<PAGE>   1


================================================================================

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 10-Q

             [X] QUARTERLY REPORT UNDER SECTION 13 OR 15 (d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934


                For the quarterly period ended September 30, 1998

                                       OR

              [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                   For the transition period from      to
                                                  -----   -----

                        Commission File Number 000-22433

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

<TABLE>
<CAPTION>
            DELAWARE                                 1311                               75-2692967
<S>                                     <C>                                     <C>    
  (State of other jurisdiction           (Primary Standard Industrial                (I.R.S. Employer
of incorporation or organization)         Classification Code Number)             Identification Number)
</TABLE>

                            6300 BRIDGE POINT PARKWAY
                               BLDG. 2, SUITE 500
                               AUSTIN, TEXAS 78730
                                 (512) 427-3300

 (Name, address, including zip code, and telephone number, including area code,
                  of Registrant's principal executive offices)


     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding twelve months (or such shorter period that the
registrant was required to file such reports) and (2) has been subject to such
filing requirements for the past 90 days. Yes  X  No    .
                                              ---    ---

As of October 31, 1998, 13,306,206 shares of Common Stock, $.01 per share, were
outstanding.


================================================================================



<PAGE>   2



                           BRIGHAM EXPLORATION COMPANY

                                      INDEX


<TABLE>
<CAPTION>
                                                                                               PAGE
PART I.       FINANCIAL INFORMATION:                                                          NUMBER
                                                                                              ------
<S>                                                                                          <C>

Item 1.       Unaudited Condensed Consolidated Financial Statements

              a)   Balance Sheets - December 31, 1997 and
                      September 30, 1998                                                         1

              b)   Statements of Operations - Three and nine months ended
                      September 30, 1997 and 1998                                                2

              c)   Statements of Cash Flows - Nine months ended
                      September 30, 1997 and 1998                                                3

              d)   Statement of Changes in Stockholders' Equity - September 30, 1998             4

              e)   Notes to Condensed Consolidated Financial Statements                          5 - 8

Item 2.       Management's Discussion and Analysis of Results of
                   Operations and Financial Condition                                            9 - 12


PART II.      OTHER INFORMATION:

Item 6.       Exhibits and Reports on Form 8-K                                                   13
</TABLE>


<PAGE>   3


PART I.       FINANCIAL INFORMATION:

Item 1.       Financial Statements

                           BRIGHAM EXPLORATION COMPANY

                             CONDENSED CONSOLIDATED
                                 BALANCE SHEETS
                                 (in thousands)

<TABLE>
<CAPTION>
                                                                                    December 31,      September 30,
                                                                                        1997              1998
                                                                                      ---------         ---------
                                                                                                       (unaudited)
<S>                                                                                   <C>               <C>      
                                     ASSETS
Current assets:
     Cash and cash equivalents                                                        $   1,701         $   1,251
     Accounts receivable                                                                  4,909             8,107
     Prepaid expenses                                                                       280               354
                                                                                      ---------         ---------
         Total current assets                                                             6,890             9,712
                                                                                      ---------         ---------

Natural gas and oil properties, at cost, net                                             84,176           133,558
Other property and equipment, at cost, net                                                1,239             1,782
Drilling advances paid                                                                       78               404
Deferred loan fees                                                                           --             3,333
Other noncurrent assets                                                                      18                12
                                                                                      ---------         ---------
                                                                                      $  92,401         $ 148,801
                                                                                      =========         =========

                      LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
     Accounts payable                                                                 $  11,892         $  13,651
     Accrued drilling costs                                                               2,406             3,203
     Participant advances received                                                          489               926
     Other current liabilities                                                              726             2,373
                                                                                      ---------         ---------
         Total current liabilities                                                       15,513            20,153
                                                                                      ---------         ---------

Notes payable                                                                            32,000            37,000
Senior subordinated notes, net                                                               --            35,574
Deferred income tax liability                                                             1,228               116
Other noncurrent liabilities                                                                507               522

Stockholders' equity:
     Preferred stock, $.01 par value, 10 million shares
         authorized, none issued and outstanding                                             --                --
     Common stock, $.01 par value, 30 million shares
         authorized, 13,306,206 issued and outstanding                                      123               133
     Additional paid-in capital                                                          44,344            58,230
     Unearned stock compensation                                                         (1,340)             (774)
     Retained earnings (accumulated deficit)                                                 26            (2,153)
                                                                                      ---------         ---------
         Total stockholders' equity                                                      43,153            55,436
                                                                                      ---------         ---------
                                                                                      $  92,401         $ 148,801
                                                                                      =========         =========
</TABLE>

   See accompanying notes to the condensed consolidated financial statements.

