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                                                                    EXHIBIT 10.4


                              CONSULTING AGREEMENT




         THIS CONSULTING AGREEMENT (this "Agreement") is made as of May 1, 1997,
by and between Brigham Oil & Gas, L.P., a Delaware limited partnership (the
"Company") and Harold D. Carter ("Consultant").

                              W I T N E S S E T H:

         WHEREAS, the Company previously had entered into a consulting agreement
with Consultant which expired for all purposes on May 1, 1997; and

         WHEREAS, the Company desires to enter into a separate agreement to
retain the services of Consultant on a current basis, and Consultant desires to
perform such services for the Company, subject to and upon the terms and
conditions contained herein;

         NOW, THEREFORE, in consideration of the mutual promises contained
herein, the parties, intending to be legally bound, agree as follows:

         1. Employment and Duties. The Company agrees to retain the services of
Consultant to perform such consulting and advisory services regarding the
operations of the Company as the Company shall request from time to time during
the term of this Agreement. Consultant shall make himself available to consult
with the Chief Executive Officer and other officers of the Company at reasonable
times, concerning matters pertaining to the acquisition, exploration,
development and operation of Company properties, the overall business plan,
operating and capital budgets and other fiscal policy issues of the Company,
employee issues, and, in general, any issue concerning the business affairs of
the Company.

         2. Amount of Service. It is understood that Consultant's time
commitment to the Company may vary over time consistent with the needs of the
Company and Consultant agrees to devote such time and attention to the
performance and fulfillment of such duties, functions and responsibilities as is
necessary to fulfill such duties. Notwithstanding the foregoing, it is
specifically understood and agreed that Consultant may act as a consultant or
perform services for other parties other than the Company and therefore will
only be required to devote a portion of his time to his services under this
Agreement, which will not exceed 50% of his normal working time without his
consent. Consultant shall be deemed an independent contractor for all purposes.

         3. Compensation. The Company shall pay Consultant for his services
under this Agreement a consulting fee of $7,200 per month during the term of
this Agreement. All federal withholding and other employment and income related
taxes shall be the responsibility of Consultant.

         4. Business Expenses. Consultant shall be reimbursed by the Company for
any out of pocket expenses reasonably paid or incurred by him in connection with
the performance of his duties hereunder upon presentation of expense statements
or vouchers or such other supporting information reasonably evidencing such
expenses.

         5. Office Expenses. Consultant shall be solely responsible for any
office expenses and overhead incurred by Consultant in the performance of his
duties hereunder; provided, however, that during thee term of this Agreement the
Company shall pay Associated Energy Managers directly $1,000 per month to offset
some of Consultant's office expenses and/or overhead incurred in connection with
services under this Agreement. As partial consideration for the $1,000 per month
payment to Associated Energy Managers 


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as aforesaid, the Company and its employees shall have reasonable limited access
to Consultant's office conference room and phones for purposes of conducting the
Company's business and affairs while traveling in Dallas, Texas.

         6. Term. The term of this Agreement shall commence on the date hereof
and terminate on December 31, 1998.

         7. Termination. This Agreement shall terminate upon the first to occur
of (i) the expiration of the term hereof, (ii) the death, disability or other
incapacity of Consultant, or (iii) the written consent of both parties to this
Agreement. For purposes of this Agreement, the "disability or incapacity" of
Consultant shall occur if, as a result of Consultant's incapacity due to
physical or mental illness, Consultant shall have been absent from his services
hereunder on a continuous basis for the entire period of six consecutive months,
and within thirty (30) days after written notice of termination is given (which
may occur before or after the end of such six-month period) shall not have
returned to performing his services hereunder.

         8. Limited Liability. With regard to the services to be performed by
Consultant pursuant to the terms of this Agreement, Consultant shall not be
liable to the Company, or to anyone who may claim any right due to his
relationship with the Company, for any acts or omissions in the performance of
said services on the part of Consultant or on the part of the agents or
employees of Consultant, except when said acts or omissions of Consultant are
due to his willful misconduct or gross negligence. The Company shall hold
Consultant free and harmless from any obligations, costs, claims, judgments,
attorneys' fees and attachments arising from or growing out of the services
rendered to the Company pursuant to the terms of this Agreement or in any way
connected with the rendering of said services, except when the same shall arise
due to the willful misconduct or gross negligence of Consultant, and Consultant
is adjudged to be guilty of willful misconduct or gross negligence by a court of
competent jurisdiction.

