ANCILLARY AGREEMENT

                                    RECITALS:

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

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

                                   AGREEMENT:

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

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

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

                                 MISCELLANEOUS:

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




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

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

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


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


                                    BRIGHAM OIL & GAS, L.P.

                                    By:   Brigham, Inc., as General Partner

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