<PAGE>   1





                                CREDIT AGREEMENT



                          DATED AS OF JANUARY 26, 1998


                                     AMONG

                            BRIGHAM OIL & GAS, L.P.
                                  AS BORROWER,


                               BANK OF MONTREAL,
                                   AS AGENT,

                                      AND

                          THE LENDERS SIGNATORY HERETO
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                               TABLE OF CONTENTS
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ARTICLE I

         DEFINITIONS AND ACCOUNTING MATTERS

         Section 1.01  Terms Defined Above . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         Section 1.02  Certain Defined Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         Section 1.03  Accounting Terms and Determinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  15

ARTICLE II

         COMMITMENTS

         Section 2.01  Loans and Letters of Credit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  15
         Section 2.02  Borrowings, Continuations and Conversions and Letters of Credit . . . . . . . . . . . . . . . .  16
         Section 2.03  Changes of Commitments  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  18
         Section 2.04  Fees  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  19
         Section 2.05  Several Obligations   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  20
         Section 2.06  Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  20
         Section 2.07  Prepayments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  20
         Section 2.08  Borrowing Base  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  21
         Section 2.09  Assumption of Risks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  22
         Section 2.10  Obligation to Reimburse and to Prepay . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  23
         Section 2.11  Lending Offices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  25

ARTICLE III

         PAYMENTS OF PRINCIPAL AND INTEREST

         Section 3.01  Repayment of Loans  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  25
         Section 3.02  Interest  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  25

ARTICLE IV

         PAYMENTS; PRO RATA TREATMENT; COMPUTATIONS; ETC.

         Section 4.01  Payments  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  26
         Section 4.02  Pro Rata Treatment  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  26
         Section 4.03  Computations  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  27
         Section 4.04  Non-receipt of Funds by the Agent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  27
         Section 4.05  Set-off, Sharing of Payments, Etc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  27
         Section 4.06  Taxes  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
</TABLE>
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ARTICLE V

         CAPITAL ADEQUACY

         Section 5.01  Additional Costs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  31
         Section 5.02  Limitation on Eurodollar Loans  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  33
         Section 5.03  Illegality  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  33
         Section 5.04  Base Rate Loans Pursuant to Sections 5.01, 5.02 and 5.03  . . . . . . . . . . . . . . . . . . .  34
         Section 5.05  Compensation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  34
         Section 5.06  Replacement Lenders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  34

ARTICLE VI

         CONDITIONS PRECEDENT

         Section 6.01  Initial Funding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  36
         Section 6.02  Initial, Subsequent Loans and Letters of Credit . . . . . . . . . . . . . . . . . . . . . . . .  37
         Section 6.03  Conditions Precedent for the Benefit of Lenders . . . . . . . . . . . . . . . . . . . . . . . .  38
         Section 6.04  No Waiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  38

ARTICLE VII

         REPRESENTATIONS AND WARRANTIES

         Section 7.01  Corporate Existence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  38
         Section 7.02  Financial Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  38
         Section 7.03  Litigation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  39
         Section 7.04  No Breach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  39
         Section 7.05  Authority . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  39
         Section 7.06  Approvals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  39
         Section 7.07  Use of Loans  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  40
         Section 7.08  ERISA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  40
         Section 7.09  Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  41
         Section 7.10  Titles, etc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  41
         Section 7.11  No Material Misstatements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  42
         Section 7.12  Investment Company Act  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  42
         Section 7.13  Public Utility Holding Company Act  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  43
         Section 7.14  Subsidiaries  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  43
         Section 7.15  Location of Business and Offices  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  43
         Section 7.16  Defaults  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  43
         Section 7.17  Environmental Matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  43
         Section 7.18  Compliance with the Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  44
         Section 7.19  Insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  45
</TABLE>





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         Section 7.20  Hedging Agreements  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  45
         Section 7.21  Restriction on Liens  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  45
         Section 7.22  Material Agreements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  46
         Section 7.23  Gas Imbalances  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  46
         Section 7.24  Partnership Agreement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  46
         Section 7.25  Prior Note and Related Documents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  46

ARTICLE VIII

         AFFIRMATIVE COVENANTS

         Section 8.01  Financial Statements  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  47
         Section 8.02  Litigation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  49
         Section 8.03  Maintenance, Etc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  49
         Section 8.04  Environmental Matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  50
         Section 8.05  Further Assurances  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  51
         Section 8.06  Performance of Obligations  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  51
         Section 8.07  Engineering Reports   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  51
         Section 8.08  Intentionally Omitted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  53
         Section 8.09  Additional Collateral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  53
         Section 8.10  ERISA Information and Compliance  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  54
         Section 8.11  Subsidiary Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  54

ARTICLE IX

         NEGATIVE COVENANTS

         Section 9.01  Debt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  55
         Section 9.02  Liens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  56
         Section 9.03  Investments, Loans and Advances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  56
         Section 9.04  Dividends, Distributions and Redemptions  . . . . . . . . . . . . . . . . . . . . . . . . . . .  57
         Section 9.05  Sales and Leasebacks  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  57
         Section 9.06  Nature of Business  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  58
         Section 9.07  Limitation on Leases  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  58
         Section 9.08  Mergers, Etc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  58
         Section 9.09  Proceeds of Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  58
         Section 9.10  ERISA Compliance  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  58
         Section 9.11  Sale or Discount of Receivables   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  60
         Section 9.12  Capital Expenditures  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  60
         Section 9.13  Sale of Oil and Gas Properties  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  60
         Section 9.14  Environmental Matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  60
         Section 9.15  Transactions with Affiliates  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  60
         Section 9.16  Subsidiaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  60
         Section 9.17  Negative Pledge Agreements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  61
</TABLE>





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         Section 9.18  Gas Imbalances, Take-or-Pay or Other Prepayments  . . . . . . . . . . . . . . . . . . . . . . .  61

ARTICLE X

         EVENTS OF DEFAULT; REMEDIES

         Section 10.01  Events of Default . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  61
         Section 10.02  Remedies  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  63
         Section 10.03  Production and Proceeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  64

ARTICLE XI

         THE AGENT

         Section 11.01  Appointment, Powers and Immunities  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  65
         Section 11.02  Reliance by Agent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  65
         Section 11.03  Defaults  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  65
         Section 11.04  Rights as a Lender  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  66
         Section 11.05  INDEMNIFICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  66
         Section 11.06  Non-Reliance on Agent and other Lenders . . . . . . . . . . . . . . . . . . . . . . . . . . .  66
         Section 11.07  Action by Agent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  67
         Section 11.08  Resignation or Removal of Agent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  67

ARTICLE XII

         MISCELLANEOUS

         Section 12.01  Waiver  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  68
         Section 12.02  Notices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  68
         Section 12.03  Payment of Expenses, Indemnities, etc . . . . . . . . . . . . . . . . . . . . . . . . . . . .  68
         Section 12.04  Amendments, Etc.  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  71
         Section 12.05  Successors and Assigns  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  71
         Section 12.06  Assignments and Participations  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  71
         Section 12.07  Invalidity  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  73
         Section 12.08  Counterparts  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  73
         Section 12.09  References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  73
         Section 12.10  Survival  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  73
         Section 12.11  Captions  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  73
         Section 12.12  NO ORAL AGREEMENTS  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  73
         Section 12.13  GOVERNING LAW; SUBMISSION TO JURISDICTION . . . . . . . . . . . . . . . . . . . . . . . . . .  74
         Section 12.14  Interest  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  74
         Section 12.15  Confidentiality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  75
         Section 12.16  Prior Credit Agreement  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  76
         Section 12.17  Release Regarding the Prior Note and Related Documents  . . . . . . . . . . . . . . . . . . .  76
</TABLE>





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<TABLE>
<S>                                                                                                                    <C>
         Section 12.18  Effectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  76
         Section 12.19  EXCULPATION PROVISIONS  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  77

Annex I          - List of Maximum Credit Amounts
Exhibit A        - Form of Note
Exhibit B        - Form of Borrowing, Continuation and Conversion Request
Exhibit C-1      - Form of Compliance Certificate
Exhibit C-2      - Form of Certificate Accompanying Financial Statements
Exhibit D        - List of Loan Documents
Exhibit E        - Form of Assignment Agreement
Exhibit F        - Form of Letter of Credit Agreement

Schedule 7.02    - Liabilities
Schedule 7.03    - Litigation
Schedule 7.09    - Taxes
Schedule 7.10    - Titles, etc.
Schedule 7.14    - Subsidiaries and Partnerships
Schedule 7.17    - Environmental Matters
Schedule 7.19    - Insurance
Schedule 7.20    - Hedging Agreements
Schedule 7.22    - Material Agreements
Schedule 7.23    - Gas Imbalances
Schedule 9.01    - Debt
Schedule 9.02    - Liens
Schedule 9.03    - Investments, Loans and Advances
</TABLE>





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                 THIS CREDIT AGREEMENT dated as of January 26, 1998 is among:
BRIGHAM OIL & GAS, L.P., a limited partnership formed under the laws of the
State of Delaware (the "Borrower"); each of the lenders that is a signatory
hereto or which becomes a signatory hereto as provided in Section 12.06
(individually, together with its successors and assigns, a "Lender" and,
collectively, the "Lenders"); and BANK OF MONTREAL, a Canadian bank (in its
individual capacity, "BMO"), as agent for the Lenders (in such capacity,
together with its successors in such capacity, the "Agent").


                                R E C I T A L S

         A.      Pursuant to that certain Loan Agreement (the "Original Credit
Agreement") dated as of April 1, 1996 between the Borrower and Bank One, Texas,
N.A. (the "Prior Lender") as amended by that certain First Amendment to Loan
Agreement dated as of November 10, 1997 between the Prior Lender, Borrower,
Brigham Exploration Company and Brigham, Inc. (the "First Amendment") (the
Original Credit Agreement as amended by the First Amendment being hereafter
called the "Prior Credit Agreement"), the Prior Lender provided to the Borrower
loans and extensions of credit, which loans and extensions of credit are
evidenced by a certain promissory note from the Borrower in the aggregate
principal amount of $75,000,000 (the "Prior Note").

         B.      By Assignment of Notes and Liens of even date herewith the
Lenders have acquired the Prior Note and all security for the payment of the
Prior Note and the performance of the Borrower's obligations under the Prior
Credit Agreement.

         C.      The Lenders have agreed to provide senior secured debt in the
amount of up to $75,000,000 consisting of a rearrangement of the Prior Note and
advances to the Borrower for general corporate purposes, and the Borrower, the
Agent and the Lenders now desire to set forth their agreements with respect to
such credit facility and to amend and restate in its entirety the Prior Credit
Agreement and Prior Note.

         D.      In consideration of the mutual covenants and agreements herein
contained and of the loans, extensions of credit and commitments hereinafter
referred to, the parties hereto agree as follows:

                                   ARTICLE I

                       DEFINITIONS AND ACCOUNTING MATTERS

                 Section 1.01  Terms Defined Above.  As used in this Agreement,
the terms "Agent," "BMO," "Borrower," "Lender," "Lenders," "Prior Credit
Agreement," "Prior Lender" and "Prior Note" shall have the meanings indicated
above.

                 Section 1.02  Certain Defined Terms.  As used herein, the
following terms shall have the following meanings (all terms defined in this
Article I or in other provisions of this Agreement in the singular to have the
same meanings when used in the plural and vice versa):
<PAGE>   8
         "Additional Costs" shall have the meaning assigned such term in
Section 5.01(a).

         "Affected Loans" shall have the meaning assigned such term in Section
5.04.

         "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 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.

         "Agreement" shall mean this Credit Agreement, as the same may from
time to time be amended or supplemented.

         "Aggregate Commitments" at any time shall equal the amount calculated
in accordance with Section 2.03 hereof.

         "Aggregate Maximum Credit Amounts" at any time shall equal the sum of
the Maximum Credit Amounts of the Lenders ($75,000,000), as the same may be
reduced pursuant to Section 2.03(b).

         "Applicable Lending Office" shall mean, for each Lender and for each
Type of Loan, the lending office of such Lender (or an Affiliate of such
Lender) designated for such Type of Loan on the signature pages hereof or such
other offices of such Lender (or of an Affiliate of such Lender) as such Lender
may from time to time specify to the Agent and the Borrower as the office by
which its Loans of such Type are to be made and maintained.

         "Applicable Margin" shall mean (i) until the date which is twelve (12)
months after the Closing Date, 0% per annum, and thereafter 1/4 of 1% per
annum, with respect to Base Rate Loans; and (ii) 2 1/4% per annum with respect
to Eurodollar Loans.

         "Assignment" shall have the meaning assigned such term in Section
12.06(b).

         "Base Rate" shall mean, with respect to any Base Rate Loan, for any
day, the higher of (i) the Federal Funds Rate for any such day plus 1/2 of 1%
or (ii) the Prime Rate for such day.  Each change in any interest rate provided
for herein based upon the Base Rate resulting from a change in the Base Rate
shall take effect at the time of such change in the Base Rate.





                                      -2-
<PAGE>   9
         "Base Rate Loans" shall mean Loans that bear interest at rates based 
upon the Base Rate.

         "Borrowing Base" shall mean at any time an amount equal to the amount
determined in accordance with Section 2.08.

         "Brigham Exploration" shall mean Brigham Exploration Company, a
Delaware corporation and owner of 100% of the capital stock of the General
Partner.

         "Business Day" shall mean any day other than a day on which commercial
banks are authorized or required to close in Chicago, Illinois and, where such
term is used in the definition of "Quarterly Date" or if such day relates to a
borrowing or continuation of, a payment or prepayment of principal of or
interest on, or a conversion of or into, or the Interest Period for, a
Eurodollar Loan or a notice by the Borrower with respect to any such borrowing
or continuation, payment, prepayment, conversion or Interest Period, any day
which is also a day on which dealings in Dollar deposits are carried out in the
London interbank market.

         "Closing Date" shall mean January 28, 1998.

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

         "Commitment" shall mean, for any Lender, its obligation to make Loans
up to the lesser of such Lender's Maximum Credit Amount or, when the Borrowing
Base becomes effective,  the Lender's Percentage Share of the amount equal to
the then effective Borrowing Base and to participate in the Letters of Credit
as provided in Section 2.01(b).

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





                                     -3-
<PAGE>   10
ordinary course of business; and (v) the cumulative effect of a change in
accounting principles and any gains or losses attributable to writeups or
writedowns of assets.

         "Consolidated Subsidiaries" shall mean each Subsidiary of Brigham
Exploration (whether now existing or hereafter created or acquired) the
financial statements of which shall be (or should have been) consolidated with
the financial statements of Brigham Exploration in accordance with GAAP,
including, without limitation, the Borrower.

         "Debt" shall mean, for any Person the sum of the following (without
duplication): (i) all obligations of such Person for borrowed money or
evidenced by bonds, debentures, notes or other similar instruments (including
principal, interest, fees and charges); (ii) all obligations of such Person
(whether contingent or otherwise) in respect of bankers' acceptances, letters
of credit, surety or other bonds and similar instruments; (iii) all obligations
of such Person to pay the deferred purchase price of Property or services
(other than for borrowed money) excluding Trade Payables; (iv) all obligations
under leases which shall have been, or should have been, in accordance with
GAAP, recorded as capital leases in respect of which such Person is liable
(whether contingent or otherwise); (v) all obligations under leases (other than
capital leases and oil and gas leases) which require such Person or its
Affiliate to make payments exceeding $100,000 over the term of such lease,
including payments at termination, which are substantially equal to at least
eighty percent (80%) of the purchase price of the Property subject to such
lease plus interest as an imputed rate of interest; (vi) all Debt (as described
in the other clauses of this definition) of others secured by a Lien on any
asset of such Person, whether or not such Debt is assumed by such Person; (vii)
all Debt (as described in the other clauses of this definition) of others
guaranteed by such Person or in which such Person otherwise assures a creditor
against loss of the Debt of others; (viii) all obligations or undertakings of
such Person to maintain or cause to be maintained the financial position or
covenants of others including without limitation agreements expressed as an
agreement to purchase the Debt or Property of others or otherwise;  (ix)
obligations to deliver Hydrocarbons in consideration of advance payments; (x)
obligations to pay for goods or services whether or not such goods or services
are actually received or utilized by such Person; (xi) any capital stock of
such Person in which such Person has a mandatory obligation to redeem such
stock; (xii) any Debt of a Special Entity for which such Person is liable
either by agreement or because of a Governmental Requirement; (xiii) the
undischarged balance of any production payment created by such Person or for
the creation of which such Person directly or indirectly received payment; and
(xiv) all obligations of such Person under Hedging Agreements.

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

         "Dollars" and "$" shall mean lawful money of the United States of
America.

         "EBITDA" shall mean, for any period, the sum of Consolidated Net
Income for such period plus the following expenses or charges to the extent
deducted from Consolidated Net





                                      -4-
<PAGE>   11
Income in such period: interest, taxes, depreciation, depletion and
amortization, and other non-cash charges, minus all non cash income added to
Consolidated Net Income in such period.

         "Effective Date" shall have the meaning assigned such term in Section
12.16.

         "Engineering Reports" shall have the meaning assigned such term in
Section 2.08.

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

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

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

         "ERISA Event" shall mean (i) a "Reportable Event" described in Section
4043 of ERISA and the regulations issued thereunder (other than such an event
with respect to which the requirement to give notice has been waived), (ii) the
withdrawal of the Borrower or any ERISA Affiliate from a Plan during a plan
year in which it was a "substantial employer" as defined in Section 4001(a)(2)
of ERISA, (iii) the filing of a notice of intent to terminate a Plan (other
than a defined contribution Plan) or the treatment of an amendment to such a
Plan as a termination under Section 4041 of ERISA, (iv) the institution of
proceedings to terminate a Plan by the





                                      -5-
<PAGE>   12
PBGC or (v) any other event or condition which might constitute grounds under
Section 4042 of ERISA for the termination of, or the appointment of a trustee
to administer, any Plan.

         "Eurodollar Loans" shall mean Loans the interest rates on which are
determined on the basis of rates referred to in the definition of "Eurodollar
Rate".

         "Eurodollar Rate" shall mean, with respect to any Eurodollar Loan, the
rate per annum (rounded upwards, if necessary, to the nearest 1/100 of 1%)
reported, on the date two Business Days prior to the first day of the Interest
Period for such Loan, on Telerate Access Service Page 3750 (British Bankers
Association Settlement Rate) as the London Interbank Offered Rate for U.S.
dollar deposits having a term comparable to such Interest Period and in an
amount of $1,000,000 or more (provided that, if such Page shall cease to be
publicly available or if the information contained on such Page shall cease to
be publicly available or if the information contained on such Page, in the
Agent's reasonable judgment, shall cease to accurately reflect such London
Interbank Offered Rate or if such page does not report information for the term
of the Interest Period selected by Borrower, such rate shall be that reported
by any publicly available source of similar market data selected by the Agent,
or that interpolated by Agent from such market data, which, in the Agent's
reasonable judgment, accurately reflects such London Interbank Offered Rate).

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

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





                                      -6-
<PAGE>   13
and defects, irregularities, zoning restrictions and deficiencies in title of
any rights of way or other Property which in the aggregate do not materially
impair the use of such rights of way or other Property for the purposes of
which such rights of way and other Property are held or materially impair the
value of such Property subject thereto; (vi) deposits of cash or securities to
secure the performance of bids, trade contracts, leases, statutory obligations
and other obligations of a like nature incurred in the ordinary course of
business; and (vii) Liens permitted by the Loan Documents.

         "Federal Funds Rate" shall mean, for any day, the rate per annum
(rounded upwards, if necessary, to the nearest 1/100 of 1%) equal to the
weighted average of the rates on overnight federal funds transactions with a
member of the Federal Reserve System arranged by federal funds brokers on such
day, as published by the Federal Reserve Bank of New York on the Business Day
next succeeding such day, provided that (i) if the date for which such rate is
to be determined is not a Business Day, the Federal Funds Rate for such day
shall be such rate on such transactions on the next preceding Business Day as
so published on the next succeeding Business Day, and (ii) if such rate is not
so published for any day, the Federal Funds Rate for such day shall be the
average rate charged to the Agent on such day on such transactions as
determined by the Agent.

         "Fee Letter" shall mean that certain letter agreement from the Agent
to the Borrower dated of even date with this Agreement concerning certain fees
in connection with this Agreement and any agreements or instruments executed in
connection therewith, as the same may be amended or replaced from time to time.

         "Financial Statements" shall mean the financial statement or
statements described or referred to in Section 7.02.

         "First Borrowing Base Determination Date" shall mean January 31, 1999.

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

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

         "General Partner" shall mean Brigham, Inc., a Nevada corporation,
general partner of the Borrower.

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





                                      -7-
<PAGE>   14
Authority having jurisdiction over, where applicable, the Borrower, the
Subsidiaries or any of their Property or the Agent, any Lender or any
Applicable Lending Office.

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

         "Guarantors" shall mean Brigham Exploration, the General Partner,
Brigham Holdings, I, LLC, Brigham Holdings II, LLC and any other Person who
becomes party to a Guaranty Agreement pursuant to the terms of Section 8.11.

         "Guaranty Agreements" shall mean the agreements executed by the
Guarantors in form and substance satisfactory to the Agent guarantying,
unconditionally, payment of the Indebtedness, as the same may be amended,
modified or supplemented from time to time.

         "Hedging Agreements" 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.

         "Highest Lawful Rate" shall mean, with respect to each Lender, the
maximum nonusurious interest rate, if any, that at any time or from time to
time may be contracted for, taken, reserved, charged or received on the Notes
or on other Indebtedness under laws applicable to such Lender which are
presently in effect or, to the extent allowed by law, under such applicable
laws which may hereafter be in effect and which allow a higher maximum
nonusurious interest rate than applicable laws now allow.

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

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

         "Indebtedness" shall mean any and all amounts owing or to be owing by
the Borrower  to the Agent, the Issuing Bank and/or Lenders in connection with
the Loan Documents and any Hedging Agreements now or hereafter arising between
the Borrower and any Lender and permitted by the terms of this Agreement and
all renewals, extensions and/or rearrangements of any of the above.





                                      -8-
<PAGE>   15
         "Indemnified Parties" shall have the meaning assigned such term in 
Section 12.03(b).

         "Indemnity Matters" shall mean any and all actions, suits, proceedings
(including any investigations, litigation or inquiries), claims, demands and
causes of action made or threatened against a Person and, in connection
therewith, all losses, liabilities, damages (including, without limitation,
consequential damages) or reasonable costs and expenses of any kind or nature
whatsoever incurred by such Person whether caused by the sole or concurrent
negligence of such Person seeking indemnification.

         "Initial Funding" shall mean the funding of the initial Loans or
issuance of the initial Letters of Credit pursuant to Section 6.01 hereof.

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

         "Issuing Bank" shall mean BMO or any other Lender agreed to among the
Borrower and the Agent to issue Letters of Credit.

         "Interest Period" shall mean, with respect to any Eurodollar Loan, the
period commencing on the date such Eurodollar Loan is made and ending on the
numerically corresponding day in the first, third or sixth calendar month
thereafter, as the Borrower may select as provided in Section 2.02 (or such
longer period as may be requested by the Borrower and agreed to by the Majority
Lenders), except that each Interest Period which commences on the last Business
Day of a calendar month (or on any day for which there is no numerically
corresponding day in the appropriate subsequent calendar month) shall end on
the last Business Day of the appropriate subsequent calendar month.

         Notwithstanding the foregoing:  (i) no Interest Period may end after
the Revolving Credit Termination Date; (ii) no Interest Period for any
Eurodollar Loan may end after the due date of any installment, if any, provided
for in Section 3.01 hereof to the extent that such Eurodollar Loan would need
to be prepaid prior to the end of such Interest Period in order for such
installment to be paid when due; (iii) each Interest Period which would
otherwise end on a day which is not a Business Day shall end on the next
succeeding Business Day (or, if such next succeeding Business Day falls in the
next succeeding calendar month, on the next preceding Business Day); and (iv)
no Interest Period shall have a duration of less than one month and, if the
Interest Period for any Eurodollar Loans would otherwise be for a shorter
period, such Loans shall not be available hereunder.

         "LC Commitment" at any time shall mean $20,000,000.

         "LC Exposure" at any time shall mean the aggregate undrawn face amount
of all undrawn and uncancelled Letters of Credit and the aggregate of all
amounts drawn under all Letters of Credit and not yet reimbursed.





                                      -9-
<PAGE>   16
         "Letter of Credit Agreements" shall mean the written agreements with
the Issuing Bank, as issuing lender for any Letter of Credit, executed or
hereafter executed with the issuance by the Issuing Bank of the Letters of
Credit, such agreements to be on the Issuing Bank's customary form attached
hereto as Exhibit F or as otherwise agreed to by the Borrower and the Issuing
Bank.

