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                                                                EXHIBIT 10.36.2

                      SECOND AMENDMENT TO CREDIT AGREEMENT

         SECOND AMENDMENT TO CREDIT AGREEMENT, dated as of March 26, 1999
("this Amendment"), among Brigham Oil & Gas, L.P., a limited partnership formed
under the laws of the State of Delaware (the "Borrower"), the financial
institutions party to the Credit Agreement referred to below (each a "Lender"
and collectively the "Lenders") and Bank of Montreal, a Canadian bank, as agent
for Lenders under the Credit Agreement (in such capacity, the "Agent").

                                    RECITALS


         WHEREAS, the Borrower, the Lenders and the Agent are parties to that
certain Credit Agreement, dated as of January 26, 1998, as amended by that
certain First Amendment to Credit Agreement, dated as of August 20, 1998 (as so
amended, the "Credit Agreement"); and

         WHEREAS, the Borrower has advised the Lenders and the Agent that it
desires to amend certain provisions of the Credit Agreement, and the Borrower
has requested that the Lenders and the Agent agree to various amendments to
certain provisions of the Credit Agreement; and

         WHEREAS, the Lenders and the Agent have agreed to so amend certain
provisions of the Credit Agreement upon the terms and subject to the conditions
and limitations of this Amendment;

         NOW, THEREFORE, in consideration of the premises, covenants and
agreements contained herein, the parties hereto hereby agrees as follows:


         Section 1. Definitions. Capitalized terms used and not otherwise
defined herein are used with the meanings ascribed thereto in the Credit
Agreement. The following capitalized terms shall have the following respective
meanings when used herein:

         A. "Duke Consent Letter" shall mean that certain Letter Agreement
dated as of February 18, 1999 executed by the Borrower and the Lenders, a copy
of which is attached hereto as Exhibit A.

         B. "Duke Transaction" shall mean the transactions contemplated by the
Duke Consent Letter.

         C. "Lending Relationship" shall refer to the Credit Agreement and the
other Loan Documents, including, without limitation, this Amendment, together
with any and all negotiations, discussions, acts, omissions, renewals,
extensions, and other agreements or events related to the Credit Agreement and
such other Loan Documents, the parties' obligations thereunder and the
transactions contemplated thereby, including, without limitation, any such
negotiations, discussions, acts, omissions, renewals, extensions, other
agreements or events that (a) occurred prior to the date hereof, (b) may



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occur on the date hereof, or (c) occurred prior to the execution of this
Amendment and the instruments and documents executed and delivered in
connection herewith or relating hereto.

         D. "New Mortgage" shall mean that certain Mortgage, Deed of Trust,
Assignment of Production, Security Agreement and Financing Statement dated as
of the date hereof from Brigham Oil & Gas, L.P. to Thomas McGraw, as Trustee,
for the benefit of Bank of Montreal, as Agent.

         E. "Released Claims" shall mean any and all claims (including without
limitation any liabilities, damages, demands and causes of action arising
therefrom), whether (a) at law or in equity, (b) on the alleged commission of a
tort, (c) on the alleged breach (or anticipatory breach or repudiation) of any
contract, duty, or warranty (whether oral or written, express or implied), (d)
on the alleged violation of any statute, tariff, or regulation (whether
promulgated by the United States, any state thereof, any foreign state or
country, or any other governmental agency or entity, wherever located), or (e)
on any other factual, legal or equitable theory, including, without limitation,
any claim for damages of any type or nature, for injunctive or other relief,
for attorneys' fees, interest or any other liability whatsoever on any theory,
including without limitation any loss, cost or damage in connection with or
based upon "lender liability", unfair dealing, duress, coercion, control or
undue influence, extortion or commercial bribery, breach of an implied covenant
or duty of good faith and fair dealing, material misrepresentation or omission,
overreaching, unconscionability, conflict of interest, bad faith, malpractice,
disparate bargaining position, detrimental reliance, promissory estoppel,
estoppel by deed, waiver, laches, or any other equitable theory, equitable
subordination, breach of fiduciary duty or any other duty, or tortious
inducement to commit such breach, tortious interference with contract or
prospective business relations, negligent performance of contractual
obligations, or other theories of negligence, negligent or intentional
infliction of emotional distress, slander, libel, other defamation, fraudulent
transfer, conversion, trespass to (or clouding the title of) property, usury,
violations of the Racketeer Influenced and Corrupt Organizations Act, deceptive
trade practices, conspiracy, or any theory of liability as partners or joint
venturers, that any Releasing Party may have as of the date hereof against any
Released Party with respect to the Lending Relationship.

