<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 June 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>
<S>                                   <C>                              <C>
           DELAWARE                              1311                     75-2692967
 (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 July 31, 1998, 12,253,574 shares of Common Stock, $.01 per share, were
outstanding.

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


<PAGE>   2


                           BRIGHAM EXPLORATION COMPANY

                                      INDEX

<TABLE>
<CAPTION>

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

Item 1.       Unaudited Condensed Consolidated Financial Statements

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

              b) Statements of Operations - Three and six months ended
                      June 30, 1997 and 1998                                                     2

              c) Statements of Cash Flows - Six months ended
                      June 30, 1997 and 1998                                                     3

              d)   Notes to Condensed Consolidated Financial Statements                        4 - 6

Item 2.       Management's Discussion and Analysis of Results of
                   Operations and Financial Condition                                          7 - 10


PART II.      OTHER INFORMATION:

Item 6.       Exhibits and Reports on Form 8-K                                                11 - 12
</TABLE>


<PAGE>   3





PART I.        FINANCIAL INFORMATION:

Item 1.        Financial Statements



                           BRIGHAM EXPLORATION COMPANY
                             CONDENSED CONSOLIDATED
                                 BALANCE SHEETS
                                 (in thousands)

<TABLE>
<CAPTION>



                                                                                 December 31,     June 30,
                                                                                     1997           1998
                                                                                 ------------   ------------
                                                                                                 (unaudited)
<S>                                                                              <C>            <C>      

                                            ASSETS
Current assets:
     Cash and cash equivalents                                                     $   1,701      $   3,106
     Accounts receivable                                                               4,909          7,934
     Prepaid expenses                                                                    280            217
                                                                                   ---------      ---------
         Total current assets                                                          6,890         11,257
                                                                                   ---------      ---------

Natural gas and oil properties, at cost, net                                          84,176        114,454
Other property and equipment, at cost, net                                             1,239          1,603
Drilling advances paid                                                                    78            603
Deferred loan fees                                                                        --          1,645
Other noncurrent assets                                                                   18            137
                                                                                   ---------      ---------
                                                                                   $  92,401      $ 129,699
                                                                                   =========      =========

                                    LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
     Accounts payable                                                              $  11,892      $   7,837
     Accrued drilling costs                                                            2,406          5,206
     Participant advances received                                                       489            442
     Other current liabilities                                                           726          4,748
                                                                                   ---------      ---------
         Total current liabilities                                                    15,513         18,233
                                                                                   ---------      ---------

Notes payable                                                                         32,000         68,000
Deferred income tax liability                                                          1,228            606
Other noncurrent liabilities                                                             507            526

Stockholders' equity:
     Preferred stock, $.01 par value, 10 million shares
         authorized, none issued and outstanding                                          --             --
     Common stock, $.01 par value, 30 million shares
         authorized, 12,253,574 issued and outstanding                                   123            123
     Additional paid-in capital                                                       44,344         44,292
     Unearned stock compensation                                                      (1,340)          (880)
     Retained earnings (accumulated deficit)                                              26         (1,201)
                                                                                   ---------      ---------
         Total stockholders' equity                                                   43,153         42,334
                                                                                   ---------      ---------
                                                                                   $  92,401      $ 129,699
                                                                                   =========      =========
</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             Six Months
                                                      Ended June 30,          Ended June 30,
                                                   --------------------    --------------------
                                                     1997        1998        1997        1998
                                                   --------    --------    --------    --------
<S>                                                <C>         <C>         <C>         <C>     
Revenues:
     Natural gas and oil sales                     $  1,718    $  3,987    $  3,854    $  7,130
     Workstation revenue                                160         133         324         247
                                                   --------    --------    --------    --------
                                                      1,878       4,120       4,178       7,377
                                                   --------    --------    --------    --------
Costs and expenses:
     Lease operating                                    264         564         470         978
     Production taxes                                    92         262         219         450
     General and administrative                         753       1,139       1,455       2,293
     Depletion of natural gas and oil properties        708       1,517       1,395       2,784
     Depreciation and amortization                       64          92         172         175
     Amortization of stock compensation                  86          95         115         190
                                                   --------    --------    --------    --------
                                                      1,967       3,669       3,826       6,870
                                                   --------    --------    --------    --------
         Operating income (loss)                        (89)        451         352         507
                                                   --------    --------    --------    --------

Other income (expense):
     Interest income                                     63          40          81          77
     Interest expense                                  (156)     (1,410)       (372)     (2,432)
     Interest expense - related party                    --          --        (174)         --
                                                   --------    --------    --------    --------
                                                        (93)     (1,370)       (465)     (2,355)
                                                   --------    --------    --------    --------