         "Letters of Credit" shall mean the letters of credit issued pursuant
to Section 2.01(b) and all reimbursement obligations pertaining to any such
letters of credit, and "Letter of Credit" shall mean any one of the Letters of
Credit and the reimbursement obligations pertaining thereto.

         "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
(i) the lien or security interest arising from a mortgage, encumbrance, pledge,
security agreement, conditional sale or trust receipt or a lease, consignment
or bailment for security purposes or (ii) production payments and the like
payable out of Oil and Gas Properties.  The term "Lien" shall include
reservations, exceptions, encroachments, easements, rights of way, covenants,
conditions, restrictions, leases and other title exceptions and encumbrances
affecting Property.  For the purposes of this Agreement, a Person shall be
deemed to be the owner of any Property which it has acquired or holds subject
to a conditional sale agreement, or leases under a financing lease or other
arrangement pursuant to which title to the Property has been retained by or
vested in some other Person in a transaction intended to create a financing.

         "Loan Documents" shall mean this Agreement, the Notes, the Letters of
Credit, the Letter of Credit Agreements, the Fee Letter, the agreements or
instruments described or referred to in Exhibit D, and any and all other
agreements or instruments now or hereafter executed and delivered by the
Borrower or any Subsidiary or Affiliate of the Borrower including, without
limitation, Brigham Exploration (other than assignments, participation or
similar agreements between any Lender and any other lender or creditor with
respect to any Indebtedness pursuant to this Agreement) in connection with, or
as security for the payment or performance of the Notes, or this Agreement, or
reimbursement obligations under the Letters of Credit, as such agreements may
be amended, supplemented or restated from time to time.

         "Loans" shall mean the loans as provided for by Section 2.01(a).

         "Majority Lenders" shall mean, at any time while no Loans are
outstanding, Lenders having at least sixty-six and two-thirds percent (66-2/3%)
of the Aggregate Commitments and, at any time while Loans are outstanding,
Lenders holding at least sixty-six and two-thirds percent (66-2/3%) of the
outstanding aggregate principal amount of the Loans (without regard to any sale
by a Lender of a participation in any Loan under Section 12.06(c)).

         "Material Adverse Effect" shall mean any material and adverse effect
on (i) the assets, liabilities, financial condition, business, operations or
affairs of Brigham Exploration and its Subsidiaries taken as a whole or the
Borrower and its





                                      -10-
<PAGE>   17
Subsidiaries taken as a whole, from those reflected in the Financial Statements
or from the facts represented or warranted in any Loan Document, or (ii) the
ability of Brigham Exploration or the Borrower or  Brigham Exploration or the
Borrower and their respective Subsidiaries taken as a whole to carry out their
business as at the Closing Date or as proposed as of the Closing Date to be
conducted or meet their obligations under the Loan Documents on a timely basis.

         "Maximum Credit Amount" shall mean, as to each Lender, the amount set
forth opposite such Lender's name on Annex I under the caption "Maximum Credit
Amounts" (as the same may be reduced pursuant to Section 2.03(b) hereof pro
rata to each Lender based on its Percentage Share) as modified from time to
time to reflect any assignments permitted by Section 12.06(b).

         "Mortgage" means the "Mortgage" referred to in Exhibit D and any other
mortgages executed pursuant to Section 8.09 hereof.

         "Mortgaged Property" shall mean the Property owned by the Borrower and
which is subject to the Liens existing and to exist under the terms of the Loan
Documents.

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

         "Notes" shall mean the Notes provided for by Section 2.06, together
with any and all renewals, extensions for any period, increases,
rearrangements, substitutions or modifications thereof.

         "Oil and Gas Properties" shall mean Hydrocarbon Interests; the
Properties now or hereafter pooled or unitized with Hydrocarbon Interests; all
presently existing or future unitization, pooling agreements and declarations
of pooled units and the units created thereby (including without limitation all
units created under orders, regulations and rules of any Governmental
Authority) which may affect all or any portion of the Hydrocarbon Interests;
all operating agreements, contracts and other agreements which relate to any of
the Hydrocarbon Interests or the production, sale, purchase, exchange or
processing of Hydrocarbons from or attributable to such Hydrocarbon Interests;
all Hydrocarbons in and under and which may be produced and saved or
attributable to the Hydrocarbon Interests, including all oil in tanks, the
lands covered thereby and all rents, issues, profits, proceeds, products,
revenues and other incomes from or attributable to the Hydrocarbon Interests;
all tenements, hereditaments, appurtenances and Properties in any manner
appertaining, belonging, affixed or incidental to the Hydrocarbon Interests;
and all Properties, rights, titles, interests and estates described or referred
to above, including any and all Property, real or personal, now owned or
hereinafter acquired and situated upon, used, held for use or useful in
connection with the operating, working or development of any of such
Hydrocarbon Interests or Property (excluding drilling rigs, automotive
equipment or other personal property which may be on such premises for the
purpose of drilling a well or for other similar temporary uses) and including
any and all oil wells, gas wells, injection wells or other wells, buildings,
structures, fuel separators, liquid extraction





                                      -11-
<PAGE>   18
plants, plant compressors, pumps, pumping units, field gathering systems, tanks
and tank batteries, fixtures, valves, fittings, machinery and parts, engines,
boilers, meters, apparatus, appliances, tools, implements, cables, wires,
towers, casing, tubing and rods, similar equipment, surface leases,
rights-of-way, easements and servitudes together with all additions,
substitutions, replacements, accessions and attachments to any and all of the
foregoing.

         "Other Taxes" shall have the meaning assigned such term in Section
4.06(b).

         "Partners" shall mean the General Partner, Brigham Holdings I, LLC and
Brigham Holdings II, LLC.

         "Partnership Agreement" shall mean the written partnership agreement
of the Borrower among the Partners dated December 30, 1997, as amended from
time to time.

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

         "Percentage Share" shall mean the percentage of the Aggregate
Commitments to be provided by a Lender under this Agreement as indicated on
Annex I hereto, as modified from time to time to reflect any assignments
permitted by Section 12.06(b).

         "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.

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

         "Post-Default Rate" shall mean, in respect of any principal of any
Loan or any other amount payable by the Borrower under this Agreement or any
Note, a rate per annum during the period commencing on the date of an Event of
Default until such amount is paid in full or all Events of Default are cured or
waived equal to 2% per annum above the Base Rate as in effect from time to time
plus the Applicable Margin (if any), but in no event to exceed the Highest
Lawful Rate provided that, for a Eurodollar Loan, the "Post-Default Rate" for
such principal shall be, for the period commencing on the date of an Event of
Default and ending on the earlier to occur of the last day of the Interest
Period therefor or the date all Events of Default are cured or waived, 2% per
annum above the interest rate for such Loan as provided in Section 3.02(ii),
but in no event to exceed the Highest Lawful Rate.





                                      -12-
<PAGE>   19
         "Prime Rate" shall mean the rate of interest from time to time
announced publicly by the Agent at the Principal Office as its prime commercial
lending rate.  Such rate is set by the Agent as a general reference rate of
interest, taking into account such factors as the Agent may deem appropriate,
it being understood that many of the Agent's commercial or other loans are
priced in relation to such rate, that it is not necessarily the lowest or best
rate actually charged to any customer and that the Agent may make various
commercial or other loans at rates of interest having no relationship to such
rate.

         "Principal Office" shall mean the principal office of the Agent,
presently located at 115 South LaSalle Street, Chicago, Illinois  60603.

         "Prior Mortgage" shall have the meaning assigned to such term in the
Mortgage.

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

         "Quarterly Dates" shall mean the last day of each March, June,
September, and December,  in each year, the first of which shall be March 31,
1998; provided, however, that if any such day is not a Business Day, such
Quarterly Date shall be the next succeeding Business Day.

         "Redetermination Date" shall have the meaning assigned such term in 
Section 2.08(a).

         "Regulation D" shall mean Regulation D of the Board of Governors of
the Federal Reserve System (or any successor), as the same may be amended or
supplemented from time to time.

         "Regulatory Change" shall mean, with respect to any Lender, any change
after the Closing Date in any Governmental Requirement (including Regulation D)
or the adoption or making after such date of any interpretations, directives or
requests applying to a class of lenders (including such Lender or its
Applicable Lending Office) of or under any Governmental Requirement (whether or
not having the force of law) by any Governmental Authority charged with the
interpretation or administration thereof.

         "Required Payment" shall have the meaning assigned such term in
Section 4.04.

         "Reserve Report" shall mean a report, in form satisfactory to the
Agent, setting forth, as of the dates set forth in Section 8.07(a) and (b) (or
such other date in the event of an unscheduled redetermination); (i) the proved
oil and gas reserves attributable to the Borrower's and its Subsidiaries'
Hydrocarbon Interests together with a projection of the rate of production and
future net income, taxes, operating expenses and capital expenditures with
respect thereto as of such date, based upon the pricing assumptions consistent
with SEC reporting requirements at the time (or other pricing provided by the
Agent) and (ii) such other information as the Agent may reasonably request.
The term "Reserve Report" shall also include the Initial Reserve Report, the





                                      -13-
<PAGE>   20
First Reserve Report, the supplemental  Reserve Reports described in Section
8.07(b), and the information to be provided by the Borrower of each year
pursuant to Section 8.07(d).

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

         "Revolving Credit Termination Date" shall mean, unless the Commitments
are sooner terminated pursuant to Sections 2.03(b) or 10.02 hereof, January 26,
2001.

         "Scheduled Redetermination Date" shall have the meaning assigned such 
term in Section 2.08(d).

         "SEC" shall mean the Securities and Exchange Commission or any
successor Governmental Authority.

         "Special Entity" shall mean any joint venture, limited liability
company or partnership, general or limited partnership or any other type of
partnership or company other than a corporation in which a Person or one or
more of its other Subsidiaries is a member, owner, partner or joint venturer
and owns, directly or indirectly, at least a majority of the equity of such
entity or controls such entity, but excluding any tax partnerships that are not
classified as partnerships under state law.  For purposes of this definition,
any Person which owns directly or indirectly an equity investment in another
Person which allows the first Person to manage or elect managers who manage the
normal activities of such second Person will be deemed to "control" such second
Person (e.g. a sole general partner controls a limited partnership).

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

         "Tangible Net Worth" shall mean, as at any date, the sum of the
following for Brigham Exploration and its Consolidated Subsidiaries determined
(without duplication) in accordance with GAAP (determined without regard to any
write up or write down resulting from any changes in GAAP subsequent to
September 30, 1997):

         (i)     the amount of preferred stock and common stock at par plus the
amount of surplus of Brigham Exploration, plus





                                      -14-
<PAGE>   21
         (ii)    the retained earnings (or, in the case of retained earnings
deficit, minus the amount of such deficit), minus

         (iii)   the sum of the following:  cost of treasury shares and the
book value of all assets of Brigham Exploration and its Consolidated
Subsidiaries which should be classified as intangibles (without duplication of
deductions in respect of items already deducted in arriving at surplus and
retained earnings) but in any event including as such intangibles the
following:  goodwill, research and development costs, trademarks, trade names,
copyrights, patents and franchises, unamortized debt discount and expense, all
reserves and any writeup in the book value of assets resulting from a
revaluation thereof.

         "Taxes" shall have the meaning assigned such term in Section 4.06(a).

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

         "Type" shall mean, with respect to any Loan, a Base Rate Loan or a 
Eurodollar Loan.

         "Wholly-Owned Subsidiary" shall mean, as to a Person, any Subsidiary
of which all of the outstanding shares of stock (or other ownership interests)
having by the terms thereof ordinary voting power to elect the board of
directors (or other managing persons) of such entity, other than directors'
qualifying shares, are owned or controlled by such Person or one or more of the
Wholly-Owned Subsidiaries or by such Person and one or more of the Wholly-Owned
Subsidiaries.

                 Section 1.03  Accounting Terms and Determinations.  Unless
otherwise specified herein, all accounting terms used herein shall be
interpreted, all determinations with respect to accounting matters hereunder
shall be made, and all financial statements and certificates and reports as to
financial matters required to be furnished to the Agent or the Lenders
hereunder shall be prepared, in accordance with GAAP, applied on a basis
consistent with the audited financial statements of the Borrower referred to in
Section 7.02 (except for changes concurred with by the Borrower's independent
public accountants).


                                   ARTICLE II

                                  COMMITMENTS

                 Section 2.01  Loans and Letters of Credit.

                 (a)      Loans.  Each Lender severally agrees, on the terms of
         this Agreement, to make Loans to the Borrower during the period from
         and including (i) the Closing Date or (ii) such later date that such
         Lender becomes a party to this Agreement as provided in Section
         12.06(b), to but excluding, the Revolving Credit Termination Date in
         an aggregate principal amount at any one time outstanding up to but
         not exceeding the amount of such Lender's Commitment as then in
         effect; provided, however, that the





                                      -15-
<PAGE>   22
         aggregate principal amount of all such Loans by all Lenders hereunder
         at any one time outstanding together with the LC Exposure shall not
         exceed the Aggregate Commitments.  Subject to the terms of this
         Agreement, during the period from the Closing Date to but excluding,
         the Revolving Credit Termination Date, the Borrower may borrow, repay
         and reborrow the amount described in this Section 2.01(a).  The
         initial Loans hereunder shall include the purchase by the Lenders of
         the Prior Note which shall be concurrently therewith rearranged as an
         advance under the Notes.

                 (b)      Letters of Credit.  During the period from and
         including the Closing Date to but excluding the Revolving Credit
         Termination Date, each Issuing Bank, as issuing bank for the Lenders,
         agrees to extend credit for the account of the Borrower at any time
         and from time to time by issuing renewing,  extending or reissuing
         Letters of Credit; provided however, the LC Exposure at any one time
         outstanding shall not exceed the lesser of (i) the LC Commitment or
         (ii) the Aggregate Commitments, as then in effect, minus the aggregate
         principal amount of all Loans then outstanding.  The Lenders shall
         participate in such Letters of Credit according to their respective
         Percentage Shares.  Each of the Letters of Credit shall (i) be issued
         by an Issuing Bank, (ii) contain such terms and provisions as are
         reasonably required by such Issuing Bank, (iii) be for the account of
         the Borrower and (iv) expire not later than the earlier of one year
         from the date of issuance or Revolving Credit Termination Date.

                 (c)      Limitation on Types of Loans.  Subject to the other
         terms and provisions of this Agreement, at the option of the Borrower,
         the Loans may be Base Rate Loans or Eurodollar Loans; provided that,
         without the prior written consent of the Majority Lenders, no more
         than six (6) Eurodollar Loans may be outstanding at any time from any
         Lender.

                 Section 2.02  Borrowings, Continuations and Conversions and 
Letters of Credit.

                 (a)      Borrowings.  The Borrower shall give the Agent (which
         shall promptly notify the Lenders) advance notice as hereinafter
         provided of each borrowing hereunder, which shall specify the
         aggregate amount of such borrowing, the Type and the date (which shall
         be a Business Day) of the Loans to be borrowed and (in the case of
         Eurodollar Loans) the duration of the Interest Period therefor.

                 (b)      Minimum Amounts.  If the initial borrowing consists
         in whole or in part of Eurodollar Loans, such Eurodollar Loans shall
         be in amounts of at least $1,000,000 or any whole multiple of
         $1,000,000 in excess thereof.

                 (c)      Notices.  All borrowings, continuations and
         conversions shall require advance written notice to the Agent (which
         shall promptly notify the Lenders) in the form of Exhibit B hereto (or
         telephonic notice promptly confirmed by such a written notice),





                                      -16-
<PAGE>   23
         which in each case shall be irrevocable, from the Borrower to be
         received by the Agent not later than 11:00 a.m. Houston, Texas time at
         least one Business Day prior to the date of each Base Rate Loan
         borrowing and three Business Days prior to the date of each Eurodollar
         Loan borrowing, continuation or conversion; provided, however, for
         Base Rate Loans, Borrower may request a same day advance of up to
         $5,000,000 if the request is received by the Agent not later than
         11:00 a.m. on such day.  Without in any way limiting the Borrower's
         obligation to confirm in writing any telephonic notice, the Agent may
         act without liability upon the basis of telephonic notice believed by
         the Agent in good faith to be from the Borrower prior to receipt of
         written confirmation.  In each such case, the Borrower hereby waives
         the right to dispute the Agent's record of the terms of such
         telephonic notice except in the case of gross negligence or willful
         misconduct by the Agent.

                 (d)      Continuation Options.  Subject to the provisions made
         in this Section 2.02(d), the Borrower may elect to continue all or any
         part of any Eurodollar Loan beyond the expiration of the then current
         Interest Period relating thereto by giving advance notice as provided
         in Section 2.02(c) to the Agent (which shall promptly notify the
         Lenders) of such election, specifying the amount of such Loan to be
         continued and the Interest Period therefor.  In the absence of such a
         timely and proper election, the Borrower shall be deemed to have
         elected to convert such Eurodollar Loan to a Base Rate Loan pursuant
         to Section 2.02(e).  All or any part of any Eurodollar Loan may be
         continued as provided herein, provided that (i) any continuation of
         any such Loan shall be (as to each Loan as continued for an applicable
         Interest Period) in amounts of at least $1,000,000 or any whole
         multiple of $1,000,000 in excess thereof and (ii) no Default shall
         have occurred and be continuing.  If a Default shall have occurred and
         be continuing, each Eurodollar Loan shall be converted to a Base Rate
         Loan on the last day of the Interest Period applicable thereto.

                 (e)      Conversion Options.  The Borrower may elect to
         convert all or any part of any Eurodollar Loan on the last day of the
         then current Interest Period relating thereto to a Base Rate Loan by
         giving advance notice to the Agent (which shall promptly notify the
         Lenders) of such election.  Subject to the provisions made in this
         Section 2.02(e), the Borrower may elect to convert all or any part of
         any Base Rate Loan at any time and from time to time to a Eurodollar
         Loan by giving advance notice as provided in Section 2.02(c) to the
         Agent (which shall promptly notify the Lenders) of such election.  All
         or any part of any outstanding Loan may be converted as provided
         herein, provided that (i) any conversion of any Base Rate Loan into a
         Eurodollar Loan shall be (as to each such Loan into which there is a
         conversion for an applicable Interest Period) in amounts of at least
         $1,000,000 or any whole multiple of $1,000,000 in excess thereof and
         (ii) no Default shall have occurred and be continuing.  If a Default
         shall have occurred and be continuing, no Base Rate Loan may be
         converted into a Eurodollar Loan.

                 (f)      Advances.  Not later than 11:00 a.m. Houston, Texas
         time on the date specified for each borrowing hereunder, each Lender
         shall make available the amount of





                                      -17-
<PAGE>   24
         the Loan to be made by it on such date to the Agent, to an account
         which the Agent shall specify, in immediately available funds, for the
         account of the Borrower.  The amounts so received by the Agent shall,
         subject to the terms and conditions of this Agreement, be made
         available to the Borrower by depositing the same, in immediately
         available funds, in an account of the Borrower, designated by the
         Borrower and maintained at the Principal Office.

                 (g)      Letters of Credit.  The Borrower shall give the
         Issuing Bank (which shall promptly notify the Lenders of such request
         and their Percentage Share of such Letter of Credit) advance notice to
         be received by the Issuing Bank  not later than 11:00 a.m. Houston,
         Texas time not less than three (3) Business Days prior thereto of each
         request for the issuance and at least three (3) Business Days prior to
         the date of the renewal or extension of a Letter of Credit hereunder
         which request shall specify (i) the amount of such Letter of Credit,
         (ii) the date (which shall be a Business Day) such Letter of Credit is
         to be issued, renewed or extended, (iii) the duration thereof, (iv)
         the name and address of the beneficiary thereof, (v) the form of the
         Letter of Credit and (vi) such other information as the Issuing Bank
         may reasonably request all of which shall be reasonably satisfactory
         to the Issuing Bank.  Subject to the terms and conditions of this
         Agreement, on the date specified for the issuance, renewal or
         extension of a Letter of Credit, the Issuing Bank shall issue such
         Letter of Credit to the beneficiary thereof.

                 In conjunction with the issuance of each Letter of Credit, the
         Borrower, shall execute a Letter of Credit Agreement.  In the event of
         any conflict between any provision of a Letter of Credit Agreement and
         this Agreement, the Borrower, the Issuing Bank, the Agent and the
         Lenders hereby agree that the provisions of this Agreement shall
         govern.

                 The Issuing Bank will send to the Borrower and each Lender,
         upon issuance of any Letter of Credit, or an amendment thereto, a true
         and complete copy of such Letter of Credit, or such amendment thereto.

                 Section 2.03  Changes of Commitments.

                 (a)      The Aggregate Commitments shall at all times be equal
         to the Aggregate Maximum Credit Amounts after adjustments resulting
         from reductions pursuant to Section 2.03(b) hereof until January 31,
         1999 after which date it shall be equal to the lesser of (i) the
         Aggregate Maximum Credit Amounts after adjustments resulting from
         reductions pursuant to Section 2.03(b) hereof or (ii) the Borrowing
         Base as determined from time to time.

                 (b)      The Borrower shall have the right to terminate or to
         reduce the amount of the Aggregate Maximum Credit Amounts at any time
         or from time to time upon not less than three (3) Business Days' prior
         notice to the Agent (which shall promptly notify the Lenders) of each
         such termination or reduction, which notice shall specify the
         effective date thereof and the amount of any such reduction (which
         shall not be less than





                                      -18-
<PAGE>   25

         $5,000,000 or any whole multiple of $1,000,000 in excess thereof) and
         shall be irrevocable and effective only upon receipt by the Agent.

                 (c)      The Aggregate Maximum Credit Amounts once terminated
         or reduced may not be reinstated.

                 Section 2.04  Fees.

                 (a)      Commitment Fee.  The Borrower shall pay to the Agent
         for the account of each Lender a commitment fee on the daily average
         unused amount of the Aggregate Commitments for the period from and
         including the Closing Date up to but excluding the earlier of the date
         the Aggregate Commitments are terminated or the Revolving Credit
         Termination Date at a rate per annum equal to 5/8 of 1%.  Accrued
         commitment fees shall be payable quarterly in arrears on each
         Quarterly Date and on the earlier of the date the Aggregate
         Commitments are terminated or the Revolving Credit Termination Date.

                 (b)      Letter of Credit Fees.

                          (i)     The Borrower agrees to pay the Agent, for the
                 account of the Lenders, commissions for issuing the Letters of
                 Credit on the daily average outstanding of the maximum
                 liability of the Issuing Bank existing from time to time under
                 such Letter of Credit (calculated separately for each Letter
                 of Credit) at the rate per annum equal to the Applicable
                 Margin then in effect for Eurodollar Loans, provided that each
                 Letter of Credit shall bear a minimum commission of $500.
                 Until the termination date provided therein, each Letter of
                 Credit shall be deemed to be outstanding up to the full
                 undrawn face amount of the Letter of Credit until the Issuing
                 Bank has received the canceled Letter of Credit or a written
                 cancellation of the Letter of Credit from the beneficiary of
                 such Letter of Credit in form and substance acceptable to the
                 Issuing Bank, or for any reductions in the amount of the
                 Letter of Credit (other than from a drawing), written
                 notification from the beneficiary of such Letter of Credit.
                 Such commissions are payable quarterly in arrears on each
                 Quarterly Date and upon cancellation or expiration of each
                 such Letter of Credit.

                          (ii)    The Borrower agrees to pay the Issuing Bank,
                 for its own account, an issuing fee for issuing Letters of
                 Credit on the daily average outstanding of the maximum
                 liability of the Issuing Bank existing from time to time under
                 such Letter of Credit (calculated separately for each Letter
                 of Credit) at the rate of .10% per annum, payable quarterly in
                 arrears on each Quarterly Date and upon cancellation or
                 expiration of each such Letter of Credit.

                 (c)      The Borrower shall pay to the Agent for its account
         such other fees as are set forth in the Fee Letter on the dates
         specified therein to the extent not paid prior to the Closing Date.





                                      -19-
<PAGE>   26
                 Section 2.05  Several Obligations.  The failure of any Lender
to make any Loan to be made by it or to provide funds for disbursements or
reimbursements under Letters of Credit on the date specified therefor shall not
relieve any other Lender of its obligation to make its Loan or provide funds on
such date, but no Lender shall be responsible for the failure of any other
Lender to make a Loan to be made by such other Lender or to provide funds to be
provided by such other Lender.