         F. "Released Party" shall mean each of the Agent, the Lenders and
their respective predecessors, successors, assigns, directors, officers,
partners, employees, agents, attorneys, principals and Affiliates and all other
Persons liable or who might be claimed to be liable on their behalf
(collectively, the "Released Parties").

         G. "Releasing Party" shall mean each of the Borrower and the
Guarantors and their respective predecessors, successors, assigns, directors,
officers, partners, employees, agents, attorneys, principals, Affiliates and
all other Persons who might have a claim against any Released Party
(collectively, the "Releasing Parties").



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         Section 2. Amendments to Credit Agreement. The Credit Agreement is
amended hereby as follows:

         A. Section 1.02 is amended hereby:

                  (i) by deleting the definition of the term "Aggregate Maximum
Credit Amounts" in its entirety and substituting the following therefor:

                  "'Aggregate Maximum Credit Amounts' at any time shall equal
         the sum of the Maximum Credit Amounts of the Lenders ($65,000,000), as
         the same may be reduced pursuant to Section 2.03(b) and Section
         2.07(d).";

                  (ii) by deleting the definition of the term "Applicable
Margin" in its entirety and substituting the following therefor:

                  "'Applicable Margin' shall mean (i) 2% with respect to Base
         Rate Loans and (ii) 3% with respect to Eurodollar Loans.";

                  (iii) by deleting the reference "and to participate in the
Letters of Credit as provided in Section 2.01(b)" in the definition of the term
"Commitment";

                  (iv) by deleting the reference "January 31, 1999" in the
definition of the term "First Borrowing Base Determination Date" and
substituting therefor the reference "June 1, 1999";

                  (v) by inserting in the definition of the term "Guaranty
Agreements" after the reference to "Brigham Holdings II, LLC", the reference
"Sooner Production LLC";

                  (vi) by deleting all text after the word "Loans" in the
definition of the term "Initial Funding" and inserting a period after the word
"Loans";

                  (vii) by deleting the first paragraph of the definition of
the term "Interest Period" in its entirety and substituting therefor the
following new definition:

                  "'Interest Period' shall mean, with respect to (i) any
         Eurodollar Loan made prior to the First Borrowing Base Determination
         Date, the period commencing on the date such Eurodollar Loan is made
         and ending on the numerically corresponding day in the first month
         thereafter, and (ii) any Eurodollar Loan made after the First
         Borrowing Base Determination Date, the period commencing on the date
         such Eurodollar Loan is made and ending on the numerically
         corresponding day in the first or third calendar month thereafter, as
         Borrower may select as provided in Section 2.02, 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.";



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                  (viii) by deleting the definition of the term "Issuing Bank"
in its entirety;

                  (ix) by deleting the definition of the term "LC Commitment"
in its entirety;

                  (x) by deleting the definition of the term "LC Exposure" in
its entirety;

                  (xi) by deleting the definition of the term "Letter of Credit
Agreements" in its entirety;

                  (xii) by deleting the definition of the term "Letters of
Credit" in its entirety;

                  (xiii) by deleting the reference "the Letters of Credit, the
Letter of Credit Agreements," and the reference ", or reimbursement obligations
under the Letters of Credit," in the definition of the term "Loan Documents";
and

                  (xiv) by deleting the reference "Section 8.09(a)" in the
definition of the term "Mortgage" and substituting the reference "Section
8.09(b)" therefor.

         B. Section 2.01 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the reference "and Letters of Credit" in the
section title;

                  (ii) by deleting the reference "together with the LC
Exposure" in subsection (a); and

                  (iii) by deleting the text of subsection (b) in its entirety
and substituting therefor the reference "Intentionally left blank."

         C. Section 2.02 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the reference "and Letters of Credit" in the
section title;

                  (ii) by deleting the reference "All" in the third sentence of
subsection (d) and substituting the following therefor:

                  "So long as the Borrowing Base is equal to or greater than
         the outstanding principal amount of the Loans, all"; and

                  (iii) by deleting the reference "All" in the third sentence
of subsection (e) and substituting the following therefor:

                  "So long as the Borrowing Base is equal to or greater than
         the outstanding principal amount of the Loans, all"; and


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                  (iv) by deleting subsection (g) in its entirety.

