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                                                                   EXHIBIT 10.35


                                                                           DRAFT
                                                                 August 13, 1998

                       FIRST AMENDMENT TO CREDIT AGREEMENT


            THIS FIRST AMENDMENT TO CREDIT AGREEMENT (this "Amendment") dated 
as of August ___, 1998 is among: BRIGHAM OIL & GAS, L.P., a Delaware limited
partnership (the "Borrower"); each of the Lenders (as defined in the Credit
Agreement as hereinafter defined); 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. The Borrower, the Agents, and the Lenders have entered into that
certain Credit Agreement dated as of January 26, 1998 (the "Credit Agreement"),
pursuant to which the Lenders have agreed to make certain loans and extensions
of credit to the Borrower upon the terms and conditions as provided therein; and

         B. The Borrower, the Agents, and the Lenders now desire to make certain
amendments to the Credit Agreement.

         NOW, THEREFORE, in consideration of the premises and other good and
valuable consideration and the mutual benefits, covenants and agreements herein
expressed, the parties hereto now agree as follows:

         Section 1. Certain Definitions. Unless otherwise defined herein, all
terms beginning with a capital letter which are defined in the Credit Agreement
shall have the same meanings herein as therein unless the context hereof
otherwise requires.

         Section 2. Amendments to Credit Agreement.

         (a) Additional Defined Terms. Section 1.02 of the Credit Agreement is
hereby amended and supplemented by adding the following new definitions, which
are read in their entirety as follows:

                  "First Amendment" shall mean that certain First Amendment to
         Credit Agreement dated as of August ___, 1998 among the Borrower, the
         Lenders and the Agent.

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                  "Indenture" shall mean that certain Indenture dated as of
         August ____, 1998 between Brigham Exploration, as the issuer of the
         Subordinated Debt, and Chase Bank of Texas, National Association, as
         the trustee.

                  "Securities Purchase Agreement" shall mean that certain
         Securities Purchase Agreement dated August ___, 1998 among Brigham
         Exploration, the purchasers named therein and ___, as agent for such
         purchasers regarding $50,000,000 Senior Subordinated Secured Notes due
         2003.

                  "Subordinated Debt" shall mean the Debt in the principal
         amount not to exceed $40,000,000 (plus up to an additional $10,000,000
         for interest paid in kind pursuant to Section 9.02 of the Indenture) of
         Brigham Exploration incurred under the Indenture and expressly
         subordinated to the Indebtedness pursuant to agreements in form and
         substance satisfactory to the Lenders.

                  "Subordination Agreement" shall mean that certain
         Intercreditor and Subordination Agreement dated as of August _____,
         1998, and from time to time amended, ___, ___, and Bank of Montreal.

         (b) Section 2.03. Section 2.03 (a) is hereby deleted in its entirety,
and the following is substituted therefor:

                  "(a) The Aggregate Commitments shall at all times be equal to
         $65,000,000 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, (ii) $65,000,000, or (iii) the Borrowing Base as determined
         from time to time."

         (c) Section 2.07. Section 2.07(c) of the Credit Agreement is hereby
deleted in its entirety, and the following is substituted therefor:

                  "(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 (or such shorter period as hereinafter provided) 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, provided however,
         that upon the First Borrowing Base determination such required
         prepayment shall be made on or before 15 days after such First
         Borrowing Base determination if such deficiency is ten



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         percent (10%) or more of the Borrowing Base and (ii) if a Borrowing
         Base deficiency remains after prepaying all of the Loans ause 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) Section 7.21. Section 7.21 of the Credit Agreement is hereby
deleted in its entirety, and the following is substituted therefor:

                  "Restriction on Liens. Neither the Borrower nor any Subsidiary
         is a party to or subject to any agreement or arrangement (other than
         the Loan Documents, the documents described in Section 4.01(a) through
         (d) of the Indenture, and the Indenture), or subject to any 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."

         (e) Section 9.01. Section 9.01 of the Credit Agreement is hereby
amended by adding the following new clause (i):

                  "(i) Guarantees of the Borrower and its Subsidiaries which
         have executed prior and senior guarantees of the Indebtedness in form
         and substance satisfactory to the Agent, of the Subordinated Debt,
         which Guarantees are subordinated and otherwise in form and substance
         satisfactory to the Agent consistent with the Subordination Agreement."

         (f) Section 9.02. Section 9.02 of the Credit Agreement is hereby
amended by adding the following new clause (f):

                  "(f) Liens securing the Subordinated Debt on Properties upon
         which prior Liens have been granted to secure the Indebtedness pursuant
         to documents in form and substance satisfactory to the Agent, provided
         such Liens are subordinated on terms satisfactory to the Agent
         consistent with the Subordination Agreement."

         (g) Section 9.03. Section 9.03(j)(a) of the Credit Agreement is hereby
deleted in its entirety and the following is substituted therefor:

                  (a) to Brigham Exploration, Brigham, Inc., Brigham Holdings I,
         LLC and/or Brigham Holdings II, LLC

                           (i) 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


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                           (ii) so long as no Borrowing Base deficiency exists
                  or will be created thereby, no Event of Default or, with
                  respect to Section 5.2(q), (r), (s) or (u) of the Guaranty
                  Agreement of Brigham Exploration, Default, is in existence or
                  will be created thereby, to enable Brigham Exploration to pay
                  accrued and unpaid interest owing on the "Notes" (as defined
                  in the Indenture).