                 Section 2.06  Notes.  The Loans made by each Lender shall be
evidenced by a single promissory note of the Borrower in substantially the form
of Exhibit A hereto, dated (i) the Closing Date or (ii) the effective date of
an Assignment pursuant to Section 12.06(b), payable to the order of such Lender
in a principal amount equal to its Maximum Credit Amount as in effect and
otherwise duly completed and such substitute Notes as required by Section
12.06(b).  The initial advance under the Notes shall be each Lender's
Percentage Share of the purchase price of the Prior Note.  The date, amount,
Type, interest rate and Interest Period of each Loan made by each Lender, and
all payments made on account of the principal thereof, shall be recorded by
such Lender on its books for its Note, and, prior to any transfer, may be
endorsed by such Lender on a schedule attached to such Note or any continuation
thereof or on any separate record maintained by such Lender.  Failure to make
any such notation or to attach a schedule shall not affect any Lender's or the
Borrower's rights or obligations in respect of such Loans or affect the
validity of such transfer by any Lender of its Note.

                 Section 2.07  Prepayments.

                 (a)      The Borrower may prepay the Base Rate Loans upon not
         less than one (1) Business Day's prior notice to the Agent (which
         shall promptly notify the Lenders), which notice shall specify the
         prepayment date (which shall be a Business Day) and the amount of the
         prepayment (which shall be at least $1,000,000 or the remaining
         aggregate principal balance outstanding on the Notes) and shall be
         irrevocable and effective only upon receipt by the Agent, provided
         that interest on the principal prepaid, accrued to the prepayment
         date, shall be paid on the prepayment date.  The Borrower may prepay
         Eurodollar Loans on the same condition as for Base Rate Loans and in
         addition such prepayments of Eurodollar Loans shall be subject to the
         terms of Section 5.05.

                 (b)      If, after giving effect to any termination or
         reduction of the Aggregate Maximum Credit Amounts pursuant to Section
         2.03(b), the outstanding aggregate principal amount of the Loans plus
         the LC Exposure exceeds the Aggregate Maximum Credit Amounts, the
         Borrower shall (i) prepay the Loans on the date of such termination or
         reduction in an aggregate principal amount equal to the excess,
         together with interest on the principal amount paid accrued to the
         date of such prepayment and (ii) if any excess remains after prepaying
         all of the Loans, pay to the Agent on behalf of the Lenders an amount
         equal to the excess to be held as cash collateral as provided in
         Section 2.10(b) hereof.





                                      -20-
<PAGE>   27
                 (c)      Upon any redetermination of the amount of the
         Borrowing Base in accordance with Section 2.08, if the redetermined
         Borrowing Base is less than the aggregate outstanding principal amount
         of the Loans plus the LC Exposure, then the Borrower shall within
         ninety (90) days of receipt of written notice thereof: (i) prepay the
         Loans in an aggregate principal amount equal to such excess, together
         with interest on the principal amount paid accrued to the date of such
         prepayment and (ii) if a Borrowing Base deficiency remains after
         prepaying all of the Loans because of LC Exposure, the Borrower shall
         pay to the Agent on behalf of the Lenders an amount equal to such
         Borrowing Base deficiency to be held as cash collateral as provided in
         Section 2.10(b) hereof.

                 (d)      Prepayments permitted or required under this Section
         2.07 shall be without premium or penalty, except as required under
         Section 5.05 for prepayment of Eurodollar Loans.  Any prepayments on
         the Loans may be reborrowed subject to the then effective Aggregate
         Commitments.

                 Section 2.08  Borrowing Base.

                 (a)      The Borrowing Base shall be determined in accordance
         with Section 2.08(b) by the Agent with the concurrence of all of the
         Lenders and is subject to redetermination in accordance with Section
         2.08(d).  The first determination of the Borrowing Base shall be made
         on the First Borrowing Base Determination Date.  Upon any
         determination or redetermination of the Borrowing Base, such
         determination shall remain in effect until the next successive
         Redetermination Date.  "Redetermination Date" shall mean the date that
         the Borrowing Base as determined or redetermined becomes effective
         subject to the notice requirements specified in Section 2.08(e) both
         for the scheduled determination, scheduled redeterminations and
         unscheduled redeterminations.  After the First Borrowing Base
         Determination Date, so long as any of the Commitments are in effect or
         any LC Exposure or Loans are outstanding hereunder, this facility
         shall be governed by the then effective Borrowing Base.

                 (b)      Upon receipt of the reports required by Section 8.07
         and such other reports, data and supplemental information as may from
         time to time be reasonably requested by the Agent (the "Engineering
         Reports"), the Agent will determine or redetermine, as appropriate,
         the Borrowing Base and shall take into consideration, among other
         things, liquidity, market interest rates, other Debt, Trade Payables,
         general and administrative expenses and such other factors as the
         Lenders shall deem material.  Such determination or redetermination
         will be in accordance with its normal and customary procedures for
         evaluating oil and gas reserves and other related assets as such exist
         at that particular time.   The Agent, in its sole discretion, may make
         adjustments to the rates, volumes and prices and other assumptions set
         forth therein in accordance with its normal and customary procedures
         for evaluating oil and gas reserves and other related assets as such
         exist at that particular time.  The Agent shall propose to the Lenders
         a Borrowing Base within twenty (20) days following receipt by the
         Agent and the Lenders of the





                                      -21-
<PAGE>   28
         Engineering Reports in a timely and complete manner.  After having
         received notice of such proposal by the Agent, the Lenders shall have
         ten (10) Business Days to agree or disagree with such proposal.  If at
         the end of the 10 Business Days, any Lender has not communicated its
         approval or disapproval, such silence shall be deemed to be an
         approval.  If the Lenders have not approved within 10 Business Days,
         the Lenders shall, within a reasonable period of time, agree on a new
         Borrowing Base.  The Agent and all of the Lenders must approve the
         initial Borrowing Base and any increase in the Borrowing Base.  The
         Majority Lenders (one of which must be the Agent) shall be required to
         approve a continuation or decrease in any Borrowing Base.

                 (c)      The Agent may exclude any Oil and Gas Property or
         portion of production therefrom or any income from any other Property
         from the Borrowing Base, at any time, because title information is not
         reasonably satisfactory, such Property is not Mortgaged Property or
         such Property is not assignable; provided, however, the Agent shall
         not exclude an Oil and Gas Property from the Borrowing Base solely
         because it is not Mortgaged Property if Mortgaged Property includes
         90% of Borrower's proved Hydrocarbon reserves.

                 (d)      So long as any of the Commitments are in effect and
         until payment in full of all Loans hereunder, on the First Borrowing
         Base Determination Date and on or around the last Business Day of each
         September and March, commencing September 30, 1999 (each being a
         "Scheduled Redetermination Date"), the Lenders shall determine or
         redetermine, as appropriate, the amount of the Borrowing Base in
         accordance with Section 2.08(b).  In addition, each of the Majority
         Lenders and the Borrower may initiate a redetermination of the
         Borrowing Base during any consecutive twelve (12) month period by
         specifying in writing the date on which such redetermination is to
         occur.

                 (e)      The Agent shall promptly notify in writing the
         Borrower and the Lenders of the Borrowing Base as determined or
         redetermined.  Any determination of the Borrowing Base shall not be in
         effect until written notice is received by the Borrower.

                 Section 2.09  Assumption of Risks.  The Borrower assumes all
risks of the acts or omissions of any beneficiary of any Letter of Credit or
any transferee thereof with respect to its use of such Letter of Credit.
Neither any Issuing Bank (except in the case of gross negligence, willful
misconduct or bad faith on the part of the Issuing Bank or any of its
employees), its correspondents nor any Lender shall be responsible for the
validity, sufficiency or genuineness of certificates or other documents or any
endorsements thereon, even if such certificates or other documents should in
fact prove to be invalid, insufficient, fraudulent or forged; for errors,
omissions, interruptions or delays in transmissions or delivery of any messages
by mail, telex, or otherwise, whether or not they be in code; for errors in
translation or for errors in interpretation of technical terms; the validity or
sufficiency of any instrument transferring or assigning or purporting to
transfer or assign any Letter of Credit or the rights or benefits thereunder or
proceeds thereof, in whole or in part, which may prove to be invalid or
ineffective for any reason; for the failure of any beneficiary or any
transferee of any Letter of Credit to





                                      -22-
<PAGE>   29
comply fully with conditions required in order to draw upon any Letter of
Credit; or for any other consequences arising from causes beyond the Issuing
Bank's control or the control of the Issuing Bank's correspondents.  In
addition, neither the Issuing Bank, the Agent nor any Lender shall be
responsible for any error, neglect, or default of any of the Issuing Bank's
correspondents; and none of the above shall affect, impair or prevent the
vesting of any of the Issuing Bank's, the Agent's or any Lender's rights or
powers hereunder or under the Letter of Credit Agreements, all of which rights
shall be cumulative.  The Issuing Bank and its correspondents may accept
certificates or other documents that appear on their face to be in order,
without responsibility for further investigation of any matter contained
therein regardless of any notice or information to the contrary.  In
furtherance and not in limitation of the foregoing provisions, the Borrower
agrees that any action, inaction or omission taken or not taken by the Issuing
Bank or by any correspondent for the Issuing Bank in good faith in connection
with any Letter of Credit, or any related drafts, certificates, documents or
instruments, shall be binding on the Borrower and shall not put the Issuing
Bank or its correspondents under any resulting liability to the Borrower absent
gross negligence or willful misconduct of the Issuing Bank.

                 Section 2.10  Obligation to Reimburse and to Prepay.

                 (a)      If a disbursement by the Issuing Bank is made under
         any Letter of Credit, the Borrower shall pay to the Agent within two
         (2) Business Days after notice of any such disbursement is received by
         the Borrower, the amount of each such disbursement made by the Issuing
         Bank under the Letter of Credit (if such payment is not sooner
         effected as may be required under this Section 2.10 or under other
         provisions of the Letter of Credit), together with interest on the
         amount disbursed from and including the date of disbursement until
         payment in full of such disbursed amount at a varying rate per annum
         equal to (i) the then applicable interest rate for Base Rate Loans
         through the second Business Day after notice of such disbursement is
         received by the Borrower and (ii) thereafter, the Post-Default Rate
         for Base Rate Loans (but in no event to exceed the Highest Lawful
         Rate) for the period from and including the third Business Day
         following the date of such disbursement to and including the date of
         repayment in full of such disbursed amount.  The obligations of the
         Borrower under this Agreement with respect to each Letter of Credit
         shall be absolute, unconditional and irrevocable and shall be paid or
         performed strictly in accordance with the terms of this Agreement
         under all circumstances whatsoever, including, without limitation, but
         only to the fullest extent permitted by applicable law, the following
         circumstances: (i) any lack of validity or enforceability of this
         Agreement, any Letter of Credit or any of the other Loan Documents;
         (ii) any amendment or waiver of (including any default), or any
         consent to departure from this Agreement (except to the extent
         permitted by any amendment or waiver), any Letter of Credit or any of
         the other Loan Documents; (iii) the existence of any claim, set-off,
         defense or other rights which the Borrower may have at any time
         against the beneficiary of any Letter of Credit or any transferee of
         any Letter of Credit (or any Persons for whom any such beneficiary or
         any such transferee may be acting), the Issuing Bank, the Agent, any
         Lender or any other Person, whether in connection with this Agreement,
         any Letter of Credit, the other Loan Documents, the





                                      -23-
<PAGE>   30
         transactions contemplated hereby or any unrelated transaction; (iv)
         any statement, certificate, draft, notice or any other document
         presented under any Letter of Credit proves to have been forged,
         fraudulent, insufficient or invalid in any respect or any statement
         therein proves to have been untrue or inaccurate in any respect
         whatsoever; (v) payment by the Issuing Bank under any Letter of Credit
         against presentation of a draft or certificate which appears on its
         face to comply, but does not comply, with the terms of such Letter of
         Credit; and (vi) any other circumstance or happening whatsoever,
         whether or not similar to any of the foregoing.

         Notwithstanding anything in this Agreement to the contrary, the
         Borrower will not be liable for payment or performance that results
         from the gross negligence or willful misconduct of the Issuing Bank,
         except where the Borrower actually recovers the proceeds for itself or
         the Issuing Bank of any payment made by the Issuing Bank in connection
         with such gross negligence or willful misconduct.

                 (b)      In the event of the occurrence of any Event of
         Default, a payment or prepayment pursuant to Sections 2.07(b) and (c)
         hereof or the maturity of the Notes, whether by acceleration or
         otherwise, an amount equal to the LC Exposure (or the excess in the
         case of Sections 2.07(b) and (c)) shall be deemed to be forthwith
         payable by the Borrower to the Issuing Bank, the Agent and the Lenders
         as of the date of any such occurrence; and the Borrower's obligation
         to pay such amount shall be absolute and unconditional, without regard
         to whether any beneficiary of any such Letter of Credit has attempted
         to draw down all or a portion of such amount under the terms of a
         Letter of Credit, and, to the fullest extent permitted by applicable
         law, shall not be subject to any defense or be affected by a right of
         set-off, counterclaim or recoupment which the Borrower may now or
         hereafter have against any such beneficiary, the Issuing Bank, the
         Agent, the Lenders or any other Person for any reason whatsoever.
         Such payments shall be held by the Agent on behalf of the Lenders as
         cash collateral securing the LC Exposure in an account or accounts at
         the Principal Office; and the Borrower hereby grants to and by its
         deposit with the Agent grants to the Agent a security interest in such
         cash collateral.  In the event of any such payment by the Borrower of
         amounts contingently owing under outstanding Letters of Credit and in
         the event that thereafter drafts or other demands for payment
         complying with the terms of such Letters of Credit are not made prior
         to the respective expiration dates thereof, the Agent agrees, if no
         Event of Default has occurred and is continuing or if no other amounts
         are outstanding under this Agreement, the Notes or any of the other
         Loan Documents, to remit to the Borrower amounts for which the
         contingent obligations evidenced by the Letters of Credit have ceased.

                 (c)      Each Lender severally and unconditionally agrees that
         it shall promptly reimburse the Issuing Bank an amount equal to such
         Lender's Percentage Share of any disbursement made by the Issuing Bank
         under any Letter of Credit that is not reimbursed according to this
         Section 2.10.





                                      -24-
<PAGE>   31
                 Section 2.11  Lending Offices.  The Loans of each Type made by
each Lender shall be made and maintained at such Lender's Applicable Lending
Office for Loans of such Type.


                                  ARTICLE III

                       PAYMENTS OF PRINCIPAL AND INTEREST

                 Section 3.01  Repayment of Loans.  On the Revolving Credit
Termination Date the Borrower shall repay the outstanding aggregate principal
and accrued and unpaid interest under the Notes.

                 Section 3.02  Interest.  The Borrower will pay to the Agent,
for the account of each Lender, interest on the unpaid principal amount of each
Loan made by such Lender for the period commencing on the date such Loan is
made to but excluding the date such Loan shall be paid in full, at the
following rates per annum:

         (i)     if such a Loan is a Base Rate Loan, the Base Rate (as in
effect from time to time) plus the Applicable Margin (as in effect from time to
time), but in no event to exceed the Highest Lawful Rate; and

         (ii)    if such a Loan is a Eurodollar Loan, for each Interest Period
(or portion thereof) relating thereto, the Eurodollar Rate for such Loan plus
the Applicable Margin (as in effect from time to time), but in no event to
exceed the Highest Lawful Rate.

Notwithstanding the foregoing, the Borrower will pay to the Agent, for the
account of each Lender interest at the applicable Post-Default Rate on any
principal of any Loan made by such Lender, and (to the fullest extent permitted
by law) on any other amount payable by the Borrower hereunder, under any Loan
Document or under any Note held by such Lender to or for account of such
Lender, for the period commencing on the date of an Event of Default until the
same is paid in full or all such Events of Default are cured or waived.

         Accrued interest on Base Rate Loans shall be payable on each Quarterly
Date commencing on March 31, 1998, and accrued interest on each Eurodollar Loan
shall be payable on the last day of the Interest Period therefor and, if such
Interest Period is longer than three months at three-month intervals following
the first day of such Interest Period, except that interest payable at the
Post-Default Rate shall be payable from time to time on demand and interest on
any Eurodollar Loan that is converted into a Base Rate Loan (pursuant to
Section 5.04) shall be payable on the date of conversion (but only to the
extent so converted).

         Promptly after the determination of any interest rate provided for
herein or any change therein, the Agent shall notify the Lenders to which such
interest is payable and the Borrower





                                      -25-
<PAGE>   32
thereof.  Each determination by the Agent of an interest rate or fee hereunder
shall be prima facie evidence of the amount thereof.


                                   ARTICLE IV

                PAYMENTS; PRO RATA TREATMENT; COMPUTATIONS; ETC.

                 Section 4.01  Payments.  Except to the extent otherwise
provided herein, all payments of principal, interest and other amounts to be
made by the Borrower under the Loan Documents shall be made in Dollars, in
immediately available funds, to the Agent at such account as the Agent shall
specify by notice to the Borrower from time to time, not later than noon
Houston, Texas time on the date on which such payments shall become due (each
such payment made after such time on such due date to be deemed to have been
made on the next succeeding Business Day).  Such payments shall be made without
(to the fullest extent permitted by applicable law) defense, set-off or
counterclaim.  Each payment received by the Agent under this Agreement or any
Note for account of a Lender shall be paid promptly to such Lender in
immediately available funds.  Except as provided in clause (iii) of the
definition of "Interest Period", if the due date of any payment under this
Agreement or any Note would otherwise fall on a day which is not a Business Day
such date shall be extended to the next succeeding Business Day and interest
shall be payable for any principal so extended for the period of such
extension.  At the time of each payment to the Agent of any principal of or
interest on any borrowing, the Borrower shall notify the Agent of the Loans to
which such payment shall apply.  In the absence of such notice the Agent may
specify the Loans to which such payment shall apply, but to the extent possible
such payment or prepayment will be applied first to the Loans comprised of Base
Rate Loans.

                 Section 4.02  Pro Rata Treatment.  Except to the extent
otherwise provided herein each Lender agrees that:  (i) each borrowing from the
Lenders under Section 2.01 and each continuation and conversion under Section
2.02 shall be made from the Lenders pro rata in accordance with their
Percentage Share, each payment of commitment fee or other fees under Sections
2.04(a) and (b) shall be made for account of the Lenders pro rata in accordance
with their Percentage Share, and each termination or reduction of the amount of
the Aggregate Maximum Credit Amounts under Section 2.03(b) shall be applied to
the Commitment of each Lender, pro rata according to the amounts of its
respective Commitment; (ii) each payment of principal of Loans by the Borrower
shall be made for account of the Lenders pro rata in accordance with the
respective unpaid principal amount of the Loans held by the Lenders; and (iii)
each payment of interest on Loans by the Borrower shall be made for account of
the Lenders pro rata in accordance with the amounts of interest due and payable
to the respective Lenders; and (iv) each reimbursement by the Borrower of
disbursements under Letters of Credit shall be made for account of the Issuing
Bank or, if funded by the Lenders, pro rata for the account of the Lenders, in
accordance with the amounts of reimbursement obligations due and payable to
each respective Lender.





                                      -26-
<PAGE>   33
                 Section 4.03  Computations.  Interest on Eurodollar Loans and
fees shall be computed on the basis of a year of 360 days and actual days
elapsed (including the first day but excluding the last day) occurring in the
period for which such interest is payable, unless such calculation would exceed
the Highest Lawful Rate, in which case interest shall be calculated on the per
annum basis of a year of 365 or 366 days, as the case may be.  Interest on Base
Rate Loans shall be computed on the basis of a year of 365 or 366 days, as the
case may be, and actual days elapsed (including the first day but excluding the
last day) occurring in the period for which such interest is payable.

                 Section 4.04  Non-receipt of Funds by the Agent.  Unless the
Agent shall have been notified by a Lender or the Borrower prior to the date on
which such notifying party is scheduled to make payment to the Agent (in the
case of a Lender) of the proceeds of a Loan or a payment under a Letter of
Credit to be made by it hereunder or (in the case of the Borrower) a payment to
the Agent for account of one or more of the Lenders hereunder (such payment
being herein called the "Required Payment"), which notice shall be effective
upon receipt, that it does not intend to make the Required Payment to the
Agent, the Agent may assume that the Required Payment has been made and may, in
reliance upon such assumption (but shall not be required to), make the amount
thereof available to the intended recipient(s) on such date and, if such Lender
or the Borrower (as the case may be) has not in fact made the Required Payment
to the Agent, the recipient(s) of such payment shall, on demand, repay to the
Agent the amount so made available together with interest thereon in respect of
each day during the period commencing on the date such amount was so made
available by the Agent until but excluding the date the Agent recovers such
amount at a rate per annum which, for any Lender as recipient, will be equal to
the Federal Funds Rate, and for the Borrower as recipient, will be equal to the
Base Rate plus the Applicable Margin.

                 Section 4.05  Set-off, Sharing of Payments, Etc.

                 (a)      The Borrower agrees that, in addition to (and without
         limitation of) any right of set-off, bankers' lien or counterclaim a
         Lender may otherwise have, each Lender shall have the right and be
         entitled (after consultation with the Agent), at its option, to offset
         balances held by it or by any of its Affiliates for account of the
         Borrower at any of its offices, in Dollars or in any other currency,
         against any principal of or interest on any of such Lender's Loans, or
         any other amount payable to such Lender hereunder, which is not paid
         when due (regardless of whether such balances are then due to the
         Borrower), in which case it shall promptly notify the Borrower and the
         Agent thereof, provided that such Lender's failure to give such notice
         shall not affect the validity thereof.

                 (b)      If any Lender shall obtain payment of any principal
         of or interest on any Loan made by it to the Borrower under this
         Agreement (or reimbursement as to any Letter of Credit) through the
         exercise of any right of set-off, banker's lien or counterclaim or
         similar right or otherwise, and, as a result of such payment, such
         Lender shall have received a greater percentage of the principal or
         interest (or reimbursement) then due hereunder by the Borrower to such
         Lender than the percentage received by any other





                                      -27-
<PAGE>   34
         Lenders, it shall promptly (i) notify the Agent and each other Lender
         thereof and (ii) purchase from such other Lenders participations in
         (or, if and to the extent specified by such Lender, direct interests
         in) the Loans (or participations in Letters of Credit) made by such
         other Lenders (or in interest due thereon, as the case may be) in such
         amounts, and make such other adjustments from time to time as shall be
         equitable, to the end that all the Lenders shall share the benefit of
         such excess payment (net of any expenses which may be incurred by such
         Lender in obtaining or preserving such excess payment) pro rata in
         accordance with the unpaid principal and/or interest on the Loans held
         by each of the Lenders (or reimbursements of Letters of Credit).  To
         such end all the Lenders shall make appropriate adjustments among
         themselves (by the resale of participations sold or otherwise) if such
         payment is rescinded or must otherwise be restored.  The Borrower
         agrees that any Lender so purchasing a participation (or direct
         interest) in the Loans made by other Lenders (or in interest due
         thereon, as the case may be) may exercise all rights of set-off,
         banker's lien, counterclaim or similar rights with respect to such
         participation as fully as if such Lender were a direct holder of Loans
         (or Letters of Credit) in the amount of such participation.  Nothing
         contained herein shall require any Lender to exercise any such right
         or shall affect the right of any Lender to exercise, and retain the
         benefits of exercising, any such right with respect to any other
         indebtedness or obligation of the Borrower.  If under any applicable
         bankruptcy, insolvency or other similar law, any Lender receives a
         secured claim in lieu of a set-off to which this Section 4.05 applies,
         such Lender shall, to the extent practicable, exercise its rights in
         respect of such secured claim in a manner consistent with the rights
         of the Lenders entitled under this Section 4.05 to share the benefits
         of any recovery on such secured claim.

                 Section 4.06  Taxes.

                 (a)      Payments Free and Clear.  Any and all payments by the
         Borrower hereunder shall be made, in accordance with Section 4.01,
         free and clear of and without deduction for any and all present or
         future taxes, levies, imposts, deductions, charges or withholdings,
         and all liabilities with respect thereto, excluding, in the case of
         each Lender and the Issuing Bank and the Agent, taxes imposed on its
         income, and franchise or similar taxes imposed on it, by (i) any
         jurisdiction (or political subdivision thereof) of which the Agent,
         the Issuing Bank or such Lender, as the case may be, is a citizen or
         resident or in which such Lender has an Applicable Lending Office,
         (ii) the jurisdiction (or any political subdivision thereof) in which
         the Agent or such Lender is organized, or (iii) any jurisdiction (or
         political subdivision thereof) in which such Lender or the Agent is
         presently doing business in which taxes are imposed solely as a result
         of doing business in such jurisdiction (all such non-excluded taxes,
         levies, imposts, deductions, charges, withholdings and liabilities
         being hereinafter referred to as "Taxes").  If the Borrower shall be
         required by law to deduct any Taxes from or in respect of any sum
         payable hereunder to the Lenders, the Issuing Bank or the Agent (i)
         the sum payable shall be increased by the amount necessary so that
         after making all required deductions (including deductions applicable
         to additional sums payable under this Section 4.06) such Lender, the
         Issuing Bank or the Agent (as the case may be) shall receive an amount
         equal to the





                                      -28-
<PAGE>   35
         sum it would have received had no such deductions been made, (ii) the
         Borrower shall make such deductions and (iii) the Borrower shall pay
         the full amount deducted to the relevant taxing authority or other
         Governmental Authority in accordance with applicable law.