         D. Section 2.03 of the Credit Agreement is amended hereby by deleting
the text of subsection (a) in its entirety, and substituting the following
therefor:

                  "The Aggregate Commitments shall at all times be equal to
         $65,000,000 until the First Borrowing Base Determination Date after
         which date the Aggregate Commitments shall be equal to the lesser of
         (i) the Aggregate Maximum Credit Amounts or (ii) the Borrowing Base as
         determined from time to time.".

         E. Section 2.04 of the Credit Agreement is amended hereby by deleting
the title and text of subsection (b) in their entirety and substituting
therefor the reference "Intentionally left blank."

         F. Section 2.05 of the Credit Agreement is amended hereby by deleting
the reference "or to provide funds for disbursements or reimbursements under
Letters of Credit".

         G. Section 2.07 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the reference to "plus the LC Exposure" in
subsection (b);

                  (ii) by deleting the text of subsection (c) in its entirety
and substituting the following therefor:

                  "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 then, within
ninety (90) days (or such shorter period as hereinafter provided) of receipt of
written notice of the redetermined Borrowing Base, the Borrower shall 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 following the first Borrowing Base determination such
required prepayment shall be made on or before thirty (30) days after such
first Borrowing Base determination if the amount of the required payment equals
or exceeds an amount equal to 10% of the redetermined Borrowing Base."; and

                  (iii) by inserting the following reference before the last
sentence of subsection (d):

                  "Prior to the initial Borrowing Base determination, all
prepayments on the Loans shall reduce the Maximum Credit Amounts pro tanto;
provided that immediately following any such prepayment the Maximum Credit
Amounts shall be automatically reinstated pro tanto in an aggregate amount
equal to the lesser of (i) $5,000,000 and (ii) the amount of such prepayment."



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         H. Section 2.08 of the Credit Agreement is amended hereby by as
follows:


                  (i) by deleting the reference "or any LC Exposure" in
subsection (a);

                  (ii) by deleting the text of subsection (c) in its entirety
and substituting the following therefor:

         "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. No Property of the Borrower subject
         to the New Mortgage nor any production or income therefrom shall be
         included in the Borrowing Base until such time as an amendment or
         supplement to the New Mortgage in form satisfactory to the Agent is
         filed of record, which shall contain with respect to such Property
         such representations, warranties and covenants as to title, defense of
         title, revenue and cost bearing interest, rentals paid and leases in
         effect, and such other provisions, as the Agent may request."

         I. Section 2.09 of the Credit Agreement is amended hereby by deleting
the title and text of such section in its entirety and substituting therefor
the reference "Intentionally left blank."

         J. Section 2.10 of the Credit Agreement is amended hereby by deleting
the title and text of such section in its entirety and substituting therefor
the reference "Intentionally left blank."

         K. Section 3.02 of the Credit Agreement is amended hereby by deleting
the paragraph beginning "Accrued interest on Base Rate Loans" in its entirety
and substituting the following therefor:

                  "Accrued interest on Base Rate Loans shall be payable on the
         last day of each calendar month, 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 one month
         at one-month intervals following the first day of each 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)."

         L. Section 4.02 of the Credit Agreement is amended hereby as follows:

                  (i) by inserting the word "and" before the reference "(iii)";
and


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                  (ii) by deleting the reference "and (iv) each reimbursement
by the Borrower of disbursements under Letters of Credit shall be made for the
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".

         M. Section 4.04 of the Credit Agreement is amended hereby by deleting
the reference "or a payment under a Letter of Credit to be made by it
hereunder".

         N. Section 4.05 of the Credit Agreement is amended hereby by deleting
the following references in subsection (b):

                  (i) "(or reimbursement as to any Letter of Credit)";

                  (ii) "(or reimbursement)";

                  (iii) "(or participants in Letters of Credit)";

                  (iv) "(or reimbursements of Letters of Credit)"; and

                  (v) "(or Letters of Credit)".

         O. Section 5.01 of the Credit Agreement is amended hereby by deleting
all references to "Letters of Credit" in subsections (a), (c) and (d).

         P. Section 5.06 of the Credit Agreement is amended hereby by deleting
the reference "and participation interests in Letters of Credit (if any)" in
subsection (d).

         Q. Section 6.02 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the reference "and Letters of Credit" in the
section title;

                  (ii) by deleting the reference "and to issue, renew, extend
or reissue Letters of Credit for the account of the Borrower" in the
introductory paragraph of such section; and

                  (iii) by deleting all references "or issuance, renewal,
extension or reissuance of a Letter of Credit" in subsection (c).