                                        1


<PAGE>   4

                           BRIGHAM EXPLORATION COMPANY

                             CONDENSED CONSOLIDATED
                            STATEMENTS OF OPERATIONS
                      (in thousands, except per share data)
                                   (unaudited)

<TABLE>
<CAPTION>
                                                               Three Months                          Nine Months
                                                            Ended September 30,                  Ended September 30,
                                                      --------------------------------     --------------------------------
                                                           1997             1998                1997             1998
                                                      -------------     -------------      -------------     ------------- 
<S>                                                   <C>               <C>                <C>               <C>          
Revenues:
     Natural gas and oil sales                        $       2,097     $       4,162      $       5,951     $      11,292
     Workstation revenue                                        133                75                457               322
                                                      -------------     -------------      -------------     ------------- 
                                                              2,230             4,237              6,408            11,614
                                                      -------------     -------------      -------------     ------------- 
Costs and expenses:
     Lease operating                                            317               564                787             1,542
     Production taxes                                           120               255                339               705
     General and administrative                                 995             1,069              2,450             3,362
     Depletion of natural gas and oil properties                713             1,688              2,108             4,472
     Depreciation and amortization                               59               113                231               288
     Amortization of stock compensation                          86                49                201               239
                                                      -------------     -------------      -------------     ------------- 
                                                              2,290             3,738              6,116            10,608
                                                      -------------     -------------      -------------     ------------- 
         Operating income (loss)                                (60)              499                292             1,006
                                                      -------------     -------------      -------------     ------------- 

Other income (expense):
     Interest income                                             41                37                122               114
     Interest expense                                           (87)           (1,979)              (459)           (4,411)
     Interest expense - related party                             -                 -               (173)                -
                                                      -------------     -------------      -------------     ------------- 
                                                                (46)           (1,942)              (510)           (4,297)
                                                      -------------     -------------      -------------     ------------- 

Net loss before income taxes                                   (106)           (1,443)              (218)           (3,291)
Income tax (expense) benefit                                     10               491             (4,803)            1,112
                                                      -------------     -------------      -------------     ------------- 
     Net loss                                         $         (96)    $        (952)     $      (5,021)    $      (2,179)
                                                      =============     =============      =============     ============= 

Net loss per share:
     Basic / Diluted                                  $       (0.01)    $       (0.08)     $       (0.47)    $       (0.18)

Weighted average common shares outstanding:
     Basic / Diluted                                         12,254            12,677             10,686            12,396
</TABLE>






   See accompanying notes to the condensed consolidated financial statements.

                                        2


<PAGE>   5

                           BRIGHAM EXPLORATION COMPANY

                             CONDENSED CONSOLIDATED
                            STATEMENTS OF CASH FLOWS
                                 (in thousands)
                                   (unaudited)

<TABLE>
<CAPTION>
                                                                        Nine              Nine
                                                                    Months Ended      Months Ended
                                                                    September 30,     September 30,
                                                                        1997              1998
                                                                    -------------     -------------
<S>                                                                   <C>              <C>      
Cash flows from operating activities:
     Net loss                                                         $ (5,021)        $ (2,179)
     Adjustments to reconcile net loss to cash
      provided by operating activities:
         Depletion of natural gas and oil properties                     2,108            4,472
         Depreciation and amortization                                     231              288
         Amortization of stock compensation                                201              239
         Amortization of deferred loan fees                                 --              463
         Amortization of discount on senior subordinated notes              --               74
         Changes in deferred income tax liability                        4,803           (1,112)
         Changes in working capital and other items:
            Increase in accounts receivable                             (1,042)          (3,198)
            Increase in prepaid expenses                                  (250)             (74)
            Increase (decrease) in accounts payable                       (160)           1,759
            Increase in participant advances received                    2,279              437
            Increase (decrease) in other current liabilities              (125)           1,612
            Other noncurrent assets                                        115                6
            Other noncurrent liabilities                                  (229)             (94)
                                                                      --------         --------
            Net cash provided by operating activities                    2,910            2,693
                                                                      --------         --------

Cash flows from investing activities:
     Additions to natural gas and oil properties                       (22,325)         (52,782)
     Additions to other property and equipment                            (456)            (511)
     (Increase) decrease in drilling advances paid                          35             (326)
                                                                      --------         --------
            Net cash used by investing activities                      (22,746)         (53,619)
                                                                      --------         --------

Cash flows from financing activities:
     Proceeds from issuance of common stock                             23,927            9,448
     Proceeds from issuance of senior subordinated notes                    --           40,000
     Increase in notes payable                                          13,250           83,800
     Repayment of notes payable                                        (13,250)         (78,800)
     Principal payments on capital lease obligations                      (128)            (176)
     Deferred loan fees                                                     --           (3,796)
                                                                      --------         --------
            Net cash provided by financing activities                   23,799           50,476
                                                                      --------         --------

Net increase (decrease) in cash and cash equivalents                     3,963             (450)

Cash and cash equivalents, beginning of period                           1,447            1,701
                                                                      --------         -------- 
Cash and cash equivalents, end of period                              $  5,410         $  1,251
                                                                      ========         ========
</TABLE>


   See accompanying notes to the condensed consolidated financial statements.