                 (b)      Other Taxes.  In addition, to the fullest extent
         permitted by applicable law, the Borrower agrees to pay any present or
         future stamp or documentary taxes or any other excise or property
         taxes, charges or similar levies that arise from any payment made
         hereunder or from the execution, delivery or registration of, or
         otherwise with respect to, this Agreement, any Assignment or any other
         Loan Document (hereinafter referred to as "Other Taxes").

                 (c)      INDEMNIFICATION.  TO THE FULLEST EXTENT PERMITTED BY
         APPLICABLE LAW, THE BORROWER WILL INDEMNIFY EACH LENDER, THE ISSUING
         BANK AND THE AGENT FOR THE FULL AMOUNT OF TAXES AND OTHER TAXES
         (INCLUDING, BUT NOT LIMITED TO, ANY TAXES OR OTHER TAXES IMPOSED BY
         ANY GOVERNMENTAL AUTHORITY ON AMOUNTS PAYABLE UNDER THIS SECTION 4.06)
         PAID BY SUCH LENDER, THE ISSUING BANK OR THE AGENT (ON THEIR BEHALF OR
         ON BEHALF OF ANY LENDER), AS THE CASE MAY BE, AND ANY LIABILITY
         (INCLUDING PENALTIES, INTEREST AND EXPENSES) ARISING THEREFROM OR WITH
         RESPECT THERETO, WHETHER OR NOT SUCH TAXES OR OTHER TAXES WERE
         CORRECTLY OR LEGALLY ASSERTED UNLESS THE PAYMENT OF SUCH TAXES WAS NOT
         CORRECTLY OR LEGALLY ASSERTED AND SUCH LENDER'S PAYMENT OF SUCH TAXES
         OR OTHER TAXES WAS THE RESULT OF ITS GROSS NEGLIGENCE OR WILLFUL
         MISCONDUCT.  ANY PAYMENT PURSUANT TO SUCH INDEMNIFICATION SHALL BE
         MADE WITHIN THIRTY (30) DAYS AFTER THE DATE ANY LENDER, THE ISSUING
         BANK OR THE AGENT, AS THE CASE MAY BE, MAKES WRITTEN DEMAND THEREFOR.
         IF ANY LENDER OR THE AGENT RECEIVES A REFUND OR CREDIT IN RESPECT OF
         ANY TAXES OR OTHER TAXES FOR WHICH SUCH LENDER, ISSUING BANK OR THE
         AGENT HAS RECEIVED PAYMENT FROM THE BORROWER IT SHALL PROMPTLY NOTIFY
         THE BORROWER OF SUCH REFUND OR CREDIT AND SHALL, IF NO DEFAULT HAS
         OCCURRED AND IS CONTINUING, WITHIN THIRTY (30) DAYS AFTER RECEIPT OF A
         REQUEST BY THE BORROWER (OR PROMPTLY UPON RECEIPT, IF THE BORROWER HAS
         REQUESTED APPLICATION FOR SUCH REFUND OR CREDIT PURSUANT HERETO), PAY
         AN AMOUNT EQUAL TO SUCH REFUND OR CREDIT TO THE BORROWER WITHOUT
         INTEREST (BUT WITH ANY INTEREST SO REFUNDED OR CREDITED), PROVIDED
         THAT THE BORROWER, UPON THE REQUEST OF SUCH LENDER, ISSUING BANK OR
         THE AGENT, AGREES TO RETURN SUCH REFUND OR CREDIT (PLUS PENALTIES,
         INTEREST OR OTHER CHARGES) TO SUCH LENDER OR THE AGENT IN THE EVENT
         SUCH LENDER OR THE AGENT IS REQUIRED TO REPAY SUCH REFUND OR CREDIT.

                 (d)      Lender Representations.

                          (i)     Each Lender represents that it is either (1)
                 a corporation or banking association organized under the laws
                 of the United States of America or any state thereof or (2) it
                 is entitled to complete exemption from United States
                 withholding





                                      -29-
<PAGE>   36
                 tax imposed on or with respect to any payments, including
                 fees, to be made to it pursuant to this Agreement (A) under an
                 applicable provision of a tax convention to which the United
                 States of America is a party or (B) because it is acting
                 through a branch, agency or office in the United States of
                 America and any payment to be received by it hereunder is
                 effectively connected with a trade or business in the United
                 States of America.  Each Lender that is not a corporation or
                 banking association organized under the laws of the United
                 States of America or any state thereof agrees to provide to
                 the Borrower and the Agent on the Closing Date, or on the date
                 of its delivery of the Assignment pursuant to which it becomes
                 a Lender, and at such other times as required by United States
                 law or as the Borrower or the Agent shall reasonably request,
                 two accurate and complete original signed copies of either (A)
                 Internal Revenue Service Form 4224 (or successor form)
                 certifying that all payments to be made to it hereunder will
                 be effectively connected to a United States trade or business
                 (the "Form 4224 Certification") or (B) Internal Revenue
                 Service Form 1001 (or successor form) certifying that it is
                 entitled to the benefit of a provision of a tax convention to
                 which the United States of America is a party which completely
                 exempts from United States withholding tax all payments to be
                 made to it hereunder (the "Form 1001 Certification").  In
                 addition, each Lender agrees that if it previously filed a
                 Form 4224 Certification, it will deliver to the Borrower and
                 the Agent a new Form 4224 Certification prior to the first
                 payment date occurring in each of its subsequent taxable
                 years; and if it previously filed a Form 1001 Certification,
                 it will deliver to the Borrower and the Agent a new
                 certification prior to the first payment date falling in the
                 third year following the previous filing of such
                 certification.  Each Lender also agrees to deliver to the
                 Borrower and the Agent such other or supplemental forms as may
                 at any time be required as a result of changes in applicable
                 law or regulation in order to confirm or maintain in effect
                 its entitlement to exemption from United States withholding
                 tax on any payments hereunder, provided that the circumstances
                 of such Lender at the relevant time and applicable laws permit
                 it to do so.  If a Lender determines, as a result of any
                 change in either (i) a Governmental Requirement or (ii) its
                 circumstances, that it is unable to submit any form or
                 certificate that it is obligated to submit pursuant to this
                 Section 4.06, or that it is required to withdraw or cancel any
                 such form or certificate previously submitted, it shall
                 promptly notify the Borrower and the Agent of such fact.  If a
                 Lender is organized under the laws of a jurisdiction outside
                 the United States of America, unless the Borrower and the
                 Agent have received a Form 1001 Certification or Form 4224
                 Certification satisfactory to them indicating that all
                 payments to be made to such Lender hereunder are not subject
                 to United States withholding tax, the Borrower shall withhold
                 taxes from such payments at the applicable statutory rate.
                 Each Lender agrees to indemnify and hold harmless the Borrower
                 or Agent, as applicable, from any United States taxes,
                 penalties, interest and other expenses, costs and losses
                 incurred or payable by (i) the Agent as a result of such
                 Lender's failure to submit any form or certificate that it is
                 required to provide pursuant to this Section 4.06 or (ii) the





                                      -30-
<PAGE>   37

                 Borrower or the Agent as a result of their reliance on any
                 such form or certificate which such Lender has provided to
                 them pursuant to this Section 4.06.

                          (ii)    For any period with respect to which a Lender
                 has failed to provide the Borrower with the form required
                 pursuant to this Section 4.06, if any, (other than if such
                 failure is due to a change in a Governmental Requirement
                 occurring subsequent to the date on which a form originally
                 was required to be provided), such Lender shall not be
                 entitled to indemnification under Section 4.06 with respect to
                 taxes imposed by the United States which taxes would not have
                 been imposed but for such failure to provide such forms;
                 provided, however, that should a Lender, which is otherwise
                 exempt from or subject to a reduced rate of withholding tax
                 becomes subject to taxes because of its failure to deliver a
                 form required hereunder, the Borrower shall take such steps as
                 such Lender shall reasonably request to assist such Lender to
                 recover such taxes.

                          (iii)   Any Lender claiming any additional amounts
                 payable pursuant to this Section 4.06 shall use reasonable
                 efforts (consistent with legal and regulatory restrictions) to
                 file any certificate or document requested by the Borrower or
                 the Agent or to change the jurisdiction of its Applicable
                 Lending Office or to contest any tax imposed if the making of
                 such a filing or change or contesting such tax would avoid the
                 need for or reduce the amount of any such additional amounts
                 that may thereafter accrue and would not, in the sole
                 determination of such Lender, be otherwise disadvantageous to
                 such Lender.


                                   ARTICLE V

                                CAPITAL ADEQUACY

                 Section 5.01  Additional Costs.

                 (a)      Eurodollar Regulations, etc.  The Borrower shall pay
         directly to each Lender from time to time such amounts as such Lender
         may determine to be necessary to compensate such Lender for any costs
         which it determines are attributable to its making or maintaining of
         any Eurodollar Loans or issuing or participating in Letters of Credit
         hereunder or its obligation to make any Eurodollar Loans or issue or
         participate in any Letters of Credit hereunder, or any reduction in
         any amount receivable by such Lender hereunder in respect of any of
         such Eurodollar Loans, Letters of Credit or such obligation (such
         increases in costs and reductions in amounts receivable being herein
         called "Additional Costs"), resulting from any Regulatory Change
         which: (i) changes the basis of taxation of any amounts payable to
         such Lender under this Agreement or any Note in respect of any of such
         Eurodollar Loans or Letters of Credit (other than taxes described as
         excluded under Section 4.06(a)); or (ii) imposes or modifies any
         reserve, special deposit, minimum capital, capital ratio or similar
         requirements relating to any





                                      -31-
<PAGE>   38
         extensions of credit or other assets of, or any deposits with or other
         liabilities of such Lender, or the Commitment or Loans of such Lender
         or the Eurodollar interbank market; or (iii) imposes any other
         condition affecting this Agreement or any Note (or any of such
         extensions of credit or liabilities) or such Lender's Commitment or
         Loans.  Each Lender will notify the Agent and the Borrower of any
         event occurring after the Closing Date which will entitle such Lender
         to compensation pursuant to this Section 5.01(a) as promptly as
         practicable after it obtains knowledge thereof and determines to
         request such compensation, and will designate a different Applicable
         Lending Office for the Loans of such Lender affected by such event if
         such designation will avoid the need for, or reduce the amount of,
         such compensation and will not, in the reasonable opinion of such
         Lender, be disadvantageous to such Lender, provided that such Lender
         shall have no obligation to so designate an Applicable Lending Office
         located in the United States.  If any Lender requests compensation
         from the Borrower under this Section 5.01(a), the Borrower may, by
         notice to such Lender, suspend the obligation of such Lender to make
         additional Loans of the Type with respect to which such compensation
         is requested until the Regulatory Change giving rise to such request
         ceases to be in effect (in which case the provisions of Section 5.04
         shall be applicable).

                 (b)      Regulatory Change.  Without limiting the effect of
         the provisions of Section 5.01(a), in the event that, by reason of any
         Regulatory Change or any other circumstances arising after the Closing
         Date affecting such Lender, the Eurodollar interbank market or such
         Lender's position in such market, any Lender either (i) incurs
         Additional Costs based on or measured by the excess above a specified
         level of the amount of a category of deposits or other liabilities of
         such Lender which includes deposits by reference to which the interest
         rate on Eurodollar Loans is determined as provided in this Agreement
         or a category of extensions of credit or other assets of such Lender
         which includes Eurodollar Loans or (ii) becomes subject to
         restrictions on the amount of such a category of liabilities or assets
         which it may hold, then, if such Lender so elects by notice to the
         Borrower, the obligation of such Lender to make additional Eurodollar
         Loans shall be suspended until such Regulatory Change or other
         circumstances ceases to be in effect (in which case the provisions of
         Section 5.04 shall be applicable).

                 (c)      Capital Adequacy.  Without limiting the effect of the
         foregoing provisions of this Section 5.01 (but without duplication),
         the Borrower shall pay directly to any Lender from time to time on
         request such amounts as such Lender may reasonably determine to be
         necessary to compensate such Lender or its parent or holding company
         for any costs which it determines are attributable to the maintenance
         by such Lender or its parent or holding company (or any Applicable
         Lending Office), pursuant to any Governmental Requirement resulting
         from any Regulatory Change, of capital in respect of its Commitment,
         its Note or its Loans or any interest held by it in any Letter of
         Credit, such compensation to include, without limitation, an amount
         equal to any reduction of the rate of return on assets or equity of
         such Lender or its parent or holding company (or any Applicable Lending
         Office) to a level below that which such Lender or its parent or 





                                      -32-
<PAGE>   39
         holding company (or any Applicable Lending Office) could have achieved
         but for such Regulatory Change.  Such Lender will notify the Borrower
         that it is entitled to compensation pursuant to this Section 5.01(c) as
         promptly as practicable after it determines to request such
         compensation.

                 (d)      Compensation Procedure.  Any Lender notifying the
         Borrower of the incurrence of additional costs under this Section 5.01
         shall in such notice to the Borrower and the Agent set forth in
         reasonable detail the basis and amount of its request for
         compensation.  Determinations and allocations by each Lender for
         purposes of this Section 5.01 of the effect of any Regulatory Change
         pursuant to Section 5.01(a) or (b), or of the effect of capital
         maintained pursuant to Section 5.01(c), on its costs or rate of return
         of maintaining Loans or its obligation to make Loans or issue Letters
         of Credit, or on amounts receivable by it in respect of Loans or
         Letters of Credit, and of the amounts required to compensate such
         Lender under this Section 5.01, shall be conclusive and binding for
         all purposes, provided that such determinations and allocations are
         made on a reasonable basis.  Any request for additional compensation
         under this Section 5.01 shall be paid by the Borrower within thirty
         (30) days of the receipt by the Borrower of the notice described in
         this Section 5.01(d).

                 Section 5.02  Limitation on Eurodollar Loans.  Anything herein
to the contrary notwithstanding, if, on or prior to the determination of any
Eurodollar Rate for any Interest Period:

         (i)     the Agent determines (which determination shall be conclusive,
absent manifest error) that quotations of interest rates for the relevant
deposits referred to in the definition of "Eurodollar Rate" in Section 1.02 are
not being provided in the relevant amounts or for the relevant maturities for
purposes of determining rates of interest for Eurodollar Loans as provided
herein; or

         (ii)    the Agent determines (which determination shall be conclusive,
absent manifest error) that the relevant rates of interest referred to in the
definition of "Eurodollar Rate" in Section 1.02 upon the basis of which the
rate of interest for Eurodollar Loans for such Interest Period is to be
determined are not sufficient to adequately cover the cost to the Lenders of
making or maintaining Eurodollar Loans;

then the Agent shall give the Borrower prompt notice thereof, and so long as
such condition remains in effect, the Lenders shall be under no obligation to
make additional Eurodollar Loans.

                 Section 5.03  Illegality.  Notwithstanding any other provision
of this Agreement, in the event that it becomes unlawful for any Lender or its
Applicable Lending Office to honor its obligation to make or maintain
Eurodollar Loans hereunder, then such Lender shall promptly notify the Borrower
thereof and such Lender's obligation to make Eurodollar Loans shall be
suspended until such time as such Lender may again make and maintain Eurodollar
Loans (in which case the provisions of Section 5.04 shall be applicable).





                                      -33-
<PAGE>   40
                 Section 5.04  Base Rate Loans Pursuant to Sections 5.01, 5.02
and 5.03.  If the obligation of any Lender to make Eurodollar Loans shall be
suspended pursuant to Sections 5.01, 5.02 or 5.03 ("Affected Loans"), all
Affected Loans which would otherwise be made by such Lender shall be made
instead as Base Rate Loans (and, if an event referred to in Section 5.01(b) or
Section 5.03 has occurred and such Lender so requests by notice to the
Borrower, all Affected Loans of such Lender then outstanding shall be
automatically converted into Base Rate Loans on the date specified by such
Lender in such notice) and, to the extent that Affected Loans are so made as
(or converted into) Base Rate Loans, all payments of principal which would
otherwise be applied to such Lender's Affected Loans shall be applied instead
to its Base Rate Loans.

                 Section 5.05  Compensation.  The Borrower shall pay to each
Lender within thirty (30) days of receipt of written request of such Lender
(which request shall set forth, in reasonable detail, the basis for requesting
such amounts and which shall be conclusive and binding for all purposes
provided that such determinations are made on a reasonable basis), such amount
or amounts as shall compensate it for any loss, cost, expense or liability
which such Lender determines are attributable to:

         (i)     any payment, prepayment or conversion of a Eurodollar Loan
properly made in accordance herewith by such Lender or the Borrower for any
reason (including, without limitation, the acceleration of the Loans pursuant
to Section 10.02) on a date other than the last day of the Interest Period for
such Loan; or

         (ii)    any failure by the Borrower for any reason (including but not
limited to, the failure of any of the conditions precedent specified in Article
VI to be satisfied) to borrow, continue or convert a Eurodollar Loan from such
Lender on the date for such borrowing, continuation or conversion specified in
the relevant notice given pursuant to Section 2.02(c).

Without limiting the effect of the preceding sentence, such compensation shall
include an amount equal to the excess, if any, of (i) the amount of interest
which would have accrued on the principal amount so paid, prepaid or converted
or not borrowed for the period from the date of such payment, prepayment or
conversion or failure to borrow to the last day of the Interest Period for such
Loan (or, in the case of a failure to borrow, the Interest Period for such Loan
which would have commenced on the date specified for such borrowing) at the
applicable rate of interest for such Loan provided for herein over (ii) the
interest component of the amount such Lender would have bid in the London
interbank market for Dollar deposits of leading banks in amounts comparable to
such principal amount and with maturities comparable to such period (as
reasonably determined by such Lender).

                 Section 5.06  Replacement Lenders.

                 (a)      If any Lender has notified the Borrower and the Agent
         of its incurring additional costs under Section 5.01 hereof or has
         required the Borrower to make payments for Taxes under Section 4.06
         hereof, then the Borrower may, unless such





                                      -34-
<PAGE>   41
         Lender has notified the Borrower and the Agent that the circumstances
         giving rise to such notice no longer apply, terminate, in whole but
         not in part, the Commitment of any Lender (other than the Agent) (the
         "Terminated Lender") at any time upon five (5) Business Days' prior
         written notice to the Terminated Lender and the Agent (such notice
         referred to herein as a "Notice of Termination").

                 (b)      In order to effect the termination of the Commitment
         of the Terminated Lender, the Borrower shall: (i) obtain an agreement
         with one or more Lenders to increase their Commitment or Commitments
         and/or (ii) request any one or more other banking institutions to
         become parties to this Agreement in place and instead of such
         Terminated Lender and agree to accept a Commitment or Commitments;
         provided, however, that such one or more other banking institutions
         are reasonably acceptable to the Agent and become parties by executing
         an Assignment (the Lenders or other banking institutions that agree to
         accept in whole or in part the Commitment of the Terminated Lender
         being referred to herein as the "Replacement Lenders"), such that the
         aggregate increased and/or accepted Commitments of the Replacement
         Lenders under clauses (i) and (ii) above equal the Commitment of the
         Terminated Lender.

                 (c)      The Notice of Termination shall include the name of
         the Terminated Lender, the date the termination will occur (the
         "Termination Date"), and the Replacement Lender or Replacement Lenders
         to which the Terminated Lender will assign its Commitment and, if
         there will be more than one Replacement Lender, the portion of the
         Terminated Lender's Commitment to be assigned to each Replacement
         Lender.

                 (d)      On the Termination Date, (i) the Terminated Lender
         shall by execution and delivery of an Assignment assign its Commitment
         to the Replacement Lender or Replacement Lenders (pro rata, if there
         is more than one Replacement Lender, in proportion to the portion of
         the Terminated Lender's Commitment to be assigned to each Replacement
         Lender) indicated in the Notice of Termination and shall assign to the
         Replacement Lender or Replacement Lenders each of its Loans (if any)
         then outstanding and participation interests in Letters of Credit (if
         any) then outstanding pro rata as aforesaid), (ii) the Terminated
         Lender shall endorse its Note, payable without recourse,
         representation or warranty to the order of the Replacement Lender or
         Replacement Lenders (pro rata as aforesaid), (iii) the Replacement
         Lender or Replacement Lenders shall purchase the Note held by the
         Terminated Lender (pro rata as aforesaid) at a price equal to the
         unpaid principal amount thereof plus interest and facility and other
         fees accrued and unpaid to the Termination Date, and (iv) the
         Replacement Lender or Replacement Lenders will thereupon (pro rata as
         aforesaid) succeed to and be substituted in all respects for the
         Terminated Lender with like effect as if becoming a Lender pursuant to
         the terms of Section 12.06(b), and the Terminated Lender will have the
         rights and benefits of an assignor under Section 12.06(b).  To the
         extent not in conflict, the terms of Section 12.06(b) shall supplement
         the provisions of this Section 5.06(d).  For each assignment made
         under this Section 5.06, the Replacement Lender shall pay to the





                                      -35-
<PAGE>   42
         Agent the processing fee provided for in Section 12.06(b).  The
         Borrower will be responsible for the payment of any breakage costs
         associated with termination of the  Terminated Lender, as set forth in
         Section 5.05.


                                   ARTICLE VI

                              CONDITIONS PRECEDENT

                 Section 6.01  Initial Funding.

                 The obligation of the Lenders to make the Initial Funding
(which shall include the purchase price of the Prior Note) is subject to the
receipt by the Agent and the Lenders of all fees payable pursuant to Section
2.04 on or before the Closing Date and the receipt by the Agent of the
following documents and satisfaction of the other conditions provided in this
Section 6.01, each of which shall be satisfactory to the Agent in form and
substance:

                 (a)      A certificate of the Secretary or an Assistant
         Secretary of each of Brigham Exploration, the General Partner and the
         manager of each other Guarantor setting forth (i) resolutions of its
         board of directors with respect to its authorization to execute and
         deliver the Loan Documents to which it is a party and to enter into
         the transactions contemplated in those documents, (ii) the officers
         (y) who are authorized to sign the Loan Documents to which it is a
         party and (z) who will, until replaced by another officer or officers
         duly authorized for that purpose, act as its representative for the
         purposes of signing documents and giving notices and other
         communications in connection with this Agreement and the transactions
         contemplated hereby, (iii) specimen signatures of its authorized
         officers, and (iv) its articles or certificate of incorporation and
         bylaws or operating agreement, certified as being true and complete.
         The Agent and the Lenders may conclusively rely on such certificate
         until the Agent receives notice in writing from the Borrower to the
         contrary.

                 (b)      Certificates of the appropriate state agencies with
         respect to the existence, qualification and good standing of the
         Borrower and the Guarantors.

                 (c)      A compliance certificate which shall be substantially
         in the form of Exhibit C-1, duly and properly executed by a
         Responsible Officer and dated as of the Closing Date.

                 (d)      The Notes, duly completed and executed.

                 (e)      The Loan Documents described on Exhibit D (other than
         the Guarantees of Brigham Holdings I, LLC and Brigham Holdings II,
         LLC), duly completed and executed in sufficient number of counterparts
         for recording, if necessary, including the





                                      -36-
<PAGE>   43
         Assignment of Notes and Liens and all corresponding assignments of the
         financing statements perfecting the security interests of the Prior
         Lender.

                 (f)      An opinion of Thompson & Knight, P.C., special
         counsel to the Borrower and the Guarantors.

                 (g)      A certificate of insurance coverage of the Borrower
         evidencing that the Borrower is carrying insurance in accordance with
         Section 7.19 hereof.

                 (h)      Title information as the Agent may require from
         attorneys satisfactory to the Agent setting forth the status of title
         to at least 85% of the value of the Oil and Gas Properties included in
         the Initial Reserve Report.

                 (i)      The Agent shall be reasonably satisfied with the
         environmental condition of the Mortgaged Properties.

                 (j)      The Agent shall have been furnished with appropriate
         UCC search certificates reflecting no prior liens or security
         interests.

                 (k)      The Agent shall have received an assignment of the
         Prior Note and all Liens securing same in recordable form.