         R. The introductory language to Article VII of the Credit Agreement is
amended hereby by deleting the reference "and issuance, renewal, extension or
reissuance of a Letter of Credit".

         S. Section 8.01 of the Credit Agreement is amended hereby as follows:

                  (i) by inserting the following new subsection (c):



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                  "(c) Monthly Financial Statements. As soon as available and
         in any event within thirty (30) days after the end of each calendar
         month that is not also the end of one of Brigham Exploration's first
         three fiscal quarterly periods or of Brigham Exploration's fiscal
         year, consolidated statements of income and changes in financial
         position 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
         balance sheets as at the end of such period and, beginning March 31,
         2000, statements 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 such 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).";

                  (ii) by relettering the existing subsections (c) through (i)
as subsections (d) through (j);

                  (iii) by deleting in subsection (i), as relettered by (ii)
above, the reference "Concurrent with the First Reserve Report and each January
1 Reserve Report thereafter" and substituting therefor the reference "On or
before January 31 of each year"; and

                  (iv) by inserting after the reference "paragraph (a) or (b)"
in the final paragraph of Section 8.01 of the reference "or (c)".

         T. Section 8.07 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the text of subsection (a) in its entirety
     and substituting therefor the reference "Intentionally left blank"; and

                  (ii) by deleting the reference "January 31, 1999 " in the
     first sentence of subsection (b) and substituting therefor the reference 
     "June 1, 1999"; and;

                  (ii) by deleting each reference to "January 1" in subsection
     (b) and substituting therefor the reference "January 31".

         U. Section 8.09 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the text of subsection (a) in its entirety
and substituting the following therefor:

                  "The Borrower will grant and will cause each of its
         Subsidiaries to grant to the Agent as security for the Indebtedness a
         perfected Lien on the Borrower's or such Subsidiary's interest in any
         Oil and Gas Properties 


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         acquired after the date hereof at the cash acquisition cost to the
         Borrower or such Subsidiary equal to or exceeding $1,000,000, 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 New Mortgage (subject to such changes as are necessary as
         a result of, to reflect and/or to account for changes in applicable
         law) and in sufficient executed (and acknowledged where necessary or
         appropriate) counterparts for recording purposes.";

                  (ii) by inserting the following new subsection (b):

                  "(b) The Borrower will grant and will cause each of its
         Subsidiaries to grant to the Agent as security for the Indebtedness a
         first-priority Lien interest (subject only to Excepted Liens and the
         matters set forth on Schedule 7.10 hereto) on the Borrower's or such
         Subsidiary's interest in any Oil and Gas Properties identified after
         the Closing Date as containing proved Hydrocarbon reserves, 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 (subject to such changes as are necessary as a
         result of, to reflect and/or to account for changes in applicable law)
         and in sufficient executed (and acknowledged where necessary or
         appropriate) counterparts for recording purposes.";

                  (iii) by relettering subsections (b) and (c) as subsections
(c) and (d);

                  (iv) by deleting in subsection (c), as relettered by (iii)
above, the reference "Section 8.09(a)" and substituting therefor the reference
"Section 8.09(b)";

                  (v) by deleting the reference "80%" in subsection (c) (as
relettered by (iii) above) and substituting therefor the reference "90%"; and

                  (vi) by inserting after the reference "Loan Document in any
state" in subsection (d), as relettered by (iii) above, the following
reference:

                  "other than the New Mortgage and any other mortgage filed
         pursuant to subsection (a) of this Section 8.09 or any other mortgage
         substantially in the form of the New Mortgage."

         V. Section 9.01 of the Credit Agreement is amended hereby by deleting
the text of subsection (h) in its entirety and substituting the following
therefor:

                  "Debt of the Borrower described on Schedule 9.01(h) and such
         other Debt of the Borrower related to the acquisition of software and
         licensing rights related thereto that does not exceed $100,000 at any
         one time outstanding."



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         W. Section 9.13 of the Credit Agreement is amended hereby by deleting
the reference "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".

         X. Section 9.16 of the Credit Agreement is amended hereby as follows:

                  (i) by inserting a period after the reference "investment in
a Subsidiary"; and

                  (ii) by deleting the reference ", unless such Subsidiary is
or becomes a Guarantor and provided further, that all" and substituting
therefor the reference "All".

         Y. Section 10.01 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting in subsection (a) the reference ", or any
reimbursement obligation for a disbursement made under any Letter of Credit";
and

                  (ii) by deleting subsection (k) it its entirety and
relettering subsections (l) through (o) as subsections (k) through (n).