                                        3


<PAGE>   6

                           BRIGHAM EXPLORATION COMPANY

                             CONDENSED CONSOLIDATED
                  STATEMENT OF CHANGES IN STOCKHOLDERS' EQUITY
                                 (in thousands)
                                   (unaudited)


<TABLE>
<CAPTION>
                                                                                                      Retained
                                            Common Stock             Additional       Unearned        Earnings/
                                    ---------------------------       Paid-in          Stock           (Accum.
                                      Shares          Amounts         Capital       Compensation       Deficit)           Total
                                    -----------      ----------      ----------     ------------      ----------       ----------
<S>                                  <C>             <C>             <C>             <C>              <C>              <C>       
Balance, December 31, 1997           12,253,574      $      123      $   44,344      $   (1,340)      $       26       $   43,153

     Net loss for the period
         ended Sept. 30, 1998                --              --              --              --           (2,179)          (2,179)
     Issuance of common stock         1,052,632              10          13,938              --               --           13,948
     Amortization of unearned
         stock compensation                  --              --              --             514               --              514
     Stock options forfeited                 --              --             (52)             52               --               --

                                    -----------      ----------      ----------      ----------       ----------       ----------
Balance, September 30, 1998          13,306,206      $      133      $   58,230      $     (774)      $   (2,153)      $   55,436
                                    ===========      ==========      ==========      ==========       ==========       ==========
</TABLE>






   See accompanying notes to the condensed consolidated financial statements.

                                       4

<PAGE>   7

                           BRIGHAM EXPLORATION COMPANY

                             NOTES TO THE CONDENSED
                        CONSOLIDATED FINANCIAL STATEMENTS
                                   (unaudited)


1.   Organization and Nature of Operations

     Brigham Exploration Company (the "Company") is a Delaware corporation
     formed on February 25, 1997 for the purpose of exchanging its common stock
     for the common stock of Brigham, Inc. and the partnership interests of
     Brigham Oil & Gas, L.P. (the "Partnership"). Brigham, Inc. is a Texas
     corporation whose only asset is its ownership interest in the Partnership.
     The Partnership was formed in May 1992 to explore and develop onshore
     domestic natural gas and oil properties using 3-D seismic imaging and other
     advanced technologies. Since its inception, the Partnership has focused its
     exploration and development of natural gas and oil properties in West
     Texas, the Anadarko Basin and the onshore Gulf Coast.

     Pursuant to an exchange agreement dated February 26, 1997 (the "Exchange
     Agreement") and upon the initial filing on February 27, 1997 of a
     registration statement with the Securities and Exchange Commission (the
     "SEC") for the public offering of common stock (the "Offering"), the
     shareholders of Brigham, Inc. transferred all of the outstanding stock of
     Brigham, Inc. to the Company in exchange for 3,859,821 shares of common
     stock of the Company. Pursuant to the Exchange Agreement, the Partnership's
     other general partner and the limited partners also transferred all of
     their partnership interests to the Company in exchange for 3,314,286 shares
     of common stock of the Company. Furthermore, the holders of the
     Partnership's subordinated convertible notes transferred these notes to the
     Company in exchange for 1,754,464 shares of common stock. These
     transactions are referred to as the "Exchange." In completing the Exchange,
     the Company issued 8,928,571 shares of common stock to the stockholders of
     Brigham, Inc., the partners of the Partnership and the holder of the
     Partnership's subordinated notes payable. As a result of the Exchange, the
     Company now owns all the partnership interests in the Partnership.

     In May 1997, the Company sold 3,325,000 shares of its common stock in the
     Offering at a price of $8.00 per share. With a portion of the proceeds from
     the Offering, the Company repaid the then outstanding borrowings ($13.3
     million) under the Company's revolving credit facility.

2.   Basis of Presentation

     The unaudited condensed consolidated balance sheets at December 31, 1997
     and September 30, 1998 reflect the consolidated accounts of the Company.
     The unaudited condensed consolidated statements of operations and of cash
     flows for the nine months ended September 30, 1997 and 1998 include the
     results of operations and of cash flows of the Partnership for the period
     from January 1, 1997 to February 27, 1997 and of the Company for the period
     from February 25, 1997, the date of its inception, to September 30, 1997
     and for the nine months ended June 30, 1998. As the Exchange was the
     conversion of a partnership to a corporation, the Exchange was accounted
     for by the Company as a reorganization.

     The accompanying condensed consolidated financial statements are unaudited,
     and in the opinion of management, reflect all adjustments that are
     necessary for a fair presentation of the financial position and results of
     operations for the periods presented. All such adjustments are of a normal
     and recurring nature. The results of operations for the periods presented
     are not necessarily indicative of the results to be expected for the entire
     year. The unaudited condensed consolidated financial statements should be
     read in conjunction with the Company's 1997 Annual Report on Form 10-K
     pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934.