                 (l)      Such other documents as the Agent or any Lender or
         special counsel to the Agent may reasonably request.

                 Section 6.02  Initial, Subsequent Loans and Letters of Credit.
The obligation of the Lenders to purchase the Prior Note and make Loans to the
Borrower upon the occasion of each borrowing hereunder and to issue, renew,
extend or reissue Letters of Credit for the account of the Borrower (including
the Initial Funding) is subject to the further conditions precedent that, as of
the date of such Loans and after giving effect thereto:

         (a) no Default shall have occurred and be continuing;

         (b) no Material Adverse Effect shall have occurred and be continuing; 
and

         (c) the representations and warranties made by the Borrower in Article
VII and in the Loan Documents or by any Guarantor in any other Loan Document
shall be true in all material respects on and as of the date of the making of
such Loans or issuance, renewal, extension or reissuance of a Letter of Credit
with the same force and effect as if made on and as of such date and following
such new borrowing, except to the extent such representations and warranties
are expressly limited to an earlier date or the Majority Lenders may expressly
consent in writing to the contrary.

         Each request for a borrowing or issuance, renewal, extension or
reissuance of a Letter of Credit by the Borrower hereunder shall constitute a
certification by the Borrower to the effect





                                      -37-
<PAGE>   44
set forth in Section 6.02(c) (both as of the date of such notice and, unless
the Borrower otherwise notifies the Agent prior to the date of and immediately
following such borrowing or issuance, renewal, extension or reissuance of a
Letter of Credit as of the date thereof).

                 Section 6.03  Conditions Precedent for the Benefit of Lenders.
All conditions precedent to the obligations of the Lenders to make any Loan are
imposed hereby solely for the benefit of the Lenders, and no other Person may
require satisfaction of any such condition precedent or be entitled to assume
that the Lenders will refuse to make any Loan in the absence of strict
compliance with such conditions precedent.

                 Section 6.04  No Waiver.  No waiver of any condition precedent
shall preclude the Agent or the Lenders from requiring such condition to be met
prior to making any subsequent Loan or preclude the Lenders from thereafter
declaring that a subsequent failure of the Borrower to satisfy such condition
precedent constitutes a Default.


                                  ARTICLE VII

                         REPRESENTATIONS AND WARRANTIES

         The Borrower represents and warrants to the Agent and the Lenders that
(each representation and warranty herein is given as of the Closing Date and
shall be deemed repeated and reaffirmed on the dates of each borrowing and
issuance, renewal, extension or reissuance of a Letter of Credit as provided in
Section 6.02):

                 Section 7.01  Corporate Existence.  The Borrower:  (i) is a
limited partnership duly organized, legally existing and in good standing under
the laws of the jurisdiction of its formation; (ii) has all requisite power,
and has all material governmental licenses, authorizations, consents and
approvals necessary to own its assets and carry on its business as now being or
as proposed to be conducted; and (iii) is qualified to do business in all
jurisdictions in which the nature of the business conducted by it makes such
qualification necessary and where failure so to qualify would have a Material
Adverse Effect.

                 Section 7.02  Financial Condition.  The audited consolidated
balance sheet of the Brigham Exploration and its Consolidated Subsidiaries as
at December 31, 1996 and the related consolidated statement of income,
stockholders' equity and cash flow of Brigham Exploration 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 Brigham Exploration and  its
Consolidated Subsidiaries as at September 30, 1997, and their related
consolidated statements of income, stockholders' equity and cash flow of
Brigham Exploration and its Consolidated Subsidiaries for the nine-month period
ended on such date heretofore furnished to the Agent, are complete and correct
and fairly present the consolidated financial condition of Brigham Exploration
and its Consolidated Subsidiaries as at said dates and the results of its
operations for the fiscal year and the nine-month period on said





                                      -38-
<PAGE>   45
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 Brigham Exploration nor any Consolidated Subsidiary has
on the Closing Date any material Debt, Trade Payables, contingent liabilities,
liabilities for taxes, unusual forward or long- term commitments or unrealized
or anticipated losses from any unfavorable commitments, except as referred to
or reflected or provided for in the Financial Statements or in Schedule 7.02.
Since December 31, 1996, 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 Brigham Exploration Consolidated Subsidiaries,
taken as a whole, have been materially and adversely affected as a result of
any fire, explosion, earthquake, flood, drought, windstorm, accident, strike or
other labor disturbance, embargo, requisition or taking of Property or
cancellation of contracts, permits or concessions by any Governmental
Authority, riot, activities of armed forces or acts of God or of any public
enemy.

                 Section 7.03  Litigation.  Except as disclosed to the Lenders
in Schedule 7.03 hereto, 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 Borrower threatened against or
affecting the Borrower or any Subsidiary which both (a) involves the
possibility of any judgment or liability against the Borrower or any Subsidiary
not fully covered by insurance (except for normal deductibles), and (b) would
be more likely than not to have a Material Adverse Effect.

                 Section 7.04  No Breach.  Neither the execution and delivery
of the Loan Documents, nor compliance with the terms and provisions hereof will
conflict with or result in a breach of, or require any consent which has not
been obtained as of the Closing Date under, the Partnership Agreement, the
respective charter or by-laws of any Subsidiary or any Governmental Requirement
or any material agreement or instrument to which the Borrower or any Subsidiary
is a party or by which it is bound or to which it or its Properties are
subject, or constitute a default under any such agreement or instrument, or
result in the creation or imposition of any Lien upon any of the material
revenues or assets of the Borrower or any Subsidiary pursuant to the terms of
any such agreement or instrument other than the Liens created by the Loan
Documents.

                 Section 7.05  Authority.  The Borrower and each Subsidiary has
all necessary power and authority to execute, deliver and perform its
obligations under the Loan Documents to which it is a party; and the execution,
delivery and performance by the Borrower and each Subsidiary of the Loan
Documents to which it is a party, have been duly authorized by all necessary
action on its part; and the Loan Documents constitute the legal, valid and
binding obligations of the Borrower and each Subsidiary, enforceable in
accordance with their terms, except as such enforceability may be limited by
bankruptcy, insolvency, fraudulent transfer and similar laws affecting
creditors' rights generally or by general principles of equity.

                 Section 7.06  Approvals.  No authorizations, approvals or
consents of, and no filings or registrations with, any Governmental Authority
are necessary for the execution,





                                      -39-
<PAGE>   46
delivery or performance by the Borrower or any Subsidiary of the Loan Documents
or for the validity or enforceability thereof.

                 Section 7.07  Use of Loans.  The proceeds of the Loans shall
be used to refinance the outstanding indebtedness under the Prior Credit
Agreement and for general corporate purposes.  In no event shall the proceeds
of the Loans be used to finance in whole or in part any hostile acquisition.
The Borrower is not engaged principally, or as one of its important activities,
in the business of extending credit for the purpose, whether immediate,
incidental or ultimate, of buying or carrying margin stock (within the meaning
of Regulation G, U or X of the Board of Governors of the Federal Reserve
System) and no part of the proceeds of any Loan hereunder will be used to buy
or carry any margin stock.

                 Section 7.08  ERISA.

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

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

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

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

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

                 (f)      The actuarial present value of the benefit
         liabilities under each Plan which is subject to Title IV of ERISA does
         not, as of the end of the Borrower'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





                                      -40-
<PAGE>   47
         by $100,000 or more.  The term "actuarial present value of the benefit
         liabilities" shall have the meaning specified in section 4041 of
         ERISA.

                 (g)      None of the Borrower 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 Borrower or any ERISA
         Affiliate in its sole discretion at any time without any material
         liability.

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

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

                 Section 7.09  Taxes.  Except as set out in Schedule 7.09, the
Borrower 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 Borrower, 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 Borrower in respect of
taxes and other governmental charges are, in the opinion of the Borrower,
adequate.  No tax lien has been filed and, to the knowledge of the Borrower, no
claim is being asserted with respect to any such tax, fee or other charge,
except for any taxes, fees or other charges which are being contested in good
faith and by proper proceedings and against which adequate reserves are being
maintained.

                 Section 7.10  Titles, etc.

                 (a)      Subject to the matters set out in Schedule 7.10, each
         of the Borrower and the Subsidiaries has good and defensible title to
         (i) the Oil and Gas Properties that are both evaluated (A) in the most
         recently delivered Reserve Report and (B) described in Part One of
         Exhibit A to the Mortgage or in Exhibit A to a Prior Mortgage, free
         and clear of all Liens except Liens permitted by Section 9.02, and
         (ii) to the best of Borrower's knowledge, the balance of Borrower's
         material (individually or in the aggregate) Oil and Gas Properties
         (and/or those of the Subsidiaries) that are described in the Mortgage
         or that are otherwise evaluated in the most recently delivered Reserve
         Report, free and clear (to the best of Borrower's knowledge) of all
         Liens except Liens permitted by Section 9.02.  Except for immaterial
         divergences, after giving full effect to the Excepted Liens and the
         matters set forth in Schedule 7.10, the Borrower owns the net
         interests in production attributable to the Hydrocarbon Interests that
         are both (A) evaluated in the most recently delivered Reserve Report
         and (b) reflected in the Mortgage or in Exhibit A to a Prior Mortgage,
         and the ownership of such Hydrocarbon Interests shall not in any





                                      -41-
<PAGE>   48
         material respect obligate the Borrower to bear the costs and expenses
         relating to the maintenance, development and operations of each such
         Hydrocarbon Interest in an amount in excess of the working interest of
         such Hydrocarbon Interest set forth in the Mortgage or in Exhibit A to
         a Prior Mortgage (without a corresponding increase in net revenue
         interest).  The Borrower does not believe, based upon information in
         its possession, that its most recently delivered Reserve Report
         materially overstates its oil and gas reserves, bearing in mind that
         reserves are evaluated based upon estimates and assumptions with
         respect to which reasonable minds of competent reserve engineers may
         differ.

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

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

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

                 Section 7.11  No Material Misstatements.  Taken as a whole,
the written information, statements, exhibits, certificates, documents and
reports furnished to the Agent and the Lenders (or any of them) by the Borrower
or any Guarantor in connection with the negotiation of this Agreement do not
contain any material misstatement of fact or omit to state a material fact or
any fact necessary to make the statements contained therein not materially
misleading in the light of the circumstances in which made and with respect to
the Borrower or any Guarantor.  As of the Closing Date, there is no fact
peculiar to the Borrower or Guarantor which has a Material Adverse Effect or in
the future is reasonably likely to have (so far as the Borrower can now
foresee) a Material Adverse Effect and which has not been set forth in this
Agreement or the other documents, certificates and statements furnished to the
Agent by or on behalf of the Borrower or any Guarantor prior to, or on, the
Closing Date in connection with the transactions contemplated hereby.

                 Section 7.12  Investment Company Act.  Neither the Borrower
nor any  Subsidiary is an "investment company" or a company "controlled" by an
"investment company," within the meaning of the Investment Company Act of 1940,
as amended.





                                      -42-
<PAGE>   49
                 Section 7.13  Public Utility Holding Company Act.  Neither the
Borrower nor any Subsidiary is a "holding company," or a "subsidiary company"
of a "holding company," or an "affiliate" of a "holding company" or of a
"subsidiary company" of a "holding company," or a "public utility" within the
meaning of the Public Utility Holding Company Act of 1935, as amended.

                 Section 7.14  Subsidiaries.  Except as set forth on Schedule
7.14 or as allowed by Section 9.16, the Borrower has no Subsidiaries.

                 Section 7.15  Location of Business and Offices.  As of the
Closing Date, the Borrower's principal place of business and chief executive
offices are located at the address stated on the signature page of this
Agreement.  The principal place of business and chief executive office of each
Subsidiary are located at the addresses stated on Schedule 7.14.

                 Section 7.16  Defaults.  The Borrower is not in default nor
has any event or circumstance occurred which, but for the expiration of any
applicable grace period or the giving of notice, or both, would constitute a
default under any material agreement or instrument to which the Borrower is a
party or by which the Borrower is bound which default would have a Material
Adverse Effect.  No Default hereunder has occurred and is continuing.

                 Section 7.17  Environmental Matters.  Except as provided in
Schedule 7.17 or for matters which are more likely than not to not to have a
Material Adverse Effect (or with respect to (c), (d) and (e) below, where the
failure to take such actions is more likely than not to not have a Material
Adverse Effect):

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

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

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





                                      -43-
<PAGE>   50
                 (d)      All hazardous substances, solid waste, and oil and
         gas exploration and production wastes, if any, generated at any and
         all Property of Brigham Exploration and each of its Subsidiaries have
         in the past, during Borrower's tenure of ownership and to the best of
         Borrower's knowledge, prior thereto, been transported, treated and
         disposed of in accordance with Environmental Laws and so as not to
         pose an imminent and substantial endangerment to public health or
         welfare or the environment, and, to the best knowledge of the
         Borrower, all such transport carriers and treatment and disposal
         facilities have been and are operating in compliance with
         Environmental Laws and so as not to pose an imminent and substantial
         endangerment to public health or welfare or the environment, and are
         not the subject of any existing, pending or threatened action,
         investigation or inquiry by any Governmental Authority in connection
         with any Environmental Laws;

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

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

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

                 Section 7.18  Compliance with the Law.  Neither the Borrower
nor any Subsidiary has violated any Governmental Requirement or failed to
obtain any license, permit, franchise or other governmental authorization
necessary for the ownership of any of its Properties or the conduct of its
business, which violation or failure would have (in the event such violation or
failure were asserted by any Person through appropriate action) a Material
Adverse Effect.  Except for such acts or failures to act as would not have a
Material Adverse Effect, the Oil and Gas Properties (and properties unitized
therewith) have been maintained, operated and developed in a good and
workmanlike manner and in conformity with all applicable laws and all rules,
regulations and orders of all duly constituted authorities having jurisdiction
and in conformity with the provisions of all leases, subleases or other
contracts comprising a part of the Hydrocarbon Interests and other contracts
and agreements forming a part of the Oil and Gas Properties; specifically in
this connection, but subject to the Material Adverse Effect





                                      -44-
<PAGE>   51
qualification set forth above, (i) after the Closing Date, no Oil and Gas
Property is subject to having allowable production reduced below the full and
regular allowable (including the maximum permissible tolerance) because of any
overproduction (whether or not the same was permissible at the time) prior to
the Closing Date and (ii) none of the wells comprising a part of the Oil and
Gas Properties (or properties unitized therewith) are deviated from the
vertical more than the maximum permitted by applicable laws, regulations, rules
and orders, and such wells are, in fact, bottomed under and are producing from,
and the well bores are wholly within, the Oil and Gas Properties (or in the
case of wells located on properties unitized therewith, such unitized
properties).

                 Section 7.19  Insurance.  Schedule 7.19 attached hereto
contains an accurate and complete description of all material policies of fire,
liability, workmen's compensation and other forms of insurance owned or held by
the Borrower and each Subsidiary as of the Closing Date.  Schedule 7.19 shall
be updated by the Borrower as appropriate from time to time and the
representations in this Section 7.19 shall apply to such updated Schedules.
All such policies are in full force and effect, all premiums with respect
thereto covering all periods up to and including the Closing Date have been
paid, and no notice of cancellation or termination has been received with
respect to any such policy.  Such policies are sufficient for compliance with
all requirements of law and of all agreements to which the Borrower or any
Subsidiary is a party; are valid, outstanding and enforceable policies; provide
adequate insurance coverage in at least such amounts and against at least such
risks (but including in any event public liability) as are usually insured
against in the same general area by companies engaged in the same or a similar
business for the assets and operations of the Borrower and each Subsidiary;
will remain in full force and effect through the respective dates set forth in
Schedule 7.19 without the payment of additional premiums; and will not in any
way be affected by, or terminate or lapse by reason of, the transactions
contemplated by this Agreement.  Schedule 7.19 identifies all material risks,
if any, which the General Partner of the Borrower, the Subsidiaries and their
respective Board of Directors or officers have designated as being self
insured.  Neither the Borrower nor any Subsidiary has been refused any
insurance with respect to its assets or operations, nor has its coverage been
limited below usual and customary policy limits, by an insurance carrier to
which it has applied for any such insurance or with which it has carried
insurance during the last three years.

                 Section 7.20  Hedging Agreements.  Schedule 7.20 sets forth,
as of the Closing Date, a true and complete list of all Hedging Agreements
(including commodity price swap agreements, forward agreements or contracts of
sale which provide for prepayment for deferred shipment or delivery of oil, gas
or other commodities) of the Borrower and each Subsidiary, the material terms
thereof (including the type, term, effective date, termination date and
notional amounts or volumes), the net mark to market value thereof, all credit
support agreements relating thereto (including any margin required or
supplied), and the counterparty to each such agreement.

                 Section 7.21  Restriction on Liens.  Neither the Borrower nor
any Subsidiary is  a party to any agreement or arrangement (other than the Loan
Documents), or subject to any





                                      -45-
<PAGE>   52
order, judgment, writ or decree, which either restricts or purports to restrict
its ability to grant Liens to other Persons on or in respect of their
respective assets or Properties.

                 Section 7.22  Material Agreements. Set forth on Schedule 7.22
hereto is a complete and correct list of all material agreements, leases,
indentures, purchase agreements, obligations in respect of letters of credit,
guarantees, joint venture agreements, and other instruments in effect or to be
in effect as of the Closing Date (other than Hedging Agreements) providing for,
evidencing, securing or otherwise relating to any material Debt of the Borrower
or any Subsidiary, and all obligations of the Borrower or any Subsidiary to
issuers of surety or appeal bonds (excluding operator's bonds, plugging and
abandonment bonds, and similar surety obligations obtained in the ordinary
course of business) issued for account of the Borrower or any such  Subsidiary,
and such list correctly sets forth the names of the debtor or lessee and
creditor or lessor with respect to the Debt or lease obligations outstanding or
to be outstanding and the property subject to any Lien securing such Debt or
lease obligation.

                 Section 7.23  Gas Imbalances.  As of the Closing Date, except
as set forth in the most recent Reserve Report furnished to Agent or on
Schedule 7.23 or on the most recent certificate delivered pursuant to Section
8.07(c), on a net basis there are no gas imbalances, take or pay or other
prepayments with respect to the Borrower's or any Subsidiary's Hydrocarbon
Interests which would require the Borrower or such Subsidiary to deliver five
percent (5%) or more of the monthly production from the Borrower's and its
Subsidiaries' Hydrocarbons produced on a monthly basis from the Hydrocarbon
Interests, at some future time without then or thereafter receiving full
payment therefor.

                 Section 7.24  Partnership Agreement.  The Partnership
Agreement has not been terminated, is in full force and effect as of the date
hereof and no default has occurred and is in continuance thereunder which would
have a Material Adverse Effect.

                 Section 7.25  Prior Note and Related Documents.

         (a)     The aggregate principal balance outstanding on the Prior Note
as of the Closing Date plus all accrued interest and other amounts owing on the
Prior Note as of the Closing Date is $35,106,624.22.

         (b)     The Borrower has not assigned its rights or obligations under
the Prior Note or the Prior Credit Agreement.





                                      -46-
<PAGE>   53
                                  ARTICLE VIII

                             AFFIRMATIVE COVENANTS

         The Borrower covenants and agrees that, so long as any of the
Commitments are in effect and until payment in full of all Indebtedness
hereunder, all interest thereon and all other amounts payable by the Borrower
hereunder:

                 Section 8.01  Financial Statements.  The Borrower shall
deliver, or shall cause to be delivered, to the Agent with sufficient copies of
each for the Lenders:

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

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

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

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





                                      -47-
<PAGE>   54
         Brigham Exploration by independent accountants in connection with any
         annual, interim or special audit made by them of the books of the
         Borrower or Brigham Exploration, and a copy of any response by the
         Borrower or Brigham Exploration to such letter or report.

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

                 (f)      Notices Under Other Loan Agreements.  Promptly after
         the furnishing thereof, copies of any statement, report or notice
         furnished to any Person pursuant to the terms of any indenture, loan
         or credit or other similar agreement, other than this Agreement and
         not otherwise required to be furnished to the Lenders pursuant to any
         other provision of this Section 8.01.

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

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

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

The Borrower will furnish to the Agent, at the time it furnishes each set of
financial statements pursuant to paragraph (a) or (b) above, a certificate
substantially in the form of Exhibit C-2 hereto executed by a Responsible
Officer (i) certifying as to the matters set forth therein and stating that no
Default has occurred and is continuing (or, if any Default has occurred and is
continuing, describing the same in reasonable detail), (ii) setting forth in
reasonable detail the computations necessary to determine whether Brigham
Exploration is in compliance with Sections 5.2(q), (r) and (s) of its Guaranty
Agreement as of the end of the respective fiscal





                                      -48-
<PAGE>   55
quarter or fiscal year, and (iii) certifying that said financial statements
fairly present the consolidated and consolidating financial condition and
consolidated results of operations in accordance with GAAP, as at the end of,
and for, such period (subject to normal year-end audit adjustments).

                 Section 8.02  Litigation.  The Borrower shall promptly give to
the Agent notice of : (i) all legal or arbitral proceedings, and of all
proceedings before any Governmental Authority involving the Borrower or any
Guarantor, except proceedings which, if adversely determined within any
reasonable range of loss, would not have a Material Adverse Effect, and (ii) of
any material litigation or material proceeding against the Borrower or any
Guarantor in which the amount involved is not covered in full by insurance
(subject to normal and customary deductibles), or in which injunctive or
similar relief is sought.  The Borrower will, and will cause each of the
Guarantors to, promptly notify the Agent and each of the Lenders of any claim,
judgment, Lien or other encumbrance affecting any Property of the Borrower or
any Guarantor if the value of the claim, judgment, Lien, or other encumbrance
affecting such Property shall exceed $1,000,000.

                 Section 8.03  Maintenance, Etc.

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

                 (b)      Contemporaneously with the delivery of the financial
         statements required by Section 8.01(a) to be delivered for each year,
         the Borrower will furnish or cause to be furnished to the Agent and
         the Lenders a certificate of insurance coverage from the





                                      -49-
<PAGE>   56
         insurer in form and substance satisfactory to the Agent and, if
         requested by the Agent, will furnish the Agent and the Lenders copies
         of the applicable policies.

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

                 (d)      The Borrower will and will cause each Subsidiary to,
         at its own expense, do or cause to be done (to the extent it has the
         power to do so) all things reasonably necessary to preserve and keep
         in good repair, working order and efficiency all of its Oil and Gas
         Properties and other material Properties including, without
         limitation, all equipment, machinery and facilities, and from time to
         time will make all the reasonably necessary repairs, renewals and
         replacements so that at all times the state and condition of its Oil
         and Gas Properties and other material Properties will be fully
         preserved and maintained, except to the extent a portion of such
         Properties is not capable of producing Hydrocarbons in economically
         reasonable amounts.  The Borrower will  and will cause each Subsidiary
         to promptly: (i) pay and discharge, or make reasonable and customary
         efforts to cause to be paid and discharged, all delay rentals,
         royalties, expenses and indebtedness accruing under the leases or
         other agreements affecting or pertaining to its Oil and Gas
         Properties, (ii) perform or make reasonable and customary efforts to
         cause to be performed, in accordance with industry standards, the
         obligations required by each and all of the assignments, deeds,
         leases, sub-leases, contracts and agreements affecting its interests
         in its Oil and Gas Properties and other material Properties, (iii)
         will and will cause each Subsidiary to do all other things necessary
         to keep unimpaired, except for Liens described in Section 9.02, its
         rights with respect to its Oil and Gas Properties and other material
         Properties and prevent any forfeiture thereof or a default thereunder,
         except to the extent a portion of such Properties is no longer capable
         of producing Hydrocarbons in economically reasonable amounts.  The
         Borrower will and will cause each Subsidiary to operate its Oil and
         Gas Properties and other material Properties or cause or make
         reasonable and customary efforts to cause such Oil and Gas Properties
         and other material Properties to be operated in a good and workmanlike
         manner in accordance with the practices of the industry and in
         compliance with all applicable contracts and agreements and in
         compliance in all material respects with all Governmental
         Requirements.  The covenants contained in this Section 8.03(d) shall
         not apply to insignificant Properties unless a failure of such
         covenant could have a Material Adverse Effect.

                 Section 8.04  Environmental Matters.

