February 17, 2000

by Brigham Exploration Company
February 29th, 2000

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                                                                   EXHIBIT 10.9



                               February 17, 2000


Brigham Oil & Gas, L.P.
6300 Bridge Point Parkway
Building 2, Suite 500
Austin, Texas  78730


         Re:      Certain Fees Pursuant to Credit Agreement Dated as of
                  February 17, 2000, among Brigham Oil & Gas, L.P. (the
                  "Borrower"), Bank of Montreal, as Agent, Shell Capital Inc.
                  ("SCI") and the lenders signatory thereto (the "Credit
                  Agreement")

Ladies/Gentlemen:

         This letter (the "Fee Letter") is written to confirm our mutual
understanding with respect to certain fees in connection with the Credit
Agreement. All capitalized terms not defined herein shall have the meaning
assigned to such terms in the Credit Agreement.

         In further consideration of our agreeing to enter into the facility
evidenced by the Credit Agreement, the Borrower does hereby agree to pay
certain additional fees to SCI for its own account as follows:

         Borrower shall pay the following fees to SCI:

         1.       Engineering  Fee in the amount of $10,000 to be paid on each
                  date of  valuation of RAPRV and each Borrowing Base
                  Redetermination Date.

         2.       If the Target Asset Value of the Borrower, approved by SCI,
                  is less than the amount of outstanding Loans twelve (12)
                  months after the Closing Date, the Borrower shall pay SCI a
                  monthly fee equal to 50 basis points per annum multiplied by
                  the Convertible Amount (as such term is defined in the Equity
                  Conversion Agreement) at that time. Such fee shall accrue
                  beginning twelve (12) months after the Closing Date, shall be
                  payable monthly in arrears, and will cease to accrue upon the
                  Scheduled Asset Valuation Date on which the Target Asset
                  Value, approved by SCI, becomes greater than the amount of
                  outstanding Loans.




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         3.       If the Target Asset Value of the Borrower, approved by SCI,
                  is less than the amount of outstanding Loans eighteen (18)
                  months after the Closing Date, the Borrower shall pay SCI a
                  monthly fee equal to 100 basis points per annum (in
                  replacement of, but not in addition to, the fee described in
                  item 2 above) multiplied by the Convertible Amount (as such
                  term is defined in the Equity Conversion Agreement) at that
                  time. Such fee shall accrue beginning eighteen (18) months
                  after the Closing Date, shall be payable monthly in arrears,
                  and will cease to accrue upon the Scheduled Asset Valuation
                  Date on which the Target Asset Value, approved by SCI,
                  becomes greater than the amount of outstanding Loans.

         Any breach of the terms of items 1, 2 and 3 above shall be an Event of
Default under the Credit Agreement, subject, however, to a ten (10) Business
Day period of grace.

         This Fee Letter is further written to outline Borrower's
representation of its hedging strategy as follows:

         1.       Within five business days of the Closing Date, the Borrower
                  intends to enter into Hedging Agreements that together
                  provide a floor price covering (i) at least 70% of PDP
                  Reserves for no less than twelve (12) months after the
                  Closing Date, (ii) at least 50% of PDP Reserves for no less
                  than eighteen (18) months after the Closing Date and (iii) at
                  least 30% of PDP Reserves for no less than twenty-four (24)
                  months after the Closing Date.

         2.       Ongoing: The Borrower intends to use its best efforts to
                  maintain floor protection at levels in line with those
                  outlined in item (1) above on an on-going basis.

         As with all significant information provided to SCI, the hedging
         strategy outlined by Borrower was relied upon by SCI in making its
         decision to enter into the Credit Agreement.




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         Please evidence your acknowledgment and acceptance of the foregoing by
signing in the space provided below.

                                         SHELL CAPITAL INC.

                                         By:
                                             ----------------------------------
                                         Name:    Robert L. Roberts
                                         Title:   Vice President



ACKNOWLEDGED AND AGREED
this 17 day of February, 2000

BRIGHAM OIL & GAS, L.P.

By:      Brigham, Inc., its General Partner

         By:
             ------------------------------
         Name: Curtis F. Harrell
         Title:   Chief Financial Officer