                                        5

<PAGE>   8


                           BRIGHAM EXPLORATION COMPANY

                             NOTES TO THE CONDENSED
                        CONSOLIDATED FINANCIAL STATEMENTS
                                   (unaudited)


3.   Notes Payable

     In January 1998, the Company entered into a reserve based revolving credit
     facility (the "Credit Facility"). The Credit Facility originally provided
     for borrowings up to $75 million, all of which was immediately available
     for borrowing to fund capital expenditures. The borrowing base was reduced
     to $65 million upon issuance of the Notes. On January 31, 1999, the
     borrowing availability will be redetermined by the lender based on the
     Company's proved reserve value at that time. The Company may elect, at its
     option, to have the borrowing availability redetermined based on the
     Company's proved reserve value at any time prior to January 31, 1999.
     Amounts outstanding under the Credit Facility bear interest at either the
     lender's Base Rate or LIBOR plus 2.25%, at the Company's option. The
     Company's obligations under the Credit Facility are secured by
     substantially all of the natural gas and oil properties of the Company. A
     portion of the funds borrowed under the Credit Facility were used to repay
     in full the debt outstanding under the Company's previous revolving credit
     facility.

     In connection with the origination of the Credit Facility, certain bank
     fees and other expenses totaling approximately $1.9 million were recorded
     as deferred costs and will be amortized over the life of the loan which
     matures January 26, 2001.

4.   The Offering

     In August 1998, upon the filing of a registration statement with the SEC,
     the Company issued $50 million of debt and equity securities to two
     affiliated institutional investors. The financing transaction consisted of
     the issuance of $40 million of senior subordinated secured notes (the
     "Notes") with warrants to purchase the Company's common stock and the sale
     of $10 million of the Company's common stock, 1,052,632 shares at a price
     of $9.50 per share. The combined sale of the Notes and common stock of the
     Company generated proceeds, net of offering costs, of approximately $47.5
     million that was used to repay a portion of the then outstanding borrowings
     under the Company's Credit Facility.

     The Notes mature in August 2003, with no principal payments required until
     maturity and quarterly interest payments payable either in cash at an
     annual rate of 12% or, in limited circumstances, the issuance of additional
     notes at an annual interest rate of 13% for the first three years. The
     Company may repay the Notes in full without premium at any time prior to
     maturity. The indenture governing the Notes contains certain covenants
     including, but not limited to, limitations or restrictions on indebtedness,
     dividends and distributions, affiliate transactions, liens and sale and
     leaseback transactions. Warrants to purchase 1 million shares of the
     Company's common stock exercisable during a period of seven years at a
     price of $10.45 per share were issued in connection with the Notes.

     The Notes are fully and unconditionally guaranteed, on a joint and several
     basis, by each of the Company's subsidiaries (the "Subsidiary Guarantors"),
     all of which are directly or indirectly wholly-owned by the Company. The
     obligations of the Subsidiary Guarantors under the subsidiary guaranty
     agreements are subordinated to the senior indebtedness of the Subsidiary
     Guarantors. The assets of the parent, Brigham Exploration Company, consist
     solely of investments in its subsidiaries. Financial statements for the
     Subsidiary Guarantors are not presented because management has determined
     that they would not be material to investors.

     Concurrent with the issuance of the Notes, the Company recorded a discount
     on the Notes of $4.5 million to reflect the estimated value of the
     warrants. Also in connection with the issuance of the Notes, certain fees
     and expenses totaling approximately $1.8 million were recorded as deferred
     costs. The Note discount and deferred fees will be amortized over the five
     year term of the Notes.

                                        6

<PAGE>   9


                           BRIGHAM EXPLORATION COMPANY

                             NOTES TO THE CONDENSED
                        CONSOLIDATED FINANCIAL STATEMENTS
                                   (unaudited)



5.   Income Taxes

     Prior to the consummation of the Exchange, the Partnership was not subject
     to federal income taxes. Income and losses were passed through to its
     partners on the basis of the allocation provisions established by the
     partnership agreement. Upon consummation of the Exchange, the Partnership's
     net income became subject to federal income taxes through its ownership by
     the Company. Also, in conjunction with the Exchange, the Company recorded a
     deferred income tax liability of $5 million to recognize the temporary
     differences between the financial statement and tax bases of the assets and
     liabilities of the Partnership at the Exchange date, February 27, 1997,
     given the provisions of enacted tax laws. Subsequent to this date, the
     Company elected to record a step-up in basis of its assets for tax purposes
     as a result of the Exchange. As a result of this election, the Company
     recorded a $3.8 million deferred income tax benefit in the fourth quarter
     of 1997, which resulted in a net $1.2 million non-cash deferred income tax
     charge for the year ended December 31, 1997.