Net loss before income taxes                           (182)       (919)       (113)     (1,848)
Income tax (expense) benefit                            151         307      (4,813)        621
                                                   --------    --------    --------    --------
     Net loss                                      $    (31)   $   (612)   $ (4,926)   $ (1,227)
                                                   ========    ========    ========    ========

Net loss per share:
     Basic / Diluted                               $  (0.00)   $  (0.05)   $  (0.50)   $  (0.10)

Weighted average common shares outstanding:
     Basic / Diluted                                 10,840      12,254       9,890      12,254
</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>


                                                              Six             Six
                                                          Months Ended    Months Ended
                                                            June 30,        June 30,
                                                              1997           1998
                                                          ------------    ------------

<S>                                                       <C>             <C>          
Cash flows from operating activities:
  Net loss                                                $     (4,926)   $     (1,227)
  Adjustments to reconcile net loss to cash
   provided by operating activities:
     Depletion of natural gas and oil properties                 1,395           2,784
     Depreciation and amortization                                 172             175
     Amortization of stock compensation                            115             190
     Amortization of deferred loan fees                             --             266
     Changes in deferred income tax liability                    4,813            (622)
     Changes in working capital and other items                 (1,764)         (3,258)
                                                          ------------    ------------
       Net cash used by operating activities                      (195)         (1,692)
                                                          ------------    ------------

Cash flows from investing activities:
  Additions to natural gas and oil properties                  (11,796)        (30,044)
  Additions to other property and equipment                       (183)           (315)
  Increase in drilling advances paid                              (126)           (525)
                                                          ------------    ------------
      Net cash used by investing activities                    (12,105)        (30,884)
                                                          ------------    ------------

Cash flows from financing activities:
  Proceeds from issuance of common stock                        23,929              --
  Increase in notes payable                                      5,250          70,800
  Repayment of notes payable                                   (13,250)        (34,800)
  Principal payments on capital lease obligations                  (87)           (108)
  Deferred loan fees                                                --          (1,911)
                                                          ------------    ------------
      Net cash provided by financing activities                 15,842          33,981
                                                          ------------    ------------
Net increase in cash and cash equivalents                        3,542           1,405

Cash and cash equivalents, beginning of period                   1,447           1,701
                                                          ------------    ------------
Cash and cash equivalents, end of period                  $      4,989    $      3,106
                                                          ============    ============
</TABLE>





   See accompanying notes to the condensed consolidated financial statements.

                                       3


<PAGE>   6


                          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
         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 June 30, 1998 reflect the consolidated accounts of the
         Company. The unaudited condensed consolidated statements of operations
         and of cash flows for the six months ended June 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 June 30, 1997 and for the six 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.






                                       4


<PAGE>   7


                          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 provides
         for borrowings up to $75 million, all of which was immediately
         available for borrowing to fund capital expenditures, until January 31,
         1999, at which time 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.       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.

5.       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 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 six months ended June 30, 1997 is
         based on shares of common stock issued upon consummation of the
         Exchange (Note 1). At June 30, 1997 and 1998, options to purchase
         644,097 and 935,987, 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.



                                       5




<PAGE>   8




                           BRIGHAM EXPLORATION COMPANY

                             NOTES TO THE CONDENSED
                        CONSOLIDATED FINANCIAL STATEMENTS
                                   (UNAUDITED)

6.     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.

7.     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 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.

8.     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.


                                       6

<PAGE>   9


                           BRIGHAM EXPLORATION COMPANY

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

Results of Operations

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

         Natural gas and oil sales. Natural gas and oil sales increased 132%
from $1.7 million in the second quarter of 1997 to $4 million in the second
quarter of 1998. Of this net increase, $3.8 million was attributable to an
increase in production, offset by $1.5 million attributable to a decrease in the
average sales price for natural gas and oil. Production volumes for natural gas
increased 462% from 215 MMcf in the second quarter of 1997 to 1,207 MMcf in the
second quarter of 1998. The average price received for natural gas increased
from $2.07 per Mcf in the second quarter of 1997 to $2.13 per Mcf in the second
quarter of 1998. Production volumes for oil increased 83% from 64 MBbls in the
second quarter of 1997 to 117 MBbls in the second quarter of 1998. The average
price received for oil decreased 39% from $19.93 per Bbl in the second quarter
of 1997 to $12.17 per Bbl in the second quarter of 1998. Natural gas and oil
sales were increased by production from wells completed since the second 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 $38,700
for the second quarter of 1998, compared to an increase in oil revenues of
$34,192 for the second quarter of 1997.