         Z. Section 10.02 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting in subsections (a) and (b) the reference
"(including without limitation the payment of cash collateral to secure the LC
Exposure as provided in Section 2.10(b) hereof)"; and

                  (ii) by deleting in subsection (c) the reference "fifth to
serve as cash collateral to be held by the Agent to secure the LC Exposure;".

         AA. Section 11.03 of the Credit Agreement is amended hereby by
deleting the reference "or failure to reimburse for Letter of Credit drawings".

         BB. Section 11.04 of the Credit Agreement is amended hereby by
deleting the reference "and its participation in the issuance of Letters of
Credit".

         CC. Section 12.03 of the Credit Agreement is amended hereby as
follows:

                  (i) by deleting the reference "OR LETTERS OF CREDIT" in
subsection (b); and

                  (ii) by deleting the reference "THE ISSUANCE, EXECUTION AND
DELIVERY OR TRANSFER OF OR PAYMENT OR FAILURE TO PAY UNDER ANY LETTER OF
CREDIT," in subsection (b).

         DD. Section 12.06 of the Credit Agreement is amended hereby as
follows:


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                  (i) by deleting the reference "or any Letters of Credit" in
subsection (a);

                  (ii) by deleting the first three sentences of subsection (b)
in their entirety and substituting the following therefor:

                  "Any Lender may sell, assign, transfer or negotiate to one or
         more other lenders, commercial banks, insurance companies, other
         financial institutions or any other Person all or any portion of its
         rights and obligations hereunder, and acceptance of such assignment by
         any assignee shall constitute the agreement of such assignee to be
         bound by the terms of this Agreement applicable to the assigning
         Lender. Promptly after receiving evidence of an assignment under this
         Section 12.06(b), the Agent shall send a notice of such assignment to
         the Borrower. Upon receipt of such notice and of the Notes that 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 interests.";

                  (iii) by deleting the reference "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)" in subsection (c);

                  (iv) by deleting all references "or Letters of Credit" in
subsection (c);

                  (v) by deleting the reference "to which the Borrower has
consented (such consent not to be unreasonably withheld)" in subsection (d);
and

                  (vi) by deleting the last sentence of subsection (d) in its
entirety.

         EE. the Credit Agreement is amended hereby by deleting all references
to "the Issuing Bank" in:

                  (i) the definition of the term "Indebtedness";

                  (ii) subsections (a) and (c) of Section 4.06; and

                  (iii) Section 11.05.

         FF. the Credit Agreement is amended hereby by adding Schedule 9.01(h)
- Certain Agreements thereto.

         Section 3. Covenants. The Borrower or Brigham Exploration, as the case
may be, covenants and agrees that during the period from February 1, 1999
through and including June 1, 1999:



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         A. Brigham Exploration shall deliver weekly cash budgets reasonably
satisfactory to the Agent in the form attached hereto as Exhibit B, and weekly
cash flow statements reasonably satisfactory to the Agent based on such form,
with variance analysis to budget (including accounts receivables and accounts
payables reporting) not later than the Friday following the week to which such
budgets and statements relate.

         B. The Borrower shall not spud any wells or conduct any other drilling
operations (other than routine workovers normally expensed in accordance with
past practice) without the prior written consent of the Agent and the Lenders,
and shall not use any amounts advanced by the Lenders under the Credit
Agreement to acquire acreage, leases or seismic data or to pay any drilling
costs or expenses other than for wells for which drilling had commenced on or
before January 1, 1999; provided that the Borrower may use the Escrow Cash (as
defined in the Duke Consent Letter) to spud, drill, complete, operate and
maintain wells contemplated thereby; provided further that, notwithstanding the
foregoing, the Borrower may incur up to $300,000, in the aggregate, in
discretionary new commitments during the period from the date hereof through
and including June 1, 1999 to acquire leases and seismic data (or licenses
thereto) if, and only if, the Borrower shall grant the Agent, for the benefit
of the Lenders, a perfected Lien on its interest in any new leases acquired
pursuant to this proviso within thirty (30) days or, upon request by the Agent,
within fifteen (15) days, of any such acquisition under a form of mortgage
substantially identical to that of the New Mortgage.

         C. The Borrower shall prepay the Loans in an amount equal to the cash
proceeds of sale of any equity or equity derivative securities and the proceeds
of any asset sales requiring the consent of the Agent under the Credit
Agreement as amended hereby; provided however nothing herein shall be deemed to
constitute a consent by the Agent or any Lender to any such asset sale.