6.   Earnings Per Share

     Earnings per share have been calculated in accordance with the provisions
     of Statement of Financial Accounting Standards ("SFAS") No. 128. The
     implementation of this standard has resulted in the presentation of a basic
     EPS calculation in the consolidated financial statements as well as a
     diluted EPS calculation. Basic EPS is computed by dividing net income
     (loss) applicable to common shareholders by the weighted average number of
     common shares outstanding during each period. Diluted EPS is computed by
     dividing net income (loss) applicable to common shareholders by the
     weighted average number of common shares and common share equivalents
     outstanding, if dilutive, during each period. The number of common share
     equivalents outstanding is computed using the treasury stock method.

     Historical earnings per share for the nine months ended September 30, 1997
     is based on shares of common stock issued upon consummation of the Exchange
     (Note 1). At September 30, 1997 and 1998, options and warrants to purchase
     644,097 and 1,935,154, respectively, shares of common stock were
     outstanding but were not included in the computation of diluted EPS due to
     the anti-dilutive effect they would have on EPS if converted.

7.   Reporting Comprehensive Income

     In June 1997, the Financial Accounting Standards Board ("FASB") issued SFAS
     No. 130, "Reporting Comprehensive Income." The new standard, which is
     effective for financial statements issued for periods ending after December
     15, 1997, established standards for reporting, in addition to net income,
     comprehensive income and its components including, as applicable, foreign
     currency items, minimum pension liability adjustments and unrealized gains
     and losses on certain investments in debt and equity securities. Upon
     adoption, the Company is also required to reclassify financial statements
     for earlier periods provided for comparative purposes. The Company adopted
     this standard in the first quarter of 1998. There is no difference between
     the Company's net income as reported and comprehensive income.

8.   Segment Reporting

     In June 1997, the FASB issued SFAS No. 131, "Disclosure about Segments of
     an Enterprise and Related Information," which the Company adopted in the
     first quarter of 1998. The standard established requirements for reporting
     information about operating segments in interim financial reports issued to
     shareholders. It also

                                        7

<PAGE>   10


                           BRIGHAM EXPLORATION COMPANY

                             NOTES TO THE CONDENSED
                        CONSOLIDATED FINANCIAL STATEMENTS
                                   (unaudited)

     established standards for related disclosures about products and services,
     geographic areas and major customers. Under SFAS No. 131, operating
     segments are to be determined consistent with management's organization and
     evaluation of financial information internally for making operating
     decisions and assessing performance. The disclosure provisions of this
     standard are not applicable for interim periods in the year of adoption.
     The adoption of this new standard is not expected to have a material impact
     on the Company's consolidated balance sheet or statement of operations.



9.   Accounting for Derivative Instruments and Hedging Activities

     In June 1998, the FASB issued SFAS No. 133, "Accounting for Derivative
     Instruments and Hedging Activities." The new standard is effective for
     fiscal years beginning after June 15, 1999, but earlier application is
     permitted. SFAS No. 133 requires that all derivatives be recognized on the
     balance sheet as either assets or liabilities and measured at fair value
     regardless of any hedge relationship that exists. The corresponding gains
     and losses should be reported based on the hedge relationship that exists.
     The adoption of this new standard is not expected to have a material impact
     on the Company's consolidated balance sheet or statement of operations.



                                        8

<PAGE>   11



Item 2. Management's Discussion and Analysis of Results of Operations and
        Financial Condition

Results of Operations

Comparison of three month periods ended September 30, 1997 and September 30,
1998

     Natural gas and oil sales. Natural gas and oil sales increased 98% from
$2.1 million in the third quarter of 1997 to $4.2 million in the third quarter
of 1998. Of this net increase, $2.9 million was attributable to an increase in
production, offset by $872,000 attributable to a decrease in the average sales
price for natural gas and oil. Production volumes for natural gas increased 263%
from 330 MMcf in the third quarter of 1997 to 1,198 MMcf in the third quarter of
1998. The average price received for natural gas increased 10% from $2.10 per
Mcf in the third quarter of 1997 to $2.32 per Mcf in the third quarter of 1998.
Production volumes for oil increased 51% from 76 MBbls in the third quarter of
1997 to 114 MBbls in the third quarter of 1998. The average price received for
oil decreased 34% from $18.53 per Bbl in the third quarter of 1997 to $12.14 per
Bbl in the third quarter of 1998. Natural gas and oil sales were increased by
production from wells completed since the end of the third quarter of 1997,
partially offset by the natural decline of existing production, and from certain
wells acquired from Ward Petroleum in Grady County, Oklahoma which were included
in the Company's results of operations effective September 1, 1997. As a result
of hedging activities, natural gas revenues increased $235,900, or $0.20 per
Mcf, in the third quarter of 1998.