                 (a)  To the extent that a reasonably prudent owner or operator
         would do so under the same or similar circumstances, the Borrower will
         and will cause each Subsidiary to establish and implement such
         procedures as may be reasonably necessary to periodically





                                      -50-
<PAGE>   57
         determine and assure that any failure of the following does not have a
         Material Adverse Effect: (i) all Property of the Borrower and the
         Subsidiaries and the operations conducted thereon and other activities
         of the Borrower and the Subsidiaries are in compliance with and do not
         violate the requirements of any Environmental Laws, (ii) no oil,
         hazardous substances or solid wastes are disposed of or otherwise
         released on or to any Property owned by any such party except in
         compliance with Environmental Laws, (iii) no hazardous substance will
         be released on or to any such Property in a quantity equal to or
         exceeding that quantity which requires reporting pursuant to Section
         103 of CERCLA, and (iv) no oil, oil and gas exploration and production
         wastes or hazardous substance is released on or to any such Property
         so as to pose an imminent and substantial endangerment to public
         health or welfare or the environment.

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

                 Section 8.05  Further Assurances.  The Borrower will and will
cause each Guarantor to cure promptly any defects in the creation and issuance
of the Notes and the execution and delivery of the Loan Documents.  The
Borrower at its expense will and will cause each Guarantor to promptly execute
and deliver to the Agent upon request all such other documents, agreements and
instruments to comply with or accomplish the covenants and agreements of the
Borrower or any Guarantor, as the case may be, in the Loan Documents, or to
further evidence and more fully describe the collateral intended as security
for the Notes, or to correct any omissions in the Loan Documents, or to state
more fully the security obligations set out herein or in any of the Loan
Documents, or to perfect, protect or preserve any Liens created pursuant to any
of the Loan Documents, or to make any recordings, to file any notices or obtain
any consents, all as may be necessary or appropriate in connection therewith.

                 Section 8.06  Performance of Obligations.  The Borrower will
pay the Notes according to the reading, tenor and effect thereof; and the
Borrower will and will cause each Guarantor to do and perform every act and
discharge all of the obligations to be performed and discharged by them under
the Loan Documents, at the time or times and in the manner specified.





                                      -51-
<PAGE>   58
                 Section 8.07  Engineering Reports.

                 (a)      Not less than 30 days prior to the First Borrowing
         Base Determination Date, the Borrower shall furnish to the Agent and
         the Lenders a Reserve Report prepared as of December 1, 1998 or later
         (the "First Reserve Report") and as provided in clause 8.07(b) below.

                 (b)      On January 31, 1999 and not less than 30 days prior
         to each Scheduled Redetermination Date thereafter, commencing with the
         Scheduled Redetermination Date to occur on September 30, 1999, the
         Borrower shall furnish to the Agent and the Lenders a Reserve Report.
         The Reserve Report furnished for the September 30 Scheduled
         Redetermination Date shall be prepared as of the preceding July 1 and
         the Reserve Report furnished for the March Scheduled Redetermination
         Date (as well as the Reserve Report furnished on January 31, 1999)
         shall be prepared as of the preceding January 1.  The Reserve Report
         furnished on January 31, 1999 and the January 1 Reserve Report of each
         year beginning January 1, 2000 shall be prepared by certified
         independent petroleum engineers or other independent petroleum
         consultant(s) acceptable to the Agent and the First Reserve Report and
         the July 1 Reserve Report of each year shall be prepared by or under
         the supervision of the chief engineer or Vice President of Operations
         of the Borrower who shall certify such Reserve Report to have been
         prepared in accordance with the procedures used in the immediately
         preceding First Reserve Report or January 1 Reserve Report, as
         appropriate.  At Borrower's option, the July 1 Reserve Report of each
         year may instead consist of a report from the independent petroleum
         engineers referred to above on any new wells and a roll- forward by
         Borrower on any wells previously reported on.

                 (c)      In the event of an unscheduled redetermination, the
         Borrower shall furnish to the Agent and the Lenders a Reserve Report
         prepared by or under the supervision of the chief engineer of the
         Borrower who shall certify such Reserve Report to be true and accurate
         and to have been prepared in accordance with the procedures used in
         the immediately preceding Reserve Report.  For any unscheduled
         redetermination requested by the Lenders or the Borrower  pursuant to
         Section 2.08(d), the Borrower shall provide such Reserve Report with
         an "as of" date as required by the Majority Lenders as soon as
         possible, but in any event no later than 30 days following the receipt
         of the request by the Agent on behalf of the Lenders.

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

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





                                      -52-
<PAGE>   59
                          (A)     a certificate from a Responsible Officer
                 certifying that, to the best of his knowledge and in all
                 material respects: (i) the most recently delivered Reserve
                 Report does not in the belief of such officer and based upon
                 information in the Borrower's possession, materially overstate
                 the oil and gas reserves of the Borrower and the Subsidiaries
                 as a whole bearing in mind that reserves are evaluated based
                 upon estimates and assumptions with respect to which
                 reasonable minds of competent engineers may differ, (ii)
                 except as set forth in such Reserve Report or on an exhibit to
                 the certificate, on a net basis there are no gas imbalances,
                 take or pay or other prepayments with respect to its Oil and
                 Gas Properties evaluated in such Reserve Report which would
                 violate Section 9.18, (iii) none of its proved Hydrocarbon
                 Interests have been sold since the date of the last Borrowing
                 Base determination except as set forth on an exhibit to the
                 certificate, which certificate shall list all of its proved
                 Hydrocarbon Interests sold and in such detail as reasonably
                 required by the Majority Lenders, (iv) attached to the
                 certificate is a list of its proved Hydrocarbon Interests
                 added to and deleted from the immediately prior Reserve Report
                 and a list showing any change in working interest or net
                 revenue interest in its Hydrocarbon Interests occurring, (v)
                 at the Agent's request, attached to the certificate is a list
                 of all Persons disbursing proceeds to the Borrower from its
                 Oil and Gas Properties and (vi) except as set forth on a
                 schedule attached to the certificate all of proved Hydrocarbon
                 Interests evaluated by such Reserve Report are Mortgaged
                 Property; and

                          (B)     a certificate from a Responsible Officer
                 certifying that, to the best of his knowledge and in all
                 material respects (i) the representations of the Borrower in
                 Section 7.10 are true and correct and apply to the Hydrocarbon
                 Interests evaluated in the Reserve Report that are described
                 in the Mortgage or Exhibit A to the Prior Mortgage and (ii)
                 the Borrower has, with respect to those material Hydrocarbon
                 Interests that are evaluated in the most recently delivered
                 Reserve Report, but that are not covered by a Mortgage or a
                 Prior Mortgage, conducted overall title due diligence that, in
                 all material respects, equals or exceeds industry standards
                 given the applicable facts and circumstances.

                 Section 8.08  Intentionally Omitted.

                 Section 8.09  Additional Collateral.

                 (a)      Should any of the Borrower's or any Subsidiary's Oil
         and Gas Properties which are not Mortgaged Property be identified
         after the Closing Date as containing proved Hydrocarbon reserves or
         should the Borrower or any Subsidiary acquire any additional Oil and
         Gas Properties which are identified as containing proved Hydrocarbon
         reserves, the Borrower will grant or cause such Subsidiary to grant to
         the Agent as security for the Indebtedness a first-priority Lien
         interest (subject only to Excepted Liens and the matters set out on
         Schedule 7.10 hereto) on the Borrower's or the Subsidiary's interest
         in such Oil and Gas Properties not already subject to a Lien of the
         Loan





                                      -53-
<PAGE>   60
         Documents, which Lien will be created and perfected by and in
         accordance with the provisions of deeds of trust, security agreements
         and financing statements, or other Loan Documents, all in form
         substantially the same as the previous Mortgages and in sufficient
         executed (and acknowledged where necessary or appropriate)
         counterparts for recording purposes; provided, however that after
         January 31, 1999, if the Borrower is then in Borrowing Base
         compliance, the Mortgaged Property need only cover 90% of Borrower's
         and its Subsidiaries' proved Hydrocarbon Reserves.

                 (b)      Concurrently with the granting of the Lien or other
         action referred to in Section 8.09(a) above, the Borrower will provide
         to the Agent title information in form and substance satisfactory to
         the Agent in its sole discretion with respect to the Borrower's and
         its Subsidiaries' interests in such Oil and Gas Properties to the
         extent needed to cause the Agent to have received, together with title
         information previously delivered to the Agent, satisfactory title
         information on at least 80% of the value of the proved Hydrocarbon
         Interests evaluated by the most recent Reserve Report.

                 (c)      Also, promptly after the filing of any new Loan
         Document in any state, upon the reasonable request of the Agent, the
         Borrower will provide to the Agent an opinion addressed to the Agent
         for the benefit of the Lenders in form and substance reasonably
         satisfactory to the Agent in its sole discretion from counsel
         acceptable to Agent, stating that such Loan Document is valid, binding
         and enforceable in accordance with its terms and in legally sufficient
         form for such jurisdiction.

                 Section 8.10  ERISA Information and Compliance.  The Borrower
will promptly furnish and will cause any ERISA Affiliate to promptly furnish to
the Agent with sufficient copies to the Lenders (i) if requested by the Agent
promptly after the filing thereof with the United States Secretary of Labor,
the Internal Revenue Service or the PBGC, copies of each annual and other
report with respect to each Plan or any trust created thereunder, (ii)
immediately upon becoming aware of the occurrence of any ERISA Event or of any
"prohibited transaction," as described in section 406 of ERISA or in section
4975 of the Code, in connection with any Plan or any trust created thereunder,
a written notice signed by a Responsible Officer specifying the nature thereof,
what action the Borrower or the ERISA Affiliate is taking or proposes to take
with respect thereto, and, when known, any action taken or proposed by the
Internal Revenue Service, the Department of Labor or the PBGC with respect
thereto, and (iii) immediately upon receipt thereof, copies of any notice of
the PBGC's intention to terminate or to have a trustee appointed to administer
any Plan.  With respect to each Plan (other than a Multiemployer Plan), the
Borrower will, and will cause each ERISA Affiliate to, (i) satisfy in full and
in a timely manner, without incurring any late payment or underpayment charge
or penalty and without giving rise to any lien, all of the contribution and
funding requirements of section 412 of the Code (determined without regard to
subsections (d), (e), (f) and (k) thereof) and of section 302 of ERISA
(determined without regard to sections 303, 304 and 306 of ERISA), and (ii)
pay, or cause to be paid, to the PBGC in a timely manner, without incurring any
late payment or underpayment charge or penalty, all premiums required pursuant
to sections 4006 and 4007 of ERISA.





                                      -54-
<PAGE>   61
                 Section 8.11  Subsidiary Security.  Should the Borrower create
or acquire any  Subsidiary pursuant to Section 9.16 hereof it will promptly
grant to the Agent for the benefit of the Lenders a security interest and
pledge of all the capital stock of such Subsidiary in form and substance
satisfactory to the Agent and the Borrower will cause such Subsidiary to enter
into a guaranty of the Indebtedness in form and substance satisfactory to the
Agent.  The delivery of such security and guaranty shall be accompanied by such
back up corporate authority and opinions of counsel as the Agent may reasonably
request.

                 Section 8.12  Payment of Trade Payables.  The Borrower will
pay and cause all of its Subsidiaries to pay all of their Trade Payables now or
hereafter incurred within 60 days of the invoice or billing date, unless
subject to legal offset or unless being contested in good faith by appropriate
proceedings and reserves adequate under GAAP shall have been established
therefor.

                 Section 8.13  Certain Guaranties.  The Borrower will cause the
Guaranty Agreements of Brigham Holdings I, LLC and Brigham Holdings II, LLC
together with opinions of counsel with respect thereto in form and substance
satisfactory to the Agent  to be delivered on or before 30 days after the
Closing Date.



                                   ARTICLE IX

                               NEGATIVE COVENANTS

         The Borrower covenants and agrees that, so long as any of the
Commitments are in effect and until payment in full of the Indebtedness
hereunder, all interest thereon and all other amounts payable by the Borrower
hereunder, without the prior written consent of the Majority Lenders:

                 Section 9.01  Debt.  Neither the Borrower nor any Subsidiary
will incur, create, assume or suffer to exist any Debt, except:

                 (a)      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;

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

                 (c)      accounts payable for the deferred purchase price of
         Property or services (other than Trade Payables) from time to time
         incurred in the ordinary course of business which, if greater than 60
         days past the invoice or billing date, are being contested in good





                                      -55-
<PAGE>   62
         faith by appropriate proceedings if reserves adequate under GAAP shall
         have been established therefor;

                 (d)      Debt owing to a Guarantor which is subordinated to
         the Indebtedness as provided in such Guarantor's Guaranty Agreement or
         owing to the Borrower.

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

                 (f)      Debt of the Borrower under Hedging Agreements with a
         Lender or another investment grade counterparty the notional amounts
         on which do not exceed 75% of  Borrower's anticipated oil and/or gas
         production to be produced during the term of such Hedging Agreements
         entered into as a part of its normal business operations as a risk
         management strategy and/or hedge against changes resulting from market
         conditions related to the Borrower's and its Subsidiaries' operations;

                 (g)      Debt associated with bonds or surety obligations
         required by Governmental Requirements in connection with the operation
         of the Oil and Gas Properties; and

                 (h)      Debt of the Borrower not described in Sections
         9.01(a) through (g) which, together with all Debt of Brigham
         Exploration allowed under Section 5.2(a)(5) of Brigham Exploration
         Company's Guaranty Agreement, does not exceed $1,000,000 at any one
         time outstanding.

                 Section 9.02  Liens.  Neither the Borrower nor any Subsidiary
will create, incur, assume or permit to exist any Lien on any of its Properties
(now owned or hereafter acquired), except:

                 (a)      Liens securing the payment of any Indebtedness;

                 (b)      Excepted Liens;

                 (c)      Liens securing leases allowed under Section 9.01(e)
         but only on the Property under lease;

                 (d)      Liens disclosed on Schedule 9.02; and

                 (e)      Any Permitted Encumbrances as described in the Prior
         Mortgages or the Mortgage.

                 Section 9.03  Investments, Loans and Advances.  Neither the
Borrower nor any Subsidiary will make or permit to remain outstanding any loans
or advances to or investments in any Person, except that the foregoing
restriction shall not apply to:





                                      -56-
<PAGE>   63
                 (a)      investments, loans or advances reflected in the
         Financial Statements or which are disclosed to the Lenders in Schedule
         9.03;

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

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

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

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

                 (f)      for the Borrower only, deposits in money market funds
         investing exclusively in investments described in Section 9.03(c),
         9.03(d) or 9.03(e);

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

                 (h)      investments by the Borrower in direct or indirect
         (through a Subsidiary to the extent permitted by Section 9.16 below)
         ownership interests in additional Oil and Gas Properties and gas
         gathering systems gas plants, and similar assets related thereto; and

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

                 (j)      investments, distributions, loans and advances by the
         Borrower:

                          (a)     to Brigham Exploration, Brigham Inc., Brigham
                 Holdings I, LLC and/or Brigham Holdings II, LLC to pay Federal
                 or State taxes owing by any of them, payroll and payroll
                 related taxes and other reasonable general and administrative
                 expenses, or consisting of forgiveness of indebtedness, and

                          (b)     to Subsidiaries which are Guarantors.





                                      -57-
<PAGE>   64
                 Section 9.04  Dividends, Distributions and Redemptions.  The
Borrower 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
partners, except as permitted under Section 9.03(j)(a) above.

                 Section 9.05  Sales and Leasebacks.  Neither the Borrower nor
any Subsidiary will enter into any arrangement, directly or indirectly, with
any Person whereby the Borrower or any Subsidiary shall sell or transfer any of
its Property, whether now owned or hereafter acquired, and whereby the Borrower
or any Subsidiary shall then or thereafter rent or lease as lessee such
Property or any part thereof or other Property which the Borrower or any
Subsidiary intends to use for substantially the same purpose or purposes as the
Property sold or transferred.

                 Section 9.06  Nature of Business.  Neither the Borrower nor
any Subsidiary will allow any material change to be made in the character of
its business as an independent oil and gas exploration and production company.
Among other things, a transfer of a substantial portion of Borrower's seismic
data and Hydrocarbon Interests which do not contain identified proved
Hydrocarbon reserves (other than transfers to participants of any participation
interest earned by them in the ordinary course of Borrower's business and
abandonment of prospects) shall be considered a material change in Borrower's
business.

                 Section 9.07  Limitation on Leases.  Neither the Borrower nor
any Subsidiary will 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 Borrower and the
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.

                 Section 9.08  Mergers, Etc.  The Borrower will not and will
not permit any Subsidiary 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 Borrower, Brigham Exploration or any Guarantor
whose Guaranty Agreement is in full force and effect is the surviving entity
and no Default exists or will be created thereby.

                 Section 9.09  Proceeds of Notes.  The Borrower will not permit
the proceeds of the Notes to be used for any purpose other than those permitted
by Section 7.07.  Neither the Borrower nor any Person acting on behalf of the
Borrower has taken or will take any action which might cause any of the Loan
Documents to violate Regulation G, U or X or any other regulation of the Board
of Governors of the Federal Reserve System or to violate Section 7 of the
Securities Exchange Act of 1934 or any rule or regulation thereunder, in each
case as now in effect or as the same may hereinafter be in effect.

                 Section 9.10  ERISA Compliance.  The Borrower will not at any
time:





                                      -58-
<PAGE>   65
                 (a)      Engage in, or permit any ERISA Affiliate to engage
         in, any transaction in connection with which the Borrower or any ERISA
         Affiliate could be subjected to either a civil penalty assessed
         pursuant to section 502(c), (i) or (l) of ERISA or a tax imposed by
         Chapter 43 of Subtitle D of the Code in excess of $100,000;

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

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

                 (d)      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;

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

                 (f)      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;

                 (g)      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, (1) any Multiemployer Plan, or (2) any other Plan
         that is subject to Title IV of ERISA under which the actuarial present
         value of the benefit liabilities under such Plan exceeds the current
         value of the assets (computed on a plan termination basis in
         accordance with Title IV of ERISA) of such Plan allocable to such
         benefit liabilities;

                 (h)      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 the aggregate for all such liability
         exceeds $100,000;





                                      -59-
<PAGE>   66
                 (i)      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

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

                 Section 9.11  Sale or Discount of Receivables.  Neither the
Borrower nor any Subsidiary will discount or sell (with or without recourse)
any of its notes receivable or accounts receivable.

                 Section 9.12  Capital Expenditures.  Neither the Borrower nor
any Subsidiary will  make any expenditures to acquire non cash flow generating
fixed or capital assets, such as seismic data and unproved Oil and Gas
Properties, if, after giving effect thereto, the aggregate of all such
acquisition expenditures would exceed $21,000,000 from January 1, 1998, until
the date the Initial Borrowing Base has been set.  Costs of drilling and
development activities will not be considered "acquisition expenditures" for
the purposes of this section.

                 Section 9.13  Sale of Oil and Gas Properties.  The Borrower 
will not, and will not permit any Subsidiary to, sell, assign, farm-out, convey
or otherwise transfer any Hydrocarbon Interests except for (i) the sale of
Hydrocarbons in the ordinary course of business; (ii) assignments, farmouts,
and other disposition of Hydrocarbon Interests which do not contain identified
proved Hydrocarbon reserves, provided such assignments, farmouts, and other
dispositions are in the normal course of business (e.g., in bringing in
participants or disposing of unattractive prospects); (iii) the sale or
transfer of equipment that is no longer necessary for the business of the
Borrower or such Subsidiary or is replaced by equipment of at least comparable
value and use and (iv) during any consecutive four fiscal quarters, sales of
Hydrocarbon Interests containing identified proved Hydrocarbon reserves which
shall not exceed $2,500,000 in the aggregate.

                 Section 9.14  Environmental Matters.  Neither the Borrower nor
any Subsidiary will knowingly cause or permit any of its Property to be in
violation of, or knowingly do anything or permit anything to be done which will
subject any such Property to any remedial obligations under any Environmental
Laws, assuming disclosure to the applicable Governmental Authority of all
relevant facts, conditions and circumstances, if any, pertaining to such
Property where such violations or remedial obligations would have a Material
Adverse Effect.

                 Section 9.15  Transactions with Affiliates.  Neither the
Borrower nor any Subsidiary will enter into any transaction, including, without
limitation, any purchase, sale, lease or exchange of Property or the rendering
of any service, with any Affiliate unless such





                                      -60-
<PAGE>   67
transactions are otherwise not in violation of this Agreement, are in the
ordinary course of its business and are upon fair and reasonable terms no less
favorable to it than it would obtain in a comparable arm's length transaction
with a Person not an Affiliate.

                 Section 9.16  Subsidiaries.  The Borrower will not, and will
not permit any Subsidiary to, create any additional Subsidiaries or make any
additional investment in a Subsidiary, unless such Subsidiary is or becomes a
Guarantor and provided further, that all Subsidiaries together at no time shall
own or hold Oil and Gas Properties having proved reserves with a net discounted
present value calculated in the same manner as in the most recent Reserve
Report in excess of 10% of the total net discounted present value of proved
reserves of the Borrower and its Subsidiaries as reflected in said Reserve
Report (plus such Subsidiaries' proved reserves not included in such Reserve
Report).

                 Section 9.17  Negative Pledge Agreements.  The Borrower will
not and will not permit any Subsidiary to create, incur, assume or suffer to
exist any contract, agreement or understanding (other than the Loan Documents)
which in any way prohibits or restricts (i) the granting, conveying, creation
or imposition of any Lien on any of its Property or (ii) any Subsidiary from
paying dividends or making any other distribution to the Borrower or which
requires the consent of or notice to other Persons in connection with any of
the foregoing.

                 Section 9.18  Gas Imbalances, Take-or-Pay or Other
Prepayments.  The Borrower will not allow gas imbalances, take-or-pay or other
prepayments with respect to the Hydrocarbon Interests of the Borrower and its
Subsidiaries which would require the Borrower or its Subsidiaries to deliver
five percent (5%) or more of the Borrower's and its Subsidiaries' Hydrocarbons
produced on a monthly basis from the Hydrocarbon Interests at some future time
without then or thereafter receiving full payment therefor.


                                   ARTICLE X

                          EVENTS OF DEFAULT; REMEDIES

                 Section 10.01  Events of Default.  One or more of the
following events shall constitute an "Event of Default":

                 (a)      the Borrower shall default in the payment or
         prepayment when due of any principal of or interest on any Loan, or
         any reimbursement obligation for a disbursement made under any Letter
         of Credit, or any fees or other amount payable by it hereunder or
         under any other Loan Document and such default, other than a default
         of a payment or prepayment of principal (which shall have no cure
         period), shall continue unremedied for a period of three (3) Business
         Days; or

                 (b)      the Borrower or any Guarantor shall default in the
         payment when due of any principal of or interest on any of its other
         Debt aggregating $1,000,000 or more, or





                                      -61-
<PAGE>   68
         any event specified in any note, agreement, indenture or other
         document evidencing or relating to any such Debt shall occur if the
         effect of such event is to cause, or (with the giving of any notice or
         the lapse of time or both) to permit the holder or holders of such
         Debt (or a trustee or agent on behalf of such holder or holders) to
         cause, such Debt to become due prior to its stated maturity; or

                 (c)      any representation, warranty or certification made or
         deemed made herein or in any other Loan Document by the Borrower or
         any Guarantor, or any certificate furnished by the Borrower or any
         Guarantor to any Lender or the Agent pursuant to the provisions hereof
         or any Loan Document, shall prove to have been false or misleading as
         of the time made or furnished in any material and adverse respect; or

                 (d)      the Borrower shall default in the performance of any
         of its obligations under Article IX or Section 8.01(c) of this
         Agreement; or the Borrower shall default in the performance of any of
         its obligations under any other Article of the Agreement or under or
         any other Loan Document to which it is a party (other than the payment
         of amounts due which shall be governed by Section 10.01(a)) and such
         default shall continue unremedied for a period of thirty (30) days
         after notice thereof to the Borrower by the Agent or the Majority
         Lenders (through the Agent); or

                 (e)      any Guarantor shall default in the performance of its
         obligation to pay the Liabilities (as defined therein) at maturity or,
         with respect to Brigham Exploration, performance of any covenant under
         Section 5.1(i) or Section 5.2 of its Guaranty Agreement; or any
         Guarantor shall default in the performance of any of its other
         obligations under its Guaranty Agreement and such default shall
         continue unremedied for a period of thirty (30) days after notice
         thereof to the Guarantor by the Agent or the Majority of Lenders
         (through the Agent); or

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

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

                 (h)      a proceeding or case shall be commenced, without the
         application or consent of the Borrower, in any court of competent
         jurisdiction, seeking (i) its liquidation,





                                      -62-
<PAGE>   69
         reorganization, dissolution or winding-up, or the composition or
         readjustment of its debts, (ii) the appointment of a trustee,
         receiver, custodian, liquidator or the like of the Borrower of all or
         any substantial part of its assets, or (iii) similar relief in respect
         of the Borrower under any law relating to bankruptcy, insolvency,
         reorganization, winding-up, or composition or adjustment of debts, and
         such proceeding or case shall continue undismissed, or an order,
         judgment or decree approving or ordering any of the foregoing shall be
         entered and continue unstayed and in effect, for a period of 60 days;
         or an order for relief against the Borrower shall be entered in an
         involuntary case under the Federal Bankruptcy Code; or

                 (i)      a judgment or judgments for the payment of money in
         excess of $1,000,000 in the aggregate shall be rendered by a court
         against the Borrower and the same shall not be discharged (or
         provision shall not be made for such discharge), or a stay of
         execution thereof shall not be procured, within thirty (30) days from
         the date of entry thereof and the Borrower shall not, within said
         period of 30 days, or such longer period during which execution of the
         same shall have been stayed, appeal therefrom and cause the execution
         thereof to be stayed during such appeal; or

                 (j)      the Loan Documents after delivery thereof shall for
         any reason, except to the extent permitted by the terms thereof, cease
         to be in full force and effect and valid, binding and enforceable in
         all material respects in accordance with their terms, or cease in any
         material respect to create a valid and perfected Lien of the priority
         required thereby on any of the collateral purported to be covered
         thereby, except to the extent permitted by the terms of this
         Agreement, or the Borrower or any Guarantor shall so state in writing;
         or

                 (k)      any Letter of Credit becomes the subject matter of
         any order, judgment, injunction or any other such determination which
         has the effect of extending the Lenders' liability under any Letter of
         Credit beyond the Revolving Credit Termination Date; or

                 (l)      any Guarantor discontinues its usual business or
         suffers to exist any material change in its ownership, control or
         management; or

                 (m)      any Guarantor takes, suffers or permits to exist any
         of the events or conditions referred to in paragraphs (f), (g), (h) or
         (i) hereof or if any guaranty agreement related thereto shall for any
         reason cease to be valid and binding on such Guarantor in all material
         respects or if such Guarantor shall so state in writing; or

                 (n)      Brigham Exploration ceases to own (directly or
         indirectly) 100% of the Borrower;

                 (o)      the Borrower ceases to be the primary operating
         entity for Brigham Exploration and its Subsidiaries and the Borrower
         and its Subsidiaries cease to be the only Brigham Exploration entities
         owning Oil and Gas Properties.