         D. The Borrower shall use all amounts, other than the Escrow Cash,
received by it in connection with the Duke Transaction as working capital.

         E. The Borrower shall provide to the Agent from time to time upon
request by the Agent the certificate of a Responsible Officer of the Borrower
stating that, except as disclosed in a schedule thereto, the Borrower has not
received written notice that any mechanics' liens have been filed or will be
filed on the Mortgaged Properties; provided that mere receipt of an invoice for
services rendered shall not constitute written notice that a mechanics' lien
will be filed.

         F. The Borrower shall cause its Subsidiary, DND Oil & Gas, LLP to
transfer all assets held by it to the Borrower and, thereafter, to dissolve on
or before June 1, 1999.

         G. The Borrower will not, and will not allow any of its Subsidiaries
to, (i) transfer any assets to Quest Resources LLC or (ii) make any investments
in or loans or advances to Quest Resources LLC.

         Section 4. Conditions Precedent. This Amendment shall become binding
upon receipt by the Agent of the following documents and satisfaction of the



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other conditions provided in this Section 4, each of which must be satisfactory
to the Agent in form and substance:

         A. counterparts of this Amendment executed by the Borrower, the Agent
and the Lenders;

         B. counterparts of the New Mortgage executed by the Borrower;

         C. evidence that the New Mortgage and the related UCC-1 financing
statements have been filed in all jurisdictions necessary to perfect and
protect the security interests, assignments and Liens created thereby;

         D. certificates of the Secretary or an Assistant Secretary of the
Borrower and each of the Guarantors setting forth for each of them (i) the
resolutions of its board of directors or managers (or if such Guarantor is a
partnership, resolutions of the general partner of such partnership), as
applicable, with respect to the authorization to execute and deliver this
Amendment and consummate the transactions contemplated hereby; (ii) the
Responsible Officer of such entity authorized to sign this Amendment, and (iii)
the signature of such authorized Responsible Officer of such entity;

         E. a monthly cash budget for 1999 of Brigham Exploration and its
Subsidiaries, which shall include projected revenues, expenses and capital
expenditures;

         F. a Third Amendment to Guaranty Agreement executed by Brigham
Exploration Company;

         G. a First Amendment to Security Agreement executed by the Borrower in
favor of the Agent granting, among other things, a first priority security
interest in all of the Borrower's right, title and interest in its ownership
interests in Quest Resources LLC, and evidence that all other actions necessary
or, in the opinion of the Agent, desirable to perfect and protect the security
interests and Liens granted thereby have been taken;

         H. a First Amendment to Security Agreement executed by Brigham, Inc.
in favor of the Agent granting, among other things, a first priority security
interest in all of Brigham, Inc.'s right, title and interest in its ownership
interests in Sooner Production LLC and Quest Resources LLC, and evidence that
all other actions necessary or, in the opinion of the Agent, desirable to
perfect and protect the security interests and Liens granted thereby have been
taken;

         I. a First Amendment to Intercreditor and Subordination Agreement
executed by Brigham Exploration Company, Enron Capital & Trade Resources Corp.
and Joint Energy Development Investments II Limited Partnership, individually
and as agent for the subordinated Lender as defined therein;

         J. a Consent and Acknowledgement executed by each of the Guarantors;

         K. an opinion of counsel to Borrower substantially in the form
attached hereto as Exhibit C;



                                      13
<PAGE>   14

         L. evidence that Brigham Exploration has obtained the consent and
agreement of the holders of the Notes (as defined in the Indenture) to convert
all interest payments due under such Notes in 1999 to in kind payments as
provided in Section 1X. 2(2) of the Indenture;

         M. payment to the Agent for the ratable benefit of the Lenders of all
accrued and unpaid Interest outstanding under the Credit Agreement and the
Notes;

         N. payment of a $50,000 installment of the Amendment Fee in accordance
with Section 8.A(i) hereof;

         O. payment of the expenses of the Agent and the Lenders in accordance
with Section 8.B hereof; and

         P. such other documents as Agent or its counsel may reasonably
request.

         Section 5. Representations and Warranties.