     Lease operating expenses. Lease operating expenses increased 78% from
$317,000 for the third quarter of 1997 to $564,000 for the third quarter of
1998, while, on a per unit of production basis, lease operating expenses for the
same periods decreased 25% from $0.40 per Mcfe to $0.30 per Mcfe. The increase
in lease operating expenses was primarily due to an increase in the number of
producing wells in the third quarter of 1998 as compared with the same period in
1997. The decrease in the per unit rate was primarily due to an increase in
natural gas production as a percentage of total equivalent production (42% and
64% for the third quarters of 1997 and 1998, respectively) since a typical
natural gas well produces with lower average lease operating costs per unit of
production than a typical oil well.

     Production taxes. Production taxes increased 113% from $120,000 ($0.15 per
Mcfe) for the third quarter of 1997 to $255,000 ($0.14 per Mcfe) for the third
quarter of 1998 as a direct result of increased production volumes. The
effective average production tax rate increased from 5.7% of natural gas and oil
sales revenues to 6.1% for the third quarters of 1997 and 1998, respectively,
due to the increase in natural gas production as a percentage of total
equivalent production as natural gas is typically burdened with higher
production tax rates than oil production.

     General and administrative expenses. General and administrative expenses
increased 7% from $995,000 for the third quarter of 1997 to $1.1 million for the
third quarter of 1998. On a per unit of production basis, general and
administrative expenses decreased 55% from $1.27 per Mcfe for the third quarter
of 1997 to $0.57 per Mcfe for the third quarter of 1998.

     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 137% from $713,000 ($0.91 per Mcfe) in the third
quarter of 1997 to $1.7 million ($0.90 per Mcfe) in the third quarter of 1998.
Of this net increase, $999,000 was due to the increase in production volumes,
which was slightly offset by $24,000 due to a 1% decrease in the depletion rate.

     Interest expense. Net interest expense increased from $46,000 in the third
quarter of 1997 to $1.9 million in the third quarter of 1998. This increase was
primarily due to a higher average debt balance in the third quarter of 1998 as
compared with the third quarter of 1997 resulting from increased capital
expenditures related to the Company's exploration activities during the twelve
months ended September 30, 1998. The weighted average outstanding debt balance
increased from $2.4 million in the third quarter of 1997 to $71.6 million in the
third quarter of 1998. Interest expense increased an additional $271,000 in the
third quarter of 1998 compared to the same period in 1997 due to the non-cash
amortization of deferred financing fees and debt discounts incurred in
connection with the establishment of the Credit Facility in January 1998 and the
issuance of the Notes in August 



                                       9

<PAGE>   12

1998. Of these non-cash interest expenses, $197,000 related to the amortization
of deferred financing fees and $74,000 related to the amortization of debt
discount. The Company expects to continue to recognize deferred financing fees
in the amounts of approximately $159,000 per quarter over the term of the Credit
Facility which matures in January 2001 and approximately $90,000 per quarter
over the term of the Notes which mature in August 2003. In connection with
issuance of the Notes in August 1998, the Company recorded the Notes at a
discount of $4.5 million to reflect the estimated value of the warrants to
purchase common stock that were issued in connection with the issuance of the
Notes. The Company will amortize this debt discount over the five-year term of
the Notes based on the interest method of amortization and will include such
amortization in interest expense.

Comparison of nine month periods ended September 30, 1997 and September 30, 1998

     Natural gas and oil sales. Natural gas and oil sales increased 90% from $6
million in the first nine months of 1997 to $11.3 million in the first nine
months of 1998. Of this increase, $9.5 million was attributable to an increase
in production, offset by $4.2 million attributable to a decrease in the average
sales price for natural gas and oil. Production volumes for natural gas
increased 299% from 788 MMcf in the first nine months of 1997 to 3,145 MMcf in
the first nine months of 1998. The average price received for natural gas
decreased 9% from $2.40 per Mcf in the first nine months of 1997 to $2.18 per
Mcf in the first nine months of 1998. Production volumes for oil increased 70%
from 203 MBbls in the first nine months of 1997 to 346 MBbls in the first nine
months of 1998. The average price received for oil decreased 36% from $19.99 per
Bbl in the first nine months of 1997 to $12.82 per Bbl in the first nine months
of 1998. Natural gas and oil sales were increased by production from wells
completed since September 30, 1997, partially offset by the natural decline of
existing production, and from certain wells acquired from Ward Petroleum in
Grady County, Oklahoma which were included in the Company's results of
operations effective September 1, 1997. As a result of hedging activities,
natural gas revenues increased $274,600, or $0.09 per Mcf, for the first nine
months of 1998, compared to a decrease in oil revenues of $6,191, or $0.03 per
Bbl, for the first nine months of 1997.

