

                              and

                              Attention: Donna Lowry
                              Telecopy:  (713) 646-4039

                              PARENT:

                              BRIGHAM EXPLORATION COMPANY,
                              a Delaware corporation

                              By:  /s/ Curtis F. Harrell
                                   Curtis F. Harrell
                                   Chief Financial Officer

                                      -15-
<PAGE>

                              BOG:

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

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

                                    By:  /s/ Curtis F. Harrell
                                          Curtis F. Harrell
                                          Chief Financial Officer

                              OBLIGORS:

                              BRIGHAM, INC.,
                              A Nevada corporation

                              By:       /s/ Curtis F. Harrell
                                        Curtis F. Harrell
                                        Chief Financial Officer

                              BRIGHAM HOLDINGS I, LLC,
                              A Nevada limited liability company

                              By:       /s/ Ben M. Brigham
                              Name:     Ben M. Brigham
                              Title:    President

                              BRIGHAM HOLDINGS II, LLC,
                              A Nevada limited liability company

                              By:       /s/ Ben M. Brigham
                              Name:     Ben M. Brigham
                              Title:    President

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

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

                                      -16-
<PAGE>

                                    EXHIBIT A

                           SUBORDINATED LOAN DOCUMENTS

1.   The Subordinated Credit Agreement.

2.   Subordinated Note in the aggregate face amount of $23,000,000 issued by BOG
     in favor of the Subordinated Lender.

3.   Second Mortgage, Deed of Trust, Assignment of Production, Security
     Agreement and Financing Statement agreements dated as of October 31, 2000
     and thereafter executed by BOG in favor of the Subordinated Agent, for the
     benefit of the Subordinated Agent and the Subordinated Lender.

4.   Subordinated Guaranty Agreement dated as of October 31, 2000 executed by
     Parent in favor of the Subordinated Agent for the benefit of the
     Subordinated Agent and the Subordinated Lender.

5.   Subordinated Guaranty Agreement dated as of October 31, 2000 executed by BI
     in favor of the Subordinated Agent for the benefit of the Subordinated
     Agent and the Subordinated Lender.

6.   Subordinated Guaranty Agreement dated as of October 31, 2000 executed by
     BH-I in favor of the Subordinated Agent for the benefit of the Subordinated
     Agent and the Subordinated Lender.

7.   Subordinated Guaranty Agreement dated as of October 31, 2000 executed by
     BH-II in favor of the Subordinated Agent for the benefit of the
     Subordinated Agent and the Subordinated Lender.

8.   Second Security Agreement (Pledge) dated as of October 31, 2000 executed by
     Parent in favor of the Subordinated Agent for the benefit of the
     Subordinated Agent and the Subordinated Lender.

9.   Second Security Agreement dated as of October 31, 2000 executed by Parent
     in favor of the Subordinated Agent for the benefit of the Subordinated
     Agent and the Subordinated Lender.

10.  Second Security Agreement dated as of October 31, 2000 executed by BOG in
     favor of the Subordinated Agent for the benefit of the Subordinated Agent
     and the Subordinated Lender.

12.  Second Security Agreement (Pledge) dated as of October 31, 2000 executed by
     Brigham, Inc. in favor of the Subordinated Agent for the benefit of the
     Subordinated Agent and the Subordinated Lender.

<PAGE>

13.  Second Security Agreement (Pledge) dated as of October 31, 2000 executed by
     Brigham Holdings I in favor of the Subordinated Agent for the benefit of
     the Subordinated Agent and the Subordinated Lender.

14.  Second Security Agreement (Pledge) dated as of October 31, 2000 executed by
     Brigham Holdings II, LLC in favor of the Subordinated Agent for the benefit
     of the Subordinated Agent and the Subordinated Lender.

15.  Financing Statements in connection with any of the items above.

16.  Any guaranty agreements, pledges, security agreements or financing
     statements that may hereafter be executed by any subsidiaries of the Parent
     in favor of the Subordinated Agent or the Subordinated Lender.

                                       2

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