         (h) Section 9.17. Section 9.17 of the Credit Agreement is hereby
deleted in its entirety, and the following is substituted therefor:

                  "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 (other than the Indenture and the documents described in
         Section 4.01(a) through (d) of the Indenture) 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."

         (i) Article IX. Article IX is hereby supplemented by adding the
following new section:

                  "Section 9.19 Borrower as Operator. The Borrower will not and
         will not permit any of the Subsidiaries to voluntarily resign as
         operator of more than twenty-five percent (25%) of their currently
         operated Oil and Gas Properties unless the new operator is acceptable
         to the Majority Lenders."

         Section 3. Conditions Precedent. This Amendment shall ome binding
upon the receipt by the Agent of the following documents and satisfaction of the
other conditions provided in this Section 3, each of which must be satisfactory
to the Agent in form and substance:

                  (a) counterparts of this Amendment executed by the Borrower
         and the Lenders;

                  (b) certificates of the Secretary or an Assistant Secretary of
         the Borrower and of the Guarantor setting forth for each of them (i)
         the resolutions of its board of directors with respect to the
         authorization to execute, deliver and perform this Amendment; (ii) the
         officer of such entity authorized to sign this Amendment, and (iii) the
         signature of such authorized officer of such entity;

                  (c) evidence of the closing and concurrent funding of the
         Subordinated Debt pursuant to the Indenture and the equity issuance
         pursuant to the Securities Purchase Agreement;


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                  (d) a copy of the Securities Purchase Agreement and the
         Indenture and all documents executed with respect to the Subordinated
         Debt all in form and substance acceptable to the Lenders; and

                  (e) A security agreement executed by Brigham Exploration in
         favor of the Agent granting a first-priority security interest in all
         of Brigham Exploration's right, title and interest to the ownership
         interests of Brigham Holdings I, LLC;

                  (f) A security agreement executed by Brigham Inc. in favor of
         the Agent granting a first-priority security interest in all of Brigham
         Inc.'s right, title and interest in and to the ownership interests of
         Brigham Holdings II, LLC and the Borrower;

                  (g) A security agreement executed by Brigham Holdings II, LLC
         in favor of the Agent granting a first-priority security interest in
         all of Brigham Holdings II, LLC's right, title and interest in and to
         the partnership interests in Borrower;

                  (h) A security agreement executed by Brigham Holdings I, LLC
         in favor of the Agent granting a first priority security interest in
         all of Brigham Holdings I, LLC's right, title and interest in and to
         the partnership interests in Borrower;

                  (i) such other documents as Agent or its counsel may
         reasonably request.

         Section 4. Representations and Warranties. The Borrower hereby
reaffirms that as of the effective date of this Amendment, the representations
and warranties made by the Borrower in the Credit Agreement will be true and
correct as though made on and as of the effective date of this Amendment, and
further, the Borrower represents that no Default or Material Adverse Effect
shall have occurred and be continuing on such date.

         Section 5. Limitations. The amendments set forth herein are limited
precisely as written and shall not be deemed to (a) be a consent to, or waiver
or modification of, any other term or condition of the Credit Agreement or any
of the other Loan Documents, or (b) prejudice any right or rights which the
Lenders may now have or may have in the future under or in connection with the
Credit Agreement or any of the other Loan Documents. Except as expressly
supplemented, amended or modified hereby, the terms and provisions of the Credit
Agreement or any other Loan Documents are and shall remain in full force and
effect. In the event of a conflict between this Amendment and any of the
foregoing documents, the terms of this Amendment shall be controlling.

         Section 6. Governing Law. This Amendment and the rights and obligations
of the parties hereunder and under the Credit Agreement shall be construed in
accordance with and be governed by the laws of the State of Texas and the United
States of America.


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         Section 7. Descriptive Headings, etc. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

         Section 8. Counterparts. This Amendment may be executed in any number
of counterparts and by different parties on separate counterparts and all of
such counterparts shall together constitute one and the same instrument.

         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
executed as of the date first written above.

            NOTICE PURSUANT TO TEX. BUS. & COMM. CODE SECTION .26.02

         THIS AMENDMENT AND OTHER LOAN DOCUMENTS EXECUTED BY ANY OF THE PARTIES
BEFORE OR SUBSTANTIALLY CONTEMPORANEOUSLY WITH THE EXECUTION HEREOF TOGETHER
CONSTITUTE A WRITTEN LOAN AGREEMENT AND 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 AGREEMENT
BETWEEN THE PARTIES.

BORROWER:                         BRIGHAM OIL & GAS, L.P.

                                  By: Brigham, Inc., its General Partner



                                      By:
                                         --------------------------------
                                         Robert T. Moffett
                                         Vice President & Secretary


LENDER AND AGENT:                 BANK OF MONTREAL



                                  By:
                                     ------------------------------------
                                     Name:    Robert L. Roberts
                                     Title:   Director, U.S. Corporate Banking




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