     Lease operating expenses. Lease operating expenses increased 96% from
$787,000 in the first nine months of 1997 to $1.5 million in the first nine
months of 1998, while, on a per unit of production basis, lease operating
expenses for the same periods decreased 23% from $0.39 per Mcfe to $0.30 per
Mcfe. The increase in lease operating expenses was primarily due to an increase
in the number of producing wells for the first nine months of 1998 as compared
with the same period in 1997. The decrease in the per unit rate was primarily
due to an increase in natural gas production as a percentage of total equivalent
production (39% and 60% for the first nine months of 1997 and 1998,
respectively) since a typical natural gas well produces with lower average lease
operating costs per unit of production than a typical oil well.

     Production taxes. Production taxes increased 108% from $339,000 ($0.17 per
Mcfe) for the first nine months of 1997 to $705,000 ($0.14 per Mcfe) for the
first nine months of 1998 as a direct result of increased production volumes.
The effective average production tax rate increased from 5.7% of natural gas and
oil sales revenues to 6.2% for the nine months ended 1997 and 1998,
respectively, due to the increase in natural gas production as a percentage of
total equivalent production as natural gas is typically burdened with higher
production tax rates than oil production.

     General and administrative expenses. General and administrative expenses
increased 37% from $2.5 million in the first nine months of 1997 to $3.4 million
in the first nine months of 1998. This increase was primarily attributable to
the hiring of additional employees to support the Company's increased level of
operational activities. Additionally, office rent, other office expenses and
costs related to the administration of a public corporation increased for the
first nine months of 1998 as compared to the same period for 1997. On a per unit
of production basis, general and administrative expenses decreased 48% from
$1.22 per Mcfe for the first nine months of 1997 to $0.64 per Mcfe for the first
nine months of 1998.

     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 112% from $2.1 million ($1.05 per Mcfe) in the first
nine months of 1997 to $4.5 million ($0.86 per Mcfe) in the first nine months of
1998. Of this net increase, $3.4 million was due to the increase in production
volumes, which was 



                                       10

<PAGE>   13

offset by $1 million due to an 18% decrease in the depletion rate. The depletion
rate per unit of production decreased due to the addition of natural gas and oil
reserves at lower average capital costs.

     Interest expense. Net interest expense increased from $510,000 in the first
nine months of 1997 to $4.3 million in the first nine months of 1998. This
increase was primarily due to a higher average debt balance in the first nine
months of 1998 as compared with the same period in 1997 resulting from the
funding of increased capital expenditures related to the Company's exploration
activities during the twelve months ended September 30, 1998. The weighted
average outstanding debt balance increased from $9.5 million in the first nine
months of 1997 to $58.1 million in the first nine months of 1998. Interest
expense increased an additional $537,000 in the first nine months of 1998
compared to the same period in 1997 due to the non-cash amortization of deferred
financing fees and debt discounts incurred in connection with the establishment
of the Credit Facility in January 1998 and the issuance of the Notes in August
1998. Of these non-cash interest expenses, $463,000 related to the amortization
of deferred financing fees and $74,000 related to the amortization of debt
discounts.

Liquidity and Capital Resources

     The Company's primary sources of capital have been debt borrowings
(revolving credit facility and private placement debt), working capital, the
sale of interests in projects and sales of equity. During May 1997, as described
in Note 1 to the Condensed Consolidated Financial Statements included herein,
the Company completed an initial public offering of common stock of the Company
that generated proceeds of approximately $24 million, net of offering costs,
that were used to repay all outstanding debt ($13.3 million) under the Company's
then existing revolving credit facility and to fund capital expenditures. In
August 1998, the Company issued $50 million of debt and equity securities, as
described in Note 4 to the Condensed Consolidated Financial Statements included
herein, that generated proceeds of approximately $47.5 million, net of offering
costs, that were used to repay a portion of then outstanding borrowings under
the Credit Facility, thereby increasing the Company's borrowing availability
under its Credit Facility to fund capital expenditures.

Cash Flow Analysis

     In the first nine months of 1998, cash flow provided by operations was $2.7
million primarily as a result of the net effects of increased natural gas and
oil revenues, net of lease operating expenses, production taxes and general and
administrative expenses, and increases in interest expenses and working capital
components. Cash flow used in investing activities was $53.6 million in the
first nine months of 1998 primarily as a result of capital expenditures related
to exploration activities. Cash flow provided by financing activities was $50.5
million in the first nine months of 1998 primarily as a result of borrowings in
excess of repayments under the Credit Facility, the issuance of the Notes and
the issuance of $10 million of common stock to fund the difference between cash
flow from operations and cash flow from investing activities.

Revolving Credit Facility

     The Company's $75 million credit agreement (the "Credit Facility") has a
current borrowing base of $65 million. On January 31, 1999, the Credit Facility
borrowing base will be redetermined by the lenders based primarily on the
Company's then proved reserve value. Principal outstanding under the Credit
Facility is due at maturity on January 26, 2001 with interest due monthly for
base rate traunches or periodically as Eurodollar traunches mature. The
Company's obligations under the Credit Facility are secured by substantially all
of the natural gas and oil properties of the Company. At November 10, 1998, the
Company had $48 million in borrowings outstanding under the Credit Facility,
which bear interest at an average annual rate of 7.6%.