         9. Confidentiality. Consultant will maintain the confidentiality of,
and will not disclose without the Company's express consent, any and all
proprietary or confidential information of the Company. The provisions of this
paragraph will be deemed to encompass any and all confidential or proprietary
information of the Company that was obtained by Consultant since the
commencement of Consultant's employment with the Company. This paragraph will
continue after, and will not be deemed to be extinguished or terminated by, the
termination of this Agreement or of Consultant's employment by the Company. For
purposes of this paragraph "proprietary or confidential information" of the
Company does not include (a) information that is or becomes generally available
to the public other than as a result of disclosure by the Consultant in breach
of this Agreement, (b) information that was or is available to Consultant on a
non-confidential basis, (c) information that is or was conceived, created or
independently developed by Consultant, or (d) information that is disclosed by
Consultant to others on behalf of the Company or to further the business
opportunities or best interests of the Company.

         10. Miscellaneous. (a) Notices. Any notice or communication required or
permitted hereunder shall be given in writing and shall be (i) sent by first
class registered or certified United States mail, postage prepaid, (ii) sent by
overnight or express mail or expedited delivery service, (iii) delivered by hand
or (iv) transmitted by wire, telex or telefax, addressed as follows:


         If to Consultant:                  Harold D. Carter
                                            5949 Sherry Lane, Suite 620
                                            Dallas, Texas  75225
                                            Telephone No.:  (214) 692-7785
                                            Fax No.:  (214) 692-7820

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         If to the Company:                 Brigham Oil & Gas, L.P.
                                            6300 Bridge Point Parkway
                                            Bldg.2, Suite 500
                                            Austin, Texas  78730
                                            Attn:  Ben M. Brigham
                                            Telephone No.:  (512) 427-3300
                                            Fax No.:  (512) 427-3400

or to such other address or to the attention of such other person as hereafter
shall be designated in writing by the applicable party in accordance herewith.
Any such notice or communication shall be deemed to have been given as of the
date of first attempted delivery at the address and in the manner provided
above.

         (b) Successors and Assigns. This Agreement is personal in nature and
neither of the parties hereto shall, without the consent of the other, assign or
transfer this Agreement or any rights or obligations hereunder; provided,
however, that in the event of a merger, consolidation or transfer or sale of all
or substantially all of the assets of the Company, this Agreement shall be
binding upon the successor to the Company's business and assets.

         (c) Interpretation. When the context in which words are used in this
Agreement indicates that such is the intent, words in the singular number shall
include the plural and vice versa.

         (d) Severability. Every provision in this Agreement is intended to be
severable. In the event that any provision of this Agreement shall be held to be
invalid, the same shall not affect in any respect whatsoever the validity of the
remaining provisions of this Agreement.

         (e) Remedies. If any action at law or equity is necessary to enforce or
interpret the terms of this Agreement, the prevailing party shall be entitled to
reasonable attorney's fees, costs and necessary disbursements in addition to any
other relief to which he may be entitled.

         (f) Captions. Any section or paragraph titles or captions contained in
this Agreement are for convenience only and shall not be deemed a part of the
context of this Agreement.

         (g) Entire Agreement. This Agreement contains the entire understanding
and agreement between the parties and supersedes any prior written or oral
agreements between them respecting the subject matter contained herein. There
are no representations, agreements, arrangements or understandings, oral or
written, between and among the parties hereto relating to the subject matter of
this Agreement which are not fully expressed herein.

         (h) No Waiver. The failure of any party to insist upon strict
performance of a covenant hereunder or of any obligation hereunder, irrespective
of the length of time for which such failure continues, shall not be a waiver of
such party's right to demand strict compliance in the future. No consent or
waiver, express or implied, to or of any breach or default in the performance of
any obligation hereunder shall constitute a consent or waiver to or of any other
breach or default in the performance of the same or any obligation hereunder.

         (i) Amendment. This Agreement may be changed, modified or amended only
by an instrument in writing duly executed by all of the parties hereto. Any such
amendment shall be effective as of such date as may be determined by the parties
hereto.


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         (j) Choice of Law. THIS AGREEMENT AND THE RIGHTS AND OBLIGATIONS OF THE
PARTIES HEREUNDER SHALL BE GOVERNED BY TEXAS LAW.

         IN WITNESS WHEREOF, the parties have executed this Agreement or caused
the same to be executed by their duly authorized corporate officers, all as of
the day and year first above written.






"Consultant"
                                            /s/ HAROLD D. CARTER
                                            ------------------------------------
                                            Harold D. Carter





"Company"                                   BRIGHAM OIL & GAS, L.P.
                                            By: Brigham, Inc., its Managing 
                                                  General Partner


                                                   By: /s/ BEN M. BRIGHAM
                                                      --------------------------
                                                      Ben M. Brigham, President

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