         A. Except as provided in subsection (iii) of this Section 5.A., the
Borrower hereby reaffirms that, as of the date of this Amendment, the
representations and warranties made by the Borrower and Brigham Exploration in
the Credit Agreement are true and correct as though made on and as of the date
hereof, and further, the Borrower represents that,

                  (i) as of the date hereof, no Default or Material Adverse
Effect has occurred and is continuing except as previously disclosed to the
Agent in writing;

                  (ii) the execution, delivery and performance by the Borrower
or the Guarantors of this Amendment and the other Loan Documents and all
instruments and documents to be delivered by the Borrower or the Guarantors, to
the extent a party thereto, hereunder and thereunder and the creation of all
Liens provided for herein and therein: (a) are within the Borrower's or such
Guarantor's corporate power; (b) have been duly authorized by all necessary or
proper corporate action, including the consent of stockholders, members and/or
partners therein or thereof; (c) are not in contravention of any provision of
the Borrower's or such Guarantor's certificate of incorporation, bylaws or
similar organizational and/or governing documents; (d) will not violate (1) any
law or regulation or (2) any order or decree of any court or governmental
instrumentality; (e) will not conflict with or result in the breach or
termination of, constitute a default under or accelerate any performance
required by, any indenture, mortgage, deed of trust, lease, agreement or other
instrument to which the Borrower or any of the Guarantors is a party or by
which the Borrower or any of the Guarantors or any of their respective property
is bound; (f) will not result in the creation or imposition of any Lien upon
any of the property of the Borrower or the Guarantors other than those in favor
of the Agent pursuant to the terms of this Amendment and the other Loan
Documents to be delivered in connection herewith; and (g) do not require the
consent or approval of any governmental body, agency, authority or any other
Person that has not been duly obtained, made or complied with prior to the date
hereof. At or prior to the date hereof, each of this Amendment and the other
Loan Documents to be delivered in connection



                                      14
<PAGE>   15

herewith shall have been duly executed and delivered for the benefit of or on
behalf of the Borrower or the Guarantors, in each case to the extent a party
thereto, and each shall then constitute a legal, valid and binding obligation
of the Borrower or such Guarantor, enforceable against it in accordance with
its terms; and

                  (iii) notwithstanding the foregoing, the representations and
warranties contained in the last sentence of Section 7.10(a) of the Credit
Agreement (and not those contained in the first two sentences) are reaffirmed
with respect to the Mortgaged Property covered by or described in the New
Mortgage.

         B. Each of the Borrower and the Guarantors further represents and
warrants, for itself only that he or it (i) is executing this Amendment after
consultation with counsel of his or its own choosing, (ii) has read and
understands the release granted by Section 6 hereof, (iii) desires to execute
this Amendment and (iv) has the requisite authority to enter into and be bound
by this Amendment, including the release granted by Section 6 hereof.

         Section 6. Release.

         A. Each of the Releasing Parties desires and intends fully to
compromise, release and settle any and all of the Released Claims; and each of
the Releasing Parties hereby covenants, warrants and represents unto each of
the Released Parties that such Releasing Party does hereby FOREVER RELEASE,
ACQUIT, WAIVE AND DISCHARGE each of the Released Parties of and from the
Released Claims and each of the Releasing Parties hereby declares the same
FOREVER RELEASED, ACQUITTED, WAIVED, SETTLED AND DISCHARGED. This release is
effective without regard to whether (i) such Released Claims are known or
unknown, (ii) damages arising out of such Released Claims have yet accrued,
(iii) such Released Claims arose collaterally, directly, derivatively, or
otherwise between the parties hereto or (iv) an ordinary person in the same or
similar circumstances would or would not, through the exercise of due care,
have discovered such claims by the date of this Amendment. In connection with
the foregoing release:

         B. Borrower and each of the Guarantors represents and warrants that it
has the full power and authority to perform the release granted in this Section
6 and that it has not in any manner made any assignment of any Released Claim
to any third party.

         C. The release granted in this Section 6 will be effective upon
execution of this Amendment by all of the parties hereto.

         D. Each party executing this Amendment understands and agrees that the
release granted in this Section 6 is a full, final and complete release of the
Released Claims and that such release may be pleaded as an absolute and final
bar to any or all suits which may hereafter be filed or prosecuted by any one
or more of the Releasing Parties or anyone claiming by, through or under any
one or more of the Releasing Parties in respect of any of the matters released
hereby, and that no recovery on account of the Released Claims may hereafter be
had from any of the Released Parties; and that the consideration given for such
release is not an admission of liability or fault on the part of 



                                      15
<PAGE>   16

any of the Released Parties (it being the express intent of the parties hereto
to obtain peace of mind and avoid the expense and uncertainty of potential
litigation), and that none of the Releasing Parties or those claiming by,
through or under any of them will ever claim that it is.