                                      -63-
<PAGE>   70
                 Section 10.02    Remedies.

                 (a)      In the case of an Event of Default other than one
         referred to in clauses (f), (g) or (h) of Section 10.01 or in clause
         (m) to the extent it relates to clauses (f), (g) or (h),the Agent,
         upon request of the Majority Lenders, shall, by notice to the
         Borrower, cancel the Commitments and/or declare the principal amount
         then outstanding of, and the accrued interest on, the Loans and all
         other amounts payable by the Borrower hereunder and under the Notes
         (including without limitation the payment of cash collateral to secure
         the LC Exposure as provided in Section 2.10(b) hereof) to be forthwith
         due and payable, whereupon such amounts shall be immediately due and
         payable without presentment, demand, protest, notice of intent to
         accelerate, notice of acceleration or other formalities of any kind,
         all of which are hereby expressly waived by the Borrower.

                 (b)      In the case of the occurrence of an Event of Default
         referred to in clauses (f), (g) or (h) of Section 10.01 or in clause
         (m) to the extent it relates to clauses (f), (g) or (h), the
         Commitments shall be automatically canceled and the principal amount
         then outstanding of, and the accrued interest on, the Loans and all
         other amounts payable by the Borrower hereunder and under the Notes
         (including without limitation the payment of cash collateral to secure
         the LC Exposure as provided in Section 2.10(b) hereof) shall become
         automatically immediately due and payable without presentment, demand,
         protest, notice of intent to accelerate, notice of acceleration or
         other formalities of any kind, all of which are hereby expressly
         waived by the Borrower.

                 (c)      All proceeds received after maturity of the Notes,
         whether by acceleration or otherwise shall be applied first to
         reimbursement of expenses and indemnities provided for in the Loan
         Documents; second to accrued interest on the Notes; third to fees;
         fourth pro rata to principal outstanding on the Notes and other
         Indebtedness; fifth to serve as cash collateral to be held by the
         Agent to secure the LC Exposure; and any excess shall be paid to the
         Borrower or as otherwise required by any Governmental Requirement.

                 Section 10.03    Production and Proceeds.  Notwithstanding
that, by the terms of the various Mortgages and other Loan Documents, the
Borrower and any other mortgagors are and will be assigning to Agent all of the
Hydrocarbons covered thereby and all of the products thereof and proceeds and
revenues attributable thereto and all payments in lieu of such Hydrocarbons (in
this section collectively called the "Production and Proceeds"), so long as no
Default has occurred and is continuing (a) the Borrower and such mortgagors may
continue to receive all such Production and Proceeds, subject, however, to the
Liens created under the Mortgages and other Loan Documents, and (b) upon the
Borrower's request the Agent will confirm to any purchasers of Hydrocarbons,
title examiners, or other Persons that the Borrower and such mortgagors
continue to have the right so to receive such Production and Proceeds until
notification by the Agent of the occurrence of a Default.  During the
continuance of a Default, however, the Agent may exercise its rights and
remedies granted under the Mortgages and the other Loan Documents, including
the rights and remedies granted under the Mortgages and the other Loan
Documents, including the right to obtain possession of all Production and
Proceeds





                                      -64-
<PAGE>   71
then held by the Borrower and such mortgagors and to receive directly from the
purchasers of Hydrocarbons all other Production Proceeds.  In no case shall any
failure by the Agent to collect directly any such Production and Proceeds
constitute in any way a release of any of its rights under the Loan Documents.


                                   ARTICLE XI

                                   THE AGENT

                 Section 11.01  Appointment, Powers and Immunities.  Each
Lender hereby irrevocably appoints and authorizes the Agent to act as its agent
hereunder and  under the other Loan Documents with such powers as are
specifically delegated to the Agent by the terms of this Agreement and the
other Loan Documents, together with such other powers as are reasonably
incidental thereto.  The Agent (which term as used in this sentence and in
Section 11.05 and the first sentence of Section 11.06 shall include reference
to its Affiliates and its and its Affiliates' officers, directors, employees,
attorneys, accountants, experts and agents):  (i) shall have no duties or
responsibilities except those expressly set forth in the Loan Documents, and
shall not by reason of the Loan Documents be a trustee or fiduciary for any
Lender; (ii) makes no representation or warranty to any Lender and shall not be
responsible to the Lenders for any recitals, statements, representations or
warranties contained in this Agreement, or in any certificate or other document
referred to or provided for in, or received by any of them under, this
Agreement, or for the value, validity, effectiveness, genuineness, execution,
effectiveness, legality, enforceability or sufficiency of this Agreement, any
Note or any other document referred to or provided for herein or for any
failure by the Borrower or any other Person (other than the Agent) to perform
any of its obligations hereunder or thereunder or for the existence, value,
perfection or priority of any collateral security or the financial or other
condition of the Borrower, the Subsidiaries or any other obligor or guarantor;
(iii) except pursuant to Section 11.07 shall not be required to initiate or
conduct any litigation or collection proceedings hereunder; and (iv) SHALL NOT
BE RESPONSIBLE FOR ANY ACTION TAKEN OR OMITTED TO BE TAKEN BY IT HEREUNDER OR
UNDER ANY OTHER DOCUMENT OR INSTRUMENT REFERRED TO OR PROVIDED FOR HEREIN OR IN
CONNECTION HEREWITH INCLUDING ITS OWN ORDINARY NEGLIGENCE, EXCEPT FOR ITS OWN
GROSS NEGLIGENCE OR WILLFUL MISCONDUCT.  The Agent may employ agents,
accountants, attorneys and experts and shall not be responsible for the
negligence or misconduct of any such agents, accountants, attorneys or experts
selected by it in good faith or any action taken or omitted to be taken in good
faith by it in accordance with the advice of such agents, accountants,
attorneys or experts.  The Agent may deem and treat the payee of any Note as
the holder thereof for all purposes hereof unless and until a written notice of
the assignment or transfer thereof permitted hereunder shall have been filed
with the Agent.  The Agent is authorized to release any collateral that is
permitted to be sold or released pursuant to the terms of the Loan Documents.

                 Section 11.02  Reliance by Agent.  The Agent shall be entitled
to rely upon any certification, notice or other communication (including any
thereof by telephone, telex, telecopier, telegram or cable) believed by it to
be genuine and correct and to have been signed





                                      -65-
<PAGE>   72
or sent by or on behalf of the proper Person or Persons, and upon advice and
statements of legal counsel, independent accountants and other experts selected
by the Agent.

                 Section 11.03  Defaults.  The Agent shall not be deemed to
have knowledge of the occurrence of a Default (other than the non-payment of
principal of or interest on Loans or of fees or failure to reimburse for Letter
of Credit drawings) unless the Agent has received notice from a Lender or the
Borrower specifying such Default and stating that such notice is a "Notice of
Default."  In the event that the Agent receives such a notice of the occurrence
of a Default, the Agent shall give prompt notice thereof to the Lenders.  In
the event of a payment Default, the Agent shall give each Lender prompt notice
of each such payment Default.

                 Section 11.04  Rights as a Lender.   With respect to its
Commitments and the Loans made by it and its participation in the issuance of
Letters of Credit, BMO (and any successor acting as Agent) in its capacity as a
Lender hereunder shall have the same rights and powers hereunder as any other
Lender and may exercise the same as though it were not acting as the Agent, and
the term "Lender" or "Lenders" shall, unless the context otherwise indicates,
include the Agent in its individual capacity.  BMO (and any successor acting as
Agent) and its Affiliates may (without having to account therefor to any
Lender) accept deposits from, lend money to and generally engage in any kind of
banking, trust or other business with the Borrower (and any of its Affiliates)
as if it were not acting as the Agent, and BMO and its Affiliates may accept
fees and other consideration from the Borrower for services in connection with
this Agreement or otherwise without having to account for the same to the
Lenders.

                 Section 11.05  INDEMNIFICATION.  THE LENDERS AGREE TO
INDEMNIFY THE AGENT AND THE ISSUING BANK RATABLY IN ACCORDANCE WITH THEIR
PERCENTAGE SHARES FOR THE INDEMNITY MATTERS AS DESCRIBED IN SECTION 12.03 TO
THE EXTENT NOT INDEMNIFIED OR REIMBURSED BY THE BORROWER UNDER SECTION 12.03,
BUT WITHOUT LIMITING THE OBLIGATIONS OF THE BORROWER UNDER SAID SECTION 12.03
AND FOR ANY AND ALL OTHER LIABILITIES, OBLIGATIONS, LOSSES, DAMAGES, PENALTIES,
ACTIONS, JUDGMENTS, SUITS, COSTS, EXPENSES OR DISBURSEMENTS OF ANY KIND AND
NATURE WHATSOEVER WHICH MAY BE IMPOSED ON, INCURRED BY OR ASSERTED AGAINST THE
AGENT OR THE ISSUING BANK IN ANY WAY RELATING TO OR ARISING OUT OF: (I) THIS
AGREEMENT, THE OTHER LOAN DOCUMENTS OR ANY OTHER DOCUMENTS CONTEMPLATED BY OR
REFERRED TO HEREIN OR THE TRANSACTIONS CONTEMPLATED HEREBY, BUT EXCLUDING,
UNLESS A DEFAULT HAS OCCURRED AND IS CONTINUING, NORMAL ADMINISTRATIVE COSTS
AND EXPENSES INCIDENT TO THE PERFORMANCE OF ITS AGENCY DUTIES HEREUNDER OR (II)
THE ENFORCEMENT OF ANY OF THE TERMS OF THIS AGREEMENT, ANY OTHER LOAN DOCUMENT
OR OF ANY SUCH OTHER DOCUMENTS; WHETHER OR NOT ANY OF THE FOREGOING SPECIFIED
IN THIS SECTION 11.05 ARISES FROM THE SOLE OR CONCURRENT NEGLIGENCE OF THE
AGENT OR THE ISSUING BANK, PROVIDED THAT NO LENDER SHALL BE LIABLE FOR ANY OF
THE FOREGOING TO THE EXTENT THEY ARISE FROM THE GROSS NEGLIGENCE OR WILLFUL
MISCONDUCT OF THE AGENT.

                 Section 11.06  Non-Reliance on Agent and other Lenders.  Each
Lender acknowledges and agrees that it has, independently and without reliance
on the Agent or any





                                      -66-
<PAGE>   73
other Lender, and based on such documents and information as it has deemed
appropriate, made its own credit analysis of the Borrower and its decision to
enter into this Agreement, and that it will, independently and without reliance
upon the Agent or any other Lender, and based on such documents and information
as it shall deem appropriate at the time, continue to make its own analysis and
decisions in taking or not taking action under this Agreement.  The Agent shall
not be required to keep itself informed as to the performance or observance by
the Borrower of the Loan Documents or any other document referred to or
provided for herein or to inspect the properties or books of the Borrower.
Except for notices, reports and other documents and information expressly
required to be furnished to the Lenders by the Agent hereunder, the Agent shall
not have any duty or responsibility to provide any Lender with any credit or
other information concerning the affairs, financial condition or business of
the Borrower (or any of its Affiliates) which may come into the possession of
the Agent or any of its Affiliates.  In this regard, each Lender acknowledges
that Vinson & Elkins L.L.P. is acting in this transaction as special counsel to
the Agent only, except to the extent otherwise expressly stated in any legal
opinion or any Loan Document.  Each Lender will consult with its own legal
counsel to the extent that it deems necessary in connection with the Loan
Documents and the matters contemplated therein.

                 Section 11.07  Action by Agent.  Except for action or other
matters expressly required of the Agent hereunder, the Agent shall in all cases
be fully justified in failing or refusing to act hereunder unless it shall (i)
receive written instructions from the Majority Lenders (or all of the Lenders
as expressly required by Section 12.04) specifying the action to be taken, and
(ii) be indemnified to its satisfaction by the Lenders against any and all
liability and expenses which may be incurred by it by reason of taking or
continuing to take any such action.  The instructions of the Majority Lenders
(or all of the Lenders as expressly required by Section 12.04) and any action
taken or failure to act pursuant thereto by the Agent shall be binding on all
of the Lenders.  If a Default has occurred and is continuing, the Agent shall
take such action with respect to such Default as shall be directed by the
Majority Lenders (or all of the Lenders as required by Section 12.04) in the
written instructions (with indemnities) described in this Section 11.07,
provided that, unless and until the Agent shall have received such directions,
the Agent may (but shall not be obligated to) take such action, or refrain from
taking such action, with respect to such Default as it shall deem advisable in
the best interests of the Lenders.  In no event, however, shall the Agent be
required to take any action which exposes the Agent to personal liability or
which is contrary to this Agreement and the other Loan Documents or applicable
law.

                 Section 11.08  Resignation or Removal of Agent.  Subject to
the appointment and acceptance of a successor Agent as provided below, the
Agent may resign at any time by giving notice thereof to the Lenders and the
Borrower, and the Agent may be removed at any time with or without cause by the
Majority Lenders.  Upon any such resignation or removal, the Majority Lenders,
with the consent of Borrower, shall have the right to appoint a successor
Agent.  If no successor Agent shall have been so appointed by the Majority
Lenders and shall have accepted such appointment within thirty (30) days after
the retiring Agent's giving of notice of resignation or the Majority Lenders'
removal of the retiring Agent, then the retiring Agent may, on behalf





                                      -67-
<PAGE>   74
of the Lenders, appoint a successor Agent.  Upon the acceptance of such
appointment hereunder by a successor Agent, such successor Agent shall
thereupon succeed to and become vested with all the rights, powers, privileges
and duties of the retiring Agent, and the retiring Agent shall be discharged
from its duties and obligations hereunder.  After any retiring Agent's
resignation or removal hereunder as Agent, the provisions of this Article XI
and Section 12.03 shall continue in effect for its benefit in respect of any
actions taken or omitted to be taken by it while it was acting as the Agent.


                                  ARTICLE XII

                                 MISCELLANEOUS

                 Section 12.01  Waiver.  No failure on the part of the Agent or
any Lender to exercise and no delay in exercising, and no course of dealing
with respect to, any right, power or privilege under any of the Loan Documents
shall operate as a waiver thereof, nor shall any single or partial exercise of
any right, power or privilege under any of the Loan Documents preclude any
other or further exercise thereof or the exercise of any other right, power or
privilege.  The remedies provided herein are cumulative and not exclusive of
any remedies provided by law.

                 Section 12.02  Notices.  All notices and other communications
provided for herein and in the other Loan Documents (including, without
limitation, any modifications of, or waivers or consents under, this Agreement
or the other Loan Documents) shall be given or made by telex, telecopy, courier
or U.S. Mail or in writing and telexed, telecopied, mailed or delivered to the
intended recipient at the "Address for Notices" specified below its name on the
signature pages hereof or in the Loan Documents or, as to any party, at such
other address as shall be designated by such party in a notice to each other
party.  Except as otherwise provided in this Agreement or in the other Loan
Documents, all such communications shall be deemed to have been duly given when
transmitted, if transmitted before 1:00 p.m. Houston time on a Business Day
(otherwise on the next succeeding Business Day) by telex or telecopier and
evidence or confirmation of receipt is obtained, or personally delivered or, in
the case of a mailed notice, three (3) Business Days after the date deposited
in the mails, postage prepaid, in each case given or addressed as aforesaid.

                 Section 12.03  Payment of Expenses, Indemnities, etc.  The
Borrower agrees:

                 (a)      whether or not the transactions hereby contemplated
         are consummated, to pay all reasonable expenses of the Agent in the
         administration (both before and after the execution hereof and
         including advice of counsel as to the rights and duties of the Agent
         and the Lenders with respect thereto) of, and in connection with the
         negotiation, syndication, investigation, preparation, execution and
         delivery of, recording or filing of, preservation of rights under,
         enforcement of, and refinancing, renegotiation or restructuring of,
         the Loan Documents and any amendment, waiver or consent relating





                                      -68-
<PAGE>   75
         thereto (including, without limitation, the reasonable fees and
         disbursements of counsel and other outside consultants for the Agent
         and, in the case of enforcement, the reasonable fees and disbursements
         of counsel for the Agent and any of the Lenders); and promptly
         reimburse the Agent for all amounts expended, advanced or incurred by
         the Agent or the Lenders to satisfy any obligation of the Borrower
         under this Agreement or any other Loan Document, including without
         limitation, all costs and expenses of foreclosure;

                 (b)      TO INDEMNIFY THE AGENT AND EACH LENDER AND EACH OF
         THEIR AFFILIATES AND EACH OF THEIR OFFICERS, DIRECTORS, EMPLOYEES,
         REPRESENTATIVES, AGENTS, ATTORNEYS, ACCOUNTANTS AND EXPERTS
         ("INDEMNIFIED PARTIES") FROM, HOLD EACH OF THEM HARMLESS AGAINST AND
         PROMPTLY UPON DEMAND PAY OR REIMBURSE EACH OF THEM FOR, THE INDEMNITY
         MATTERS WHICH MAY BE INCURRED BY OR ASSERTED AGAINST OR INVOLVE ANY OF
         THEM (WHETHER OR NOT ANY OF THEM IS DESIGNATED A PARTY THERETO) AS A
         RESULT OF, ARISING OUT OF OR IN ANY WAY RELATED TO (I) ANY ACTUAL OR
         PROPOSED USE BY THE BORROWER OF THE PROCEEDS OF ANY OF THE LOANS OR
         LETTERS OF CREDIT, (II) THE EXECUTION, DELIVERY AND PERFORMANCE OF THE
         LOAN DOCUMENTS, (III) THE OPERATIONS OF THE BUSINESS OF THE BORROWER
         AND THE SUBSIDIARIES, (IV) THE FAILURE OF THE BORROWER OR ANY
         GUARANTOR TO COMPLY WITH THE TERMS OF ANY OTHER LOAN DOCUMENT OR THIS
         AGREEMENT, OR WITH ANY GOVERNMENTAL REQUIREMENT, (V) ANY INACCURACY OF
         ANY REPRESENTATION OR ANY BREACH OF ANY WARRANTY OF THE BORROWER OR
         ANY GUARANTOR SET FORTH IN ANY OF THE LOAN DOCUMENTS, (VI) THE
         ISSUANCE, EXECUTION AND DELIVERY OR TRANSFER OF OR PAYMENT OR FAILURE
         TO PAY UNDER ANY LETTER OF CREDIT, (VII) ANY ASSERTION THAT THE
         LENDERS WERE NOT ENTITLED TO RECEIVE THE PROCEEDS RECEIVED PURSUANT TO
         THE LOAN DOCUMENTS OR (VIII) ANY OTHER ASPECT OF THE LOAN DOCUMENTS,
         INCLUDING, WITHOUT LIMITATION, THE REASONABLE FEES AND DISBURSEMENTS
         OF COUNSEL AND ALL OTHER REASONABLE EXPENSES INCURRED IN CONNECTION
         WITH INVESTIGATING, DEFENDING OR PREPARING TO DEFEND ANY SUCH ACTION,
         SUIT, PROCEEDING (INCLUDING ANY INVESTIGATIONS, LITIGATION OR
         INQUIRIES) OR CLAIM AND INCLUDING ALL INDEMNITY MATTERS ARISING BY
         REASON OF THE ORDINARY NEGLIGENCE OF ANY INDEMNIFIED PARTY, BUT
         EXCLUDING ALL INDEMNITY MATTERS ARISING SOLELY BY REASON OF CLAIMS
         BETWEEN THE LENDERS OR ANY LENDER AND THE AGENT OR A LENDER'S
         SHAREHOLDERS AGAINST THE AGENT OR LENDER OR BY REASON OF THE GROSS
         NEGLIGENCE OR WILLFUL MISCONDUCT ON THE PART OF ANY INDEMNIFIED PARTY;
         AND

                 (c)      TO INDEMNIFY AND HOLD HARMLESS FROM TIME TO TIME THE
         INDEMNIFIED PARTY FROM AND AGAINST ANY AND ALL LOSSES, CLAIMS, COST
         RECOVERY ACTIONS, ADMINISTRATIVE ORDERS OR PROCEEDINGS, DAMAGES AND
         LIABILITIES TO WHICH ANY SUCH PERSON MAY BECOME SUBJECT (I) UNDER ANY
         ENVIRONMENTAL LAW APPLICABLE TO THE BORROWER OR ANY OF ITS
         PROPERTIES, INCLUDING WITHOUT LIMITATION, THE TREATMENT OR DISPOSAL OF
         HAZARDOUS





                                      -69-
<PAGE>   76
         SUBSTANCES ON ANY OF THEIR PROPERTIES, (II) AS A RESULT OF THE BREACH
         OR NON-COMPLIANCE BY THE BORROWER WITH ANY ENVIRONMENTAL LAW
         APPLICABLE TO THE BORROWER, (III) DUE TO PAST OWNERSHIP BY THE
         BORROWER  OF ANY OF ITS PROPERTIES OR PAST ACTIVITY ON ANY OF ITS
         PROPERTIES WHICH, THOUGH LAWFUL AND FULLY PERMISSIBLE AT THE TIME,
         RESULTS IN PRESENT LIABILITY, (IV) THE PRESENCE, USE, RELEASE,
         STORAGE, TREATMENT OR DISPOSAL OF HAZARDOUS SUBSTANCES ON OR AT ANY OF
         THE PROPERTIES OWNED OR OPERATED BY THE BORROWER OR (V) ANY OTHER
         ENVIRONMENTAL, HEALTH OR SAFETY CONDITION IN CONNECTION WITH THE LOAN
         DOCUMENTS, PROVIDED, HOWEVER, NO INDEMNITY SHALL BE AFFORDED UNDER
         THIS SECTION 12.03(C) IN RESPECT OF ANY PROPERTY FOR ANY OCCURRENCE
         ARISING FROM THE ACTS OR OMISSIONS OF THE AGENT OR ANY LENDER DURING
         THE PERIOD AFTER WHICH SUCH PERSON, ITS SUCCESSORS OR ASSIGNS, OR
         THEIR AGENTS OR REPRESENTATIVES,  SHALL HAVE OBTAINED POSSESSION OF
         SUCH PROPERTY (WHETHER BY FORECLOSURE OR DEED IN LIEU OF FORECLOSURE,
         AS MORTGAGEE-IN-POSSESSION OR OTHERWISE).

                 (d)      No Indemnified Party may settle any claim to be
         indemnified without the consent of the indemnitor, such consent not to
         be unreasonably withheld; provided, that the indemnitor may not
         reasonably withhold consent to any settlement that an Indemnified
         Party proposes, if the indemnitor does not have the financial ability
         to pay all its obligations outstanding and asserted against the
         indemnitor at that time, including, without limitation, the maximum
         potential claims against the Indemnified Party to be indemnified
         pursuant to this Section 12.03.