         Lease operating expenses. Lease operating expense increased 114% from
$264,000 for the second quarter of 1997 to $564,000 for the second quarter of
1998, while on a per unit of production basis, lease operating expenses for the
same periods decreased 32% from $.44 per Mcfe to $.30 per Mcfe. The increase in
lease operating expenses was primarily due to an increase in the number of
producing wells in the second 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 (36% and
63% for the second 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 185% from $92,000 ($.15
per Mcfe) for the second quarter of 1997 to $262,000 ($.14 per Mcfe) for the
second quarter of 1998 as a direct result of increased production volumes. The
effective average production tax rate increased from 5% of natural gas and oil
sales revenues to 7% for the second 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 51% from $753,000 for the second quarter of 1997 to $1.1
million for the second quarter 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
second quarter of 1998 as compared to the same period for 1997. On a per unit of
production basis, general and administrative expenses decreased 52% from $1.26
per Mcfe for the second quarter of 1997 to $.60 per Mcfe for the second quarter
of 1998.

         Depletion of natural gas and oil properties. Depletion of natural gas
and oil properties increased 114% from $708,000 ($1.18 per Mcfe) in the second
quarter of 1997 to $1.5 million ($.80 per Mcfe) in the second quarter of 1998.
Of this net increase, $1.6 million was due to the increase in production volumes
which was offset by $736,000 due to a 32% decrease in the depletion rate. The
depletion rate per unit of production decreased due to an increase in natural
gas and oil reserves at lower average capital costs.


                                        7

<PAGE>   10





         Interest expense. Net interest expense increased from $93,000 in the
second quarter of 1997 to $1.4 million in the second quarter of 1998. This
increase was due to a higher average outstanding debt balance in the second
quarter of 1998 partially offset by a decreased effective interest rate. The
weighted average outstanding debt balance increased from $6.2 million in the
second quarter of 1997 to $59.6 million in the second quarter of 1998. The
effective annual interest rate decreased 2% from 9.6% in the second quarter of
1997 to 9.4% in the second quarter of 1998. In May 1997, the Company received
$23.9 million for the sale of shares of its common stock in a public offering. A
portion of these proceeds were used to repay the $13.3 million in debt
outstanding at that date. The increase in the average outstanding debt during
the second quarter of 1998 compared to the same period for 1997 was due to
increased capital expenditures related to the Company's exploration activities
during the second quarter of 1998 and the repayment of debt which occurred in
the May 1997. At June 30, 1998, the Company had $68 million in borrowings
outstanding under the Credit Facility which had an annual interest rate of 8%.
Interest expense increased an additional $159,000 in the second quarter of 1998
compared to the same period for 1997 due to the amortization of deferred loan
fees totaling approximately $1.9 million incurred in connection with the
establishment of the Credit Facility in January 1998. The amortization of these
deferred loan fees will continue to be recognized in the amount of approximately
$159,000 per quarter over the term of the Credit Facility which matures in
January 2001.

Comparison of six month periods ended June 30, 1997 and June 30, 1998

         Natural gas and oil sales. Natural gas and oil sales increased 85% from
$3.9 million in the first six months of 1997 to $7.1 million in the first six
months of 1998. Of this increase, $6.6 million was attributable to an increase
in production, offset by $3.4 million was attributable to a decrease in the
average sales price for natural gas and oil. Production volumes for natural gas
increased 326% from 457 MMcf in the first six months of 1997 to 1,947 MMcf in
the first six months of 1998. The average price received for natural gas
decreased 20% from $2.62 per Mcf in the first six months of 1997 to $2.10 per
Mcf in the first six months of 1998. Production volumes for oil increased 82%
from 127 MBbls in the first six months of 1997 to 232 MBbls in the first six
months of 1998. The average price received for oil decreased 37% from $20.87 per
Bbl in the first six months of 1997 to $13.15 per Bbl in the first six months of
1998. Natural gas and oil sales were increased by production from wells
completed since the first six months 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 $38,700 for the first six months of 1998,
compared to a decrease in oil revenues of $6,191 for the first six months of
1997.

         Lease operating expenses. Lease operating expense increased 108% from
$470,000 in the first six months of 1997 to $978,000 in the first six months of
1998, while on a per unit of production basis, lease operating expenses for the
same periods decreased 26% from $.39 per Mcfe to $.29 per Mcfe. The increase in
lease operating expenses was primarily due to an increase in the number of
producing wells for the first six 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 (38% and 58% for the first six 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 106% from $219,000 ($.18
per Mcfe) for the first six months of 1997 to $450,000 ($.13 per Mcfe) for the
first six months of 1998 as a direct result of increased production volumes. The
effective average production tax rate remained unchanged at 6% of natural gas
and oil sales revenues for the first six months of both 1997 and 1998.

         General and administrative expenses. General and administrative
expenses increased 58% from $1.5 million in the first six months of 1997 to $2.3
million n the first six 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 six months of 1998 as compared to the same period for 1997. On a per unit
of production basis, general and

                                        8

<PAGE>   11
 




administrative expenses decreased 42% from $1.19 per Mcfe for the first six
months of 1997 to $.69 per Mcfe for the first six months of 1998.

