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                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

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                                    FORM 8-K

                                 CURRENT REPORT

     Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934

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         Date of Report (Date of earliest event reported): May 10, 2004

                           BRIGHAM EXPLORATION COMPANY
             (Exact name of registrant as specified in its charter)

          Delaware                   000-22433               75-2692967
(State or other jurisdiction        (Commission            (IRS Employer
      of incorporation)             File Number)         Identification No.)

                            6300 Bridgepoint Parkway
                             Building Two, Suite 500
                               Austin, Texas 78730
          (Address, including zip code, of principal executive offices)

       Registrant's telephone number, including area code: (512) 427-3300

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Item 7. Financial Statements and Exhibits.

     (c) Exhibit 99.1 Press release dated May 10, 2004.

Item 12. Regulation FD Disclosure.

      Registrant is furnishing its press release dated May 10, 2004, which
announces the Registrant's financial results for the quarter ended March 31,
2004 and provides its second quarter 2004 forecast. The text of the press
release is furnished as attached hereto as Exhibit 99.1.

                                    SIGNATURE

      Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                           BRIGHAM EXPLORATION COMPANY

Date: May 11, 2004

                                                  By: /s/ Eugene B. Shepherd, Jr
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                                                      Eugene B. Shepherd, Jr.
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                                                      Executive Vice President &
                                                      Chief Financial Officer


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                                INDEX TO EXHIBITS

                Item Number                        Exhibit
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                99.1*                     Press Release dated May 10, 2004