                 (e)      In the case of any indemnification hereunder, the
         Agent or Lender, as appropriate shall give notice to the Borrower of
         any such claim or demand being made against the Indemnified Party and
         the Borrower shall have the non-exclusive right to join in the defense
         against any such claim or demand provided that if the Borrower
         provides a defense, the Indemnified Party shall bear its own cost of
         defense unless there is a conflict between the Borrower and such
         Indemnified Party.

                 (f)      THE FOREGOING INDEMNITIES SHALL EXTEND TO THE
         INDEMNIFIED PARTIES NOTWITHSTANDING THE SOLE OR CONCURRENT NEGLIGENCE
         OF EVERY KIND OR CHARACTER WHATSOEVER, WHETHER ACTIVE OR PASSIVE,
         WHETHER AN AFFIRMATIVE ACT OR AN OMISSION, INCLUDING WITHOUT
         LIMITATION, ALL TYPES OF NEGLIGENT CONDUCT IDENTIFIED IN THE
         RESTATEMENT (SECOND) OF TORTS OF ONE OR MORE OF THE INDEMNIFIED
         PARTIES OR BY REASON OF STRICT LIABILITY IMPOSED WITHOUT FAULT ON ANY
         ONE OR MORE OF THE INDEMNIFIED PARTIES.  TO THE EXTENT THAT AN
         INDEMNIFIED PARTY IS FOUND TO HAVE COMMITTED AN ACT OF GROSS
         NEGLIGENCE OR WILLFUL MISCONDUCT, THIS CONTRACTUAL OBLIGATION OF
         INDEMNIFICATION SHALL CONTINUE BUT SHALL ONLY EXTEND TO THE PORTION OF
         THE CLAIM THAT IS DEEMED TO HAVE OCCURRED BY REASON OF EVENTS OTHER
         THAN THE GROSS NEGLIGENCE OR WILLFUL MISCONDUCT OF SUCH INDEMNIFIED
         PARTY.





                                      -70-
<PAGE>   77
                 (g)      The Borrower's obligations under this Section 12.03
         shall survive any termination of this Agreement and the payment of the
         Notes and shall continue thereafter in full force and effect.

                 (h)      The Borrower shall pay any amounts due under this
         Section 12.03 within thirty (30) days of the receipt by the Borrower
         of notice of the amount due.

                 Section 12.04  Amendments, Etc.  Any provision of this
Agreement or any other Loan Document may be amended, modified or waived with
the Borrower's and the Majority Lenders' written consent; provided that (i) no
amendment, modification or waiver which extends the final maturity of the
Loans, increases the Aggregate Maximum Credit Amounts, allows an increase in
the Borrowing Base without the approval of all the Lenders, forgives the
principal amount of any Indebtedness outstanding under this Agreement, releases
any guarantor of the Indebtedness or releases all or substantially all of the
collateral, reduces the interest rate applicable to the Loans or the fees
payable to the Lenders generally, affects Section 2.03(a), this Section 12.04
or Section 12.06(a) or modifies the definition of "Majority Lenders" shall be
effective without consent of all Lenders; (ii) no amendment, modification or
waiver which increases the Maximum Credit Amount of any Lender shall be
effective without the consent of such Lender; and (iii) no amendment,
modification or waiver which modifies the rights, duties or obligations of the
Agent shall be effective without the consent of the Agent.

                 Section 12.05  Successors and Assigns.  This Agreement shall
be binding upon and inure to the benefit of the parties hereto and their
respective successors and permitted assigns.

                 Section 12.06  Assignments and Participations.

                 (a)      The Borrower may not assign its rights or obligations
         hereunder or under the Notes or any Letters of Credit without the
         prior consent of all of the Lenders and the Agent.

                 (b)      Any Lender may, upon the written consent of the Agent
         and the Borrower (which consent will not be unreasonably withheld),
         assign to one or more assignees all or a portion of its rights and
         obligations under this Agreement pursuant to an Assignment Agreement
         substantially in the form of Exhibit E (an "Assignment") provided,
         however, that (i) any such assignment shall be in the amount of at
         least $10,000,000 or such lesser amount to which the Borrower has
         consented and (ii) the assignee or assignor shall pay to the Agent a
         processing and recordation fee of $2,500 for each assignment.  Any
         such assignment will become effective upon the execution and delivery
         to the Agent of the Assignment and the consent of the Agent and the
         Borrower.  Promptly after receipt of an executed Assignment, the Agent
         shall send to the Borrower a copy of such executed Assignment.  Upon
         receipt of such executed Assignment and of the Notes which are the
         subject thereof, the Borrower, will, at its own expense, execute and
         deliver new Notes to the assignor and/or assignee, as appropriate, in
         accordance with their respective





                                      -71-
<PAGE>   78
         interests as they appear.  Upon the effectiveness of any assignment
         pursuant to this Section 12.06(b), the assignee will become a
         "Lender," if not already a "Lender," for all purposes of this
         Agreement and the other Loan Documents.  The assignor shall be
         relieved of its obligations hereunder to the extent of such assignment
         (and if the assigning Lender no longer holds any rights or obligations
         under this Agreement, such assigning Lender shall cease to be a
         "Lender" hereunder except that its rights under Sections 4.06, 5.01,
         5.05 and 12.03 shall not be affected).  The Agent will prepare on the
         last Business Day of each month during which an assignment has become
         effective pursuant to this Section 12.06(b), a new Annex I giving
         effect to all such assignments effected during such month, and will
         promptly provide the same to the Borrower and each of the Lenders.

                 (c)      Each Lender may transfer, grant or assign
         participations in all or any part of such Lender's interests hereunder
         pursuant to this Section 12.06(c) to any Person, provided that: (i)
         such Lender shall remain a "Lender" for all purposes of this Agreement
         and the transferee of such participation shall not constitute a
         "Lender" hereunder; (ii) no such participant to which the Borrower has
         not consented (such consent not to be unreasonably withheld) shall be
         given any non-public information provided by the Borrower or the
         Guarantors under the Loan Documents; and (iii) no participant under
         any such participation shall have rights to approve any amendment to
         or waiver of any of the Loan Documents except to the extent such
         amendment or waiver would (x) forgive any principal owing on any
         Indebtedness or extend the final maturity of the Loans, (y) reduce the
         interest rate (other than as a result of waiving the applicability of
         any post-default increases in interest rates) or fees applicable to
         any of the Commitments or Loans or Letters of Credit in which such
         participant is participating, or postpone the payment of any thereof,
         or (z) release any guarantor of the Indebtedness or release all or
         substantially all of the collateral (except as provided in the Loan
         Documents) supporting any of the Commitments or Loans or Letters of
         Credit in which such participant is participating.  In the case of any
         such participation, the participant shall not have any rights under
         this Agreement or any of the other Loan Documents (the participant's
         rights against the granting Lender in respect of such participation to
         be those set forth in the agreement with such Lender creating such
         participation), and all amounts payable by the Borrower hereunder
         shall be determined as if such Lender had not sold such participation,
         provided that such participant shall be entitled to receive additional
         amounts under Article V on the same basis as if it were a Lender and
         be indemnified under Section 12.03 as if it were a Lender.  In
         addition, each agreement creating any participation must include an
         agreement by the participant to be bound by the provisions of Section
         12.15.

                 (d)      The Lenders may furnish any information concerning
         the Borrower in the possession of the Lenders from time to time to
         assignees and participants (including prospective assignees and
         participants to which the Borrower has consented (such consent not to
         be unreasonably withheld); provided that, such Persons agree to be
         bound by the provisions of Section 12.15 hereof.  The Borrower hereby
         consents to the sale of participations by any Lender to such Lender's
         Affiliates.





                                      -72-
<PAGE>   79
                 (e)      Notwithstanding anything in this Section 12.06 to the
         contrary, any Lender may assign and pledge its Note to any Federal
         Reserve Bank or the United States Treasury as collateral security
         pursuant to Regulation A of the Board of Governors of the Federal
         Reserve System and any operating circular issued by such Federal
         Reserve System and/or such Federal Reserve Bank.  No such assignment
         and/or pledge shall release the assigning and/or pledging Lender from
         its obligations hereunder.

                 (f)      Notwithstanding any other provisions of this Section
         12.06, no transfer or assignment of the interests or obligations of
         any Lender or any grant of participations therein shall be permitted
         if such transfer, assignment or grant would require the Borrower to
         file a registration statement with the SEC or to qualify the Loans
         under the "Blue Sky" laws of any state.

                 Section 12.07  Invalidity.  In the event that any one or more
of the provisions contained in any of the Loan Documents shall, for any reason,
be held invalid, illegal or unenforceable in any respect, such invalidity,
illegality or unenforceability shall not affect any other provision of the
Notes, this Agreement or any other Loan Document.

                 Section 12.08  Counterparts.  This Agreement may be executed
in any number of counterparts, all of which taken together shall constitute one
and the same instrument and any of the parties hereto may execute this
Agreement by signing any such counterpart.

                 Section 12.09  References.  The words "herein," "hereof,"
"hereunder" and other words of similar import when used in this Agreement refer
to this Agreement as a whole, and not to any particular article, section or
subsection.  Any reference herein to a Section shall be deemed to refer to the
applicable Section of this Agreement unless otherwise stated herein.  Any
reference herein to an exhibit or schedule shall be deemed to refer to the
applicable exhibit or schedule attached hereto unless otherwise stated herein.

                 Section 12.10  Survival. The obligations of the parties under
Section 4.06, Article V, and Sections 11.05 and 12.03 shall survive the
repayment of the Loans and the termination of the Commitments.  To the extent
that any payments on the Indebtedness or proceeds of any collateral are
subsequently invalidated, declared to be fraudulent or preferential, set aside
or required to be repaid to a trustee, debtor in possession, receiver or other
Person under any bankruptcy law, common law or equitable cause, then to such
extent, the Indebtedness so satisfied shall be revived and continue as if such
payment or proceeds had not been received and the Agent's and the Lenders'
Liens, security interests, rights, powers and remedies under this Agreement and
each other Loan Document shall continue in full force and effect.  In such
event, each Loan Document shall be automatically reinstated and the Borrower
shall take such action as may be reasonably requested by the Agent and the
Lenders to effect such reinstatement.

                 Section 12.11  Captions.  Captions and section headings
appearing herein are included solely for convenience of reference and are not
intended to affect the interpretation of any provision of this Agreement.





                                      -73-
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                 Section 12.12  NO ORAL AGREEMENTS.  THE LOAN DOCUMENTS EMBODY
THE ENTIRE AGREEMENT AND UNDERSTANDING BETWEEN THE PARTIES AND SUPERSEDE ALL
OTHER AGREEMENTS AND UNDERSTANDINGS BETWEEN SUCH PARTIES RELATING TO THE
SUBJECT MATTER HEREOF AND THEREOF.  THE LOAN DOCUMENTS REPRESENT THE FINAL
AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR,
CONTEMPORANEOUS OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES.  THERE ARE NO
UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.

                 Section 12.13  GOVERNING LAW; SUBMISSION TO JURISDICTION.

                 (a)      THIS AGREEMENT AND THE NOTES SHALL BE GOVERNED BY,
         AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF TEXAS
         EXCEPT TO THE EXTENT THAT UNITED STATES FEDERAL LAW PERMITS ANY LENDER
         TO CHARGE INTEREST AT THE RATE ALLOWED BY THE LAWS OF THE STATE WHERE
         SUCH LENDER IS LOCATED.  TEX. REV. CIV. STAT. ANN. ART.  5069, CH. 15
         (WHICH REGULATES CERTAIN REVOLVING CREDIT LOAN ACCOUNTS AND REVOLVING
         TRI-PARTY ACCOUNTS) SHALL NOT APPLY TO THIS AGREEMENT OR THE NOTES.

                 (b)      ANY LEGAL ACTION OR PROCEEDING WITH RESPECT TO THE
         LOAN DOCUMENTS SHALL BE BROUGHT IN THE COURTS OF THE STATE OF TEXAS OR
         OF THE UNITED STATES OF AMERICA FOR THE SOUTHERN DISTRICT OF TEXAS,
         AND, BY EXECUTION AND DELIVERY OF THIS AGREEMENT, THE BORROWER HEREBY
         ACCEPTS FOR ITSELF AND (TO THE EXTENT PERMITTED BY LAW) IN RESPECT OF
         ITS PROPERTY, GENERALLY AND UNCONDITIONALLY, THE JURISDICTION OF THE
         AFORESAID COURTS.  THE BORROWER HEREBY IRREVOCABLY WAIVES ANY
         OBJECTION, INCLUDING, WITHOUT LIMITATION, ANY OBJECTION TO THE LAYING
         OF VENUE OR BASED ON THE GROUNDS OF FORUM NON CONVENIENS, WHICH IT MAY
         NOW OR HEREAFTER HAVE TO THE BRINGING OF ANY SUCH ACTION OR PROCEEDING
         IN SUCH RESPECTIVE JURISDICTIONS.  THIS SUBMISSION TO JURISDICTION IS
         NON-EXCLUSIVE AND DOES NOT PRECLUDE THE AGENT OR ANY LENDER FROM
         OBTAINING JURISDICTION OVER THE BORROWER IN ANY COURT OTHERWISE HAVING
         JURISDICTION.

                 (c)      EACH OF THE BORROWER AND EACH LENDER HEREBY (I)
         IRREVOCABLY AND UNCONDITIONALLY WAIVE, TO THE FULLEST EXTENT PERMITTED
         BY LAW, TRIAL BY JURY IN ANY LEGAL ACTION OR PROCEEDING RELATING TO
         THIS AGREEMENT OR ANY OTHER LOAN DOCUMENT AND FOR ANY COUNTERCLAIM
         THEREIN; (II) IRREVOCABLY WAIVE, TO THE MAXIMUM EXTENT NOT PROHIBITED
         BY LAW, ANY RIGHT IT MAY HAVE TO CLAIM OR RECOVER IN ANY SUCH
         LITIGATION ANY SPECIAL, EXEMPLARY, PUNITIVE OR CONSEQUENTIAL DAMAGES,
         OR DAMAGES OTHER THAN, OR IN ADDITION TO, ACTUAL DAMAGES; (III)
         CERTIFY THAT NO PARTY HERETO NOR ANY REPRESENTATIVE OR AGENT OF
         COUNSEL FOR ANY PARTY HERETO HAS REPRESENTED, EXPRESSLY OR OTHERWISE,
         OR IMPLIED THAT SUCH PARTY WOULD NOT, IN THE EVENT OF LITIGATION, SEEK
         TO ENFORCE THE FOREGOING WAIVERS, AND (IV) ACKNOWLEDGE THAT IT HAS
         BEEN INDUCED TO ENTER INTO THIS AGREEMENT, THE OTHER LOAN DOCUMENTS
         AND THE TRANSACTIONS CONTEMPLATED HEREBY AND





                                      -74-
<PAGE>   81
         THEREBY BY, AMONG OTHER THINGS, THE MUTUAL WAIVERS AND CERTIFICATIONS
         CONTAINED IN THIS SECTION 12.13.

                 Section 12.14  Interest.  It is the intention of the parties
hereto that each Lender shall conform strictly to usury laws applicable to it.
Accordingly, if the transactions contemplated hereby would be usurious as to
any Lender under laws applicable to it (including the laws of the United States
of America and the State of Texas or any other jurisdiction whose laws may be
mandatorily applicable to such Lender notwithstanding the other provisions of
this Agreement), then, in that event, notwithstanding anything to the contrary
in any of the Loan Documents or any agreement entered into in connection with
or as security for the Notes, it is agreed as follows:  (i) the aggregate of
all consideration which constitutes interest under law applicable to any Lender
that is contracted for, taken, reserved, charged or received by such Lender
under any of the Loan Documents or agreements or otherwise in connection with
the Notes shall under no circumstances exceed the maximum amount allowed by
such applicable law, and any excess shall be canceled automatically and if
theretofore paid shall be credited by such Lender on the principal amount of
the Indebtedness (or, to the extent that the principal amount of the
Indebtedness shall have been or would thereby be paid in full, refunded by such
Lender to the Borrower); and (ii) in the event that the maturity of the Notes
is accelerated by reason of an election of the holder thereof resulting from
any Event of Default under this Agreement or otherwise, or in the event of any
required or permitted prepayment, then such consideration that constitutes
interest under law applicable to any Lender may never include more than the
maximum amount allowed by such applicable law, and excess interest, if any,
provided for in this Agreement or otherwise shall be canceled automatically by
such Lender as of the date of such acceleration or prepayment and, if
theretofore paid, shall be credited by such Lender on the principal amount of
the Indebtedness (or, to the extent that the principal amount of the
Indebtedness shall have been or would thereby be paid in full, refunded by such
Lender to the Borrower).  All sums paid or agreed to be paid to any Lender for
the use, forbearance or detention of sums due hereunder shall, to the extent
permitted by law applicable to such Lender, be amortized, prorated, allocated
and spread throughout the full term of the Loans evidenced by the Notes until
payment in full so that the rate or amount of interest on account of any Loans
hereunder does not exceed the maximum amount allowed by such applicable law.
If at any time and from time to time (i) the amount of interest payable to any
Lender on any date shall be computed at the Highest Lawful Rate applicable to
such Lender pursuant to this Section 12.14 and (ii) in respect of any
subsequent interest computation period the amount of interest otherwise payable
to such Lender would be less than the amount of interest payable to such Lender
computed at the Highest Lawful Rate applicable to such Lender, then the amount
of interest payable to such Lender in respect of such subsequent interest
computation period shall continue to be computed at the Highest Lawful Rate
applicable to such Lender until the total amount of interest payable to such
Lender shall equal the total amount of interest which would have been payable
to such Lender if the total amount of interest had been computed without giving
effect to this Section 12.14.  To the extent that Article 5069-1D.001 of the
Texas Revised Civil Statutes is relevant for the purpose of determining the
Highest Lawful Rate, such Lender elects to determine the applicable rate
ceiling under such Article by the weekly rate ceiling from time to time in
effect.





                                      -75-
<PAGE>   82
                 Section 12.15  Confidentiality.   In the event that the
Borrower or any Guarantor (hereinafter called the "Subject Entities') provides
to the Agent or the Lenders written confidential information or, if
communicated as confidential, oral confidential information belonging to any
Subject Entity, the Agent and the Lenders shall thereafter maintain such
information in confidence in accordance with the standards of care and
diligence that each utilizes in maintaining its own confidential information.
This obligation of confidence shall not apply to such portions of the
information which (i) are in the public domain, (ii) hereafter become part of
the public domain without the Agent or the Lenders breaching their obligation
of confidence to any Subject Entity, (iii) are previously known by the Agent or
the Lenders from some source other than any Subject Entity, (iv) are hereafter
developed by the Agent or the Lenders without using a Subject Entity's
information, (v) are hereafter obtained by or available to the Agent or the
Lenders from a third party who owes no obligation of confidence to any Subject
Entity with respect to such information, (vi) are disclosed with a Subject
Entity's consent, (vii) must be disclosed either pursuant to any Governmental
Requirement or to Persons regulating the activities of the Agent or the
Lenders, or (viii) as may be required by law or regulation or order of any
Governmental Authority in any judicial, arbitration or governmental proceeding.
Further, the Agent or a Lender may disclose any such information to any other
Lender, any independent petroleum engineers or consultants, any independent
certified public accountants, any legal counsel employed by such Person in
connection with this Agreement or any other Loan Document, including without
limitation, the enforcement or exercise of all rights and remedies thereunder,
or, subject to Section 12.06, any assignee or participant (including
prospective assignees to which the Borrower has consented and participants) in
the Loans; provided, however, that the Agent or the Lenders shall receive a
confidentiality agreement from the Person to whom such information is disclosed
such that said Person shall have the same obligation to maintain the
confidentiality of such information as is imposed upon the Agent or the Lenders
hereunder.  Notwithstanding anything to the contrary provided herein, this
obligation of confidence shall cease three (3) years from the date the
information was furnished, unless the Borrower requests in writing at least
thirty (30) days prior to the expiration of such three year period, to maintain
the confidentiality of such information for an additional three year period.

                 Section 12.16    Prior Credit Agreement.  The Prior Credit
Agreement is superseded by this Agreement and is of no further force or effect.

                 Section 12.17    Release Regarding the Prior Note and Related
Documents.  To induce Lenders to purchase the Prior Note and the rights under
certain of the documents securing said Prior Note (the "Prior Security
Documents"), the Borrower hereby fully releases and discharges the Agent and
the Lenders, and each of their officers, directors, employees, representatives,
agents and affiliates, from all claims, demands, causes of action, liabilities
or other obligations of any kind whatsoever, including, without limitation,
offsets, reductions, rebatements or claims of usury, known or unknown, whether
now existing or hereafter asserted in connection with the Prior Note and the
Prior Security Documents arising from matters occurring before the date of the
Lender's purchase.





                                      -76-
<PAGE>   83
                 Section 12.18  Effectiveness.  This Agreement shall be
effective on the Closing Date (the "Effective Date").

                 Section 12.19  EXCULPATION PROVISIONS.  EACH OF THE PARTIES
HERETO SPECIFICALLY AGREES THAT IT HAS A DUTY TO READ THIS AGREEMENT AND THE
OTHER LOAN DOCUMENTS AND AGREES THAT IT IS CHARGED WITH NOTICE AND KNOWLEDGE OF
THE TERMS OF THIS AGREEMENT AND THE  OTHER LOAN DOCUMENTS; THAT IT HAS IN FACT
READ THIS AGREEMENT AND IS FULLY INFORMED AND HAS FULL NOTICE AND KNOWLEDGE OF
THE TERMS, CONDITIONS AND EFFECTS OF THIS AGREEMENT; THAT IT HAS BEEN
REPRESENTED BY INDEPENDENT LEGAL COUNSEL OF ITS CHOICE THROUGHOUT THE
NEGOTIATIONS PRECEDING ITS EXECUTION OF THIS AGREEMENT AND THE OTHER LOAN
DOCUMENTS; AND HAS RECEIVED THE ADVICE OF ITS ATTORNEY IN ENTERING INTO THIS
AGREEMENT AND THE OTHER LOAN DOCUMENTS; AND THAT IT RECOGNIZES THAT CERTAIN OF
THE TERMS OF THIS AGREEMENT AND THE OTHER LOAN DOCUMENTS RESULT IN ONE PARTY
ASSUMING THE LIABILITY INHERENT IN SOME ASPECTS OF THE TRANSACTION AND
RELIEVING THE OTHER PARTY OF ITS RESPONSIBILITY FOR SUCH LIABILITY.  EACH PARTY
HERETO AGREES AND COVENANTS THAT IT WILL NOT CONTEST THE VALIDITY OR
ENFORCEABILITY OF ANY EXCULPATORY PROVISION OF THIS AGREEMENT AND THE OTHER
LOAN DOCUMENTS ON THE BASIS THAT THE PARTY HAD NO NOTICE OR KNOWLEDGE OF SUCH
PROVISION OR THAT THE PROVISION IS NOT "CONSPICUOUS."





                                      -77-
<PAGE>   84
                 The parties hereto have caused this Agreement to be duly
executed as of the day and year first above written.

BORROWER:                          BRIGHAM OIL & GAS, L.P.

                                   By:      Brigham, Inc., its General Partner
                                  
                                  
                                  
                                            By: /s/ CRAIG M. FLEMING
                                               ---------------------------------
                                            Name:  Craig M. Fleming
                                            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:  Craig M. Fleming




                                Signature Page 1
<PAGE>   85
LENDER AND AGENT:                  BANK OF MONTREAL




                                   By: /s/ ROBERT L. ROBERTS
                                       ---------------------------------
                                   Name:  Robert L. Roberts
                                   Title:   Director, U.S. Corporate Banking
                                  
                                   Lending Office for Base Rate Loans and
                                   Eurodollar Loans:
                                  
                                   115 South LaSalle
                                   Chicago, Illinois  60603
                                  
                                   Address for Notices:
                                  
                                   115 South LaSalle
                                   Chicago, Illinois  60603
                                  
                                   Telecopier No.:  312/750-6061
                                   Telephone No.:   312/750-4326
                                   Attention:  Farid Ali
                                  
                                   With copy to:
                                  
                                   Robert L. Roberts
                                   Director, U.S. Corporate Banking
                                   Bank of Montreal
                                   700 Louisiana, Suite 4400
                                   Houston, Texas 77002
                                   Telecopier:  (713) 546-4007
                                   Telephone:   (713) 546-9754





                                Signature Page 2