         Depletion of natural gas and oil properties. Depletion of natural gas
and oil properties increased 100% from $1.4 million ($1.14 per Mcfe) in the
first six months of 1997 to $2.8 ($.83 per Mcfe) in the first six months of
1998. Of this net increase, $2.4 million was due to the increase in production
volumes which was offset by $1 million due to a 27% decrease in the depletion
rate. The depletion rate per unit of production decreased due to an increase in
natural gas and oil reserves at lower average capital costs.

         Interest expense. Net interest expense increased from $465,000 in the
first six months of 1997 to $2.4 million in the first six months of 1998. This
increase was primarily due to a higher average outstanding balance offset
partially by a lower effective interest rate. The weighted average outstanding
debt balance increased from $13.2 million in the first six months of 1997 to
$51.3 million in the first six months of 1998. The effective interest rate
increased 16% from 8.1% in the first six months of 1997 to 9.4% in the first six
months of 1998. In May 1997, the Company received $23.9 million for the sale of
shares of its common stock in a public offering. A portion of these proceeds
were used to repay the $13.3 million in debt outstanding at that date. The
increase in the average outstanding debt during the first six months of 1998
compared to the same period for 1997 was due to increased capital expenditures
related to the Company's exploration activities during the first six months of
1998 and the repayment of debt which occurred in the first six months of 1997.
The increase in the average outstanding debt balance was primarily a result of
increased capital expenditures related to the Company's exploration activities.
Interest expense increased an additional $266,000 for the first six months of
1998 compared to the same period for 1997 due to the amortization of deferred
loan fees totaling approximately $1.9 million incurred in connection with the
establishment of the Credit Facility in January 1998. The amortization of these
deferred loan fees will continue to be recognized in the amount of approximately
$159,000 per quarter over the term of the Credit Facility which matures in
January 2001.

Liquidity and Capital Resources

         The Company's primary sources of capital have been 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 the first six months of 1998, cash flow used by operations was $1.7
million primarily as a result of the net effects of increased natural gas and
oil revenues, net of production taxes, lease operating expenses and general and
administrative expenses, and an increase in working capital components. Cash
flow used in investing activities was $30.9 million in the first six months of
1998 primarily as a result of capital expenditures related to exploration
activities. Cash flow provided by financing activities was $34 million, net of
deferred loan fees of $1.9 million, in the first six months of 1998 primarily as
a result of an increase in borrowings under the revolving credit facility to
fund the difference between cash flow from operations and cash flow from
investing activities.

         The Company anticipates filing on August 14, 1998 or shortly thereafter
a registration statement with the SEC regarding the proposed issuance of $50
million of debt and equity securities to two affiliated institutional investors.
The proposed financing transaction consists of the issuance of $40 million of
senior subordinated notes (the "Notes") with warrants to purchase common stock
and the sale of $10 million of common stock. Principal terms of the Notes
include a five year term with no principal payments until maturity in 2003 and
quarterly interest payments payable either in cash at an annual rate of 12% or,
in limited circumstances, in the issuance of additional Notes at an annual rate
of 13% for the first three years. The proceeds to be received by the Company
from this proposed offering will be used to fund a portion the Company's planned
capital expenditures and, in the interim, for the repayment of outstanding
indebtedness.

         The current borrowing base of $75 million under the Company's credit
agreement (the "Credit Facility") will be reduced to $65 million upon issuance
of the Notes.  On January 31, 1999, the Credit Facility borrowing base will be
redetermined by the lender based 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.  Borrowings under the facility currently
bear interest at an annual rate of approximately 8.6%.  The Company's
obligations under the Credit Facility are secured by substantially all of the
natural gas and oil properties of the Company.  The terms of the Notes will
permit the Company to borrow under the Credit Facility up to the lesser of $75
million or the Credit Facility borrowing base.

         The Company believes that through the foreseeable future it will be
able to comply with the financial covenants contained in the Credit Facility.
These covenants include a minimum interest coverage ratio that the Company's
lender amended in May 1998 following a determination that the Company did not
meet for the first quarter of 1998 and would not meet for the second quarter of
1998 the covenant as originally formulated.  In connection with the proposed 
issuance of Notes, the Company's lender will further amend the Credit Facility 
covenants to accommodate the Notes.  In the event that the Company in the 
future cannot meet a covenant, no assurance can be given that its lender will 
amend the covenant or waive compliance.



                                        9

<PAGE>   12




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.

                                       10

<PAGE>   13





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 13th day of August, 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




                                       11

<PAGE>   14


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                                                                          SEQUENTIALLY
    EXHIBIT                                                                 NUMBERED
      NO.                   INDEX TO EXHIBITS                                 PAGE
    -------                 -----------------                             ------------

<S>                       <C>                                            <C>  
      27                  Financial Data Schedule                         Tabbed by
                                                                          Exhibit No.
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