     The Credit Facility has certain financial covenants including current and
interest coverage ratios, as defined. Should the Company be unable to comply
with certain of the financial covenants, its lender may be unwilling to waive
noncompliance. In such instance, the Company's liquidity may be adversely
affected, which could in turn have an adverse impact on the Company's future
financial position and results of operations. The Company is currently in
compliance with all such covenants and anticipates being in compliance in the
foreseeable future.


                                       11

<PAGE>   14

Capital Expenditures

     The Company currently estimates that its net capital expenditures in 1998
will be approximately $59 million. The Company expects to incur these capital
expenditures primarily to drill 90 gross (45 net) planned wells, to acquire
approximately 1,300 gross (925 net) square miles of 3-D seismic and to continue
to add to and upgrade its 3-D seismic interpretation hardware and software. The
actual number of wells drilled, square miles acquired and costs incurred may
differ significantly from these estimates.

     Due to the Company's active 3-D seismic acquisition and drilling programs,
the Company has experienced and expects to continue to experience substantial
working capital and capital expenditure requirements. The Company believes that
cash flow from operations, borrowings under the Credit Facility and proceeds
expected to be received from potential sales of interests in certain of its
seismic projects will allow the Company to finance its operations at least
through 1998 based on current conditions. However, the Company expects that
additional financing will be required in the future to fund the Company's
planned 3-D seismic acquisition and drilling programs in 1999. In the event
additional financing is not available, the Company will be required to curtail
these activities. Such curtailment may include a reduction of the number of
wells drilled by the Company and the level of working interest retained by the
Company in its 3D seismic projects.

Year 2000

     The Year 2000 issue stems from the way dates are recorded and computed in
many computer systems because such programs use only the last two digits to
indicate the year. If uncorrected, these computer programs will be unable to
interpret dates beyond the year 1999, which could cause computer system failure
or other computer errors, thereby disrupting operations.

     The Company has reviewed the effect of the Year 2000 issue relating to its
information systems. The Company has determined that the Year 2000 issues
directly related to its information systems will not have a material impact on
its business, operations or its financial position. The Company is currently
evaluating the potential impact third party noncompliance could have on its
operations and is developing contingency plans which will be finalized in 1999.
However, the Company cannot determine what effect, if any, the Year 2000 issues
affecting its vendors, customers, other businesses and the numerous local,
state, federal and other US governmental entities with which it conducts
business or by which it is regulated or governed or taxed will have on its
business or financial position.

     The Company is expensing as incurred all costs related to the assessment
and remediation of the Year 2000 issue. These costs are being funded through
operating cash flow and are not material to the Company's consolidated financial
condition or results of operations.

Forward Looking Information

     The Company may make forward looking statements, oral or written, including
statements in this report, press releases and other filings with the SEC,
relating to the Company's drilling plans, its potential drilling locations,
capital expenditures, use of offering proceeds, the ability of expected sources
of liquidity to support working capital and capital expenditure requirements and
the Company's financial position, business strategy and other plans and
objectives for future operations. Such statements involve risks and
uncertainties, including those relating to the Company's dependence on
exploratory drilling activities, the volatility of natural gas and oil prices,
the risks associated with growth (including the risk of reduced availability of
seismic gathering and drilling services in the face of growing demand), the
substantial capital requirements of the Company's exploration and development
projects, operating hazards and uninsured risks and other factors detailed in
the Company's registration statement and other filings with the SEC. All
subsequent oral and written forward looking statements attributable to the
Company are expressly qualified in their entirety by these factors. The Company
assumes no obligation to update these statements.




                                       12

<PAGE>   15


PART II.  OTHER INFORMATION:

Item 6.   Exhibits and Reports on Form 8-K

          (a)  Exhibits

               27   Financial Data Schedule


                                   SIGNATURES

     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, in the City of Austin, State of Texas,
on the 11th day of November, 1998.

                                                  BRIGHAM EXPLORATION COMPANY


                                                  By: /s/ BEN M. BRIGHAM
                                                     --------------------------
                                                     Ben M. Brigham
                                                     Chief Executive Officer, 
                                                     President and Chairman of
                                                     the Board



                                                  By: /s/ CRAIG M. FLEMING
                                                     --------------------------
                                                     Craig M. Fleming
                                                     Chief Financial Officer

                                       13

<PAGE>   16


<TABLE>
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                                                                                                             SEQUENTIALLY
    EXHIBIT                                                                                                    NUMBERED
      NO.                                         INDEX TO EXHIBITS                                              PAGE
    -------                                       -----------------                                          ------------
<S>                                <C>                                                                   <C>    
      27                           Financial Data Schedule                                                      Tabbed by
                                                                                                               Exhibit No.

</TABLE>