         E. The parties hereto acknowledge that the release granted by this
Section 6 does not have any effect with respect to relationships between the
Borrower and each of the Guarantors and the Lenders and the Agent other than in
connection with the Lending Relationship.

         Section 7. Events of Default and Remedies.

         A. The occurrence of any one or more of the following events
(regardless of the reason therefor) shall constitute an "Event of Default"
hereunder:

                  (i) The Borrower shall fail to deliver within 30 days after
closing a First Amendment to Security Agreement executed by Brigham Holdings I,
LLC in favor of the Agent, and evidence that all other actions necessary or, in
the opinion of the Agent, desirable to perfect and protect the security
interests and Liens granted thereby have been taken;

                  (ii) The Borrower shall fail to deliver within 30 days after
closing a First Amendment to Security Agreement executed by Brigham Holdings
II, LLC in favor of the Agent, and evidence that all other actions necessary
or, in the opinion of the Agent, desirable to perfect and protect the security
interests and Liens granted thereby have been taken; and

                  (iii) The Borrower shall fail to deliver within 30 days after
closing a legal opinion of Borrower's counsel in form reasonably satisfactory
to the Agent.

         B. The occurrence and continuation of an Event of Default hereunder
shall constitute an Event of Default under the Credit Agreement as amended
hereby.

         Section 8. Payment of Fees and Expenses; Form of Payment.

         A. The Borrower agrees to pay to the Agent for the ratable benefit of
the Lenders a fee (the "Amendment Fee") in the amount of $500,000 payable by
the Borrower as follows:

                  (i) a $50,000 installment shall be due and payable on the
date hereof; and

                  (ii) a $50,000 installment shall be due with each monthly
interest payment required to be made under Section 3.02 of the Credit Agreement
as amended hereby; provided that the unpaid balance of the Amendment Fee shall
be payable on the earlier of (a) the date on which the Bank of Montreal ceases
to be the Agent or (b) the cancellation of the Commitments and repayment in
full by the Borrower of the Indebtedness.



                                      16
<PAGE>   17

         B. The Borrower agrees, whether or not the transactions contemplated
hereby are consummated, to pay all reasonable expenses of the Agent and the
Lenders (including, without limitation, all reasonable fees and disbursements
of counsel and other outside consultants for the Agent and/or the Lenders) in
connection with the negotiation, investigation, preparation, execution and
delivery of, recording and filing of, preservation of rights under and
enforcement of this Amendment and the other Loan Documents to be delivered in
connection herewith.

         C. All payments to be made by the Borrower under this Amendment shall
be made in Dollars, in immediately available funds, to the Agent at such
account as the Agent shall specify by notice in accordance with Section 4.01 of
the Credit Agreement.

         Section 9. 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 or the Agent 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 10. Non-Reliance on Agent and Other Lenders. Each Lender
acknowledges and agrees that it has, independently and without reliance on the
Agent or any other Lender, and based on such documents and information as it
has deemed appropriate, made its own decision to enter into this Amendment, 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 Amendment or the Credit Agreement. The
Agent shall not be required to keep itself informed as to the performance or
observance by the Borrower of this Amendment or any other Loan Document or any
other document referred to or provided for herein or therein 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 and under the Credit Agreement, 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
Weil, Gotshal & Manges LLP is acting in this transaction as special counsel to
the Agent only. Each Lender will consult with its own legal counsel to the
extent that it deems necessary in connection with this Amendment and the
matters contemplated herein.

         Section 11. 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.



                                      17
<PAGE>   18

         Section 12. 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 13. 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.



                                      18
<PAGE>   19

         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: /s/ Karen E. Lynch
                                        ------------------------
                                    Name: Karen E. Lynch
                                         -----------------------
                                    Title: Vice President
                                          ----------------------

AGENT:                              BANK OF MONTREAL



                                    By: /s/ Thomas E. McGraw
                                        ------------------------
                                          Thomas E. McGraw
                                          Director


LENDER:                             BANK OF MONTREAL



                                    By: /s/ Thomas E. McGraw
                                        ------------------------
                                          Thomas E. McGraw
                                          Director



                                      19
<PAGE>   20


LENDER:                             SOCIETE GENERALE, Southwest Agency



                                    By: /s/ Paul E. Cornell
                                        ------------------------
                                    Name: Paul E. Cornell  
                                         -----------------------
                                    Title: Managing Director                    
                                          ----------------------



                                      20