<PAGE>   1
 
      AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MAY 29, 1998
 
                                                     REGISTRATION NO. 333-
================================================================================
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                            ------------------------
                                    FORM S-1
 
            REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933
                            ------------------------
                          BRIGHAM EXPLORATION COMPANY
             (Exact name of Registrant as specified in its charter)
 
<TABLE>
<S>                                 <C>                                 <C>
             DELAWARE                              1311                             75-2692967
  (State or other jurisdiction of      (Primary Standard Industrial              (I.R.S. Employer
  incorporation or organization)        Classification Code Number)             Identification No.)
</TABLE>
 
                           6300 BRIDGE POINT PARKWAY
                             BUILDING 2, SUITE 500
                              AUSTIN, TEXAS 78730
                                 (512) 427-3300
 
  (Address, including zip code, and telephone number, including area code, of
                   Registrant's principal executive offices)
                            ------------------------
                                 BEN M. BRIGHAM
                       PRESIDENT, CHIEF EXECUTIVE OFFICER
                           AND CHAIRMAN OF THE BOARD
                           6300 BRIDGE POINT PARKWAY
                             BUILDING 2, SUITE 500
                              AUSTIN, TEXAS 78730
                                 (512) 427-3300
 (Name, address, including zip code, and telephone number, including area code,
                       of Registrant's agent for service)
                            ------------------------
                          Copies of Communication to:
 
<TABLE>
<S>                                                  <C>
                  JOE DANNENMAIER                                         JAY HEBERT
              THOMPSON & KNIGHT, P.C.                              VINSON & ELKINS, L.L.P.
          1700 PACIFIC AVENUE, SUITE 3300                        2001 ROSS AVENUE, SUITE 3700
                DALLAS, TEXAS 75201                                  DALLAS, TEXAS 75201
</TABLE>
 
                            ------------------------
          APPROXIMATE DATE OF COMMENCEMENT OF PROPOSED SALE TO THE PUBLIC:
As soon as practicable after the effective date of this Registration Statement.
 
     If any of the securities being registered on this Form are to be offered on
a delayed or continuous basis pursuant to Rule 415 under the Securities Act of
1933, check the following box.  [ ]
 
     If this Form is filed to register additional securities for an offering
pursuant to Rule 462(b) under the Securities Act, please check the following box
and list the Securities Act registration statement number of the earlier
effective registration statement for the same offering.  [ ]
 
     If this Form is a post-effective amendment filed pursuant to Rule 462(c)
under the Securities Act, check the following box and list the Securities Act
registration statement number of the earlier effective registration statement
for the same offering.  [ ]
 
     If this Form is a post-effective amendment filed pursuant to Rule 462(d)
under the Securities Act, check the following box and list the Securities Act
registration number of the earlier effective registration statement for the same
offering.  [ ]
 
     If delivery of the Prospectus is expected to be made pursuant to Rule 434,
please check the following box.  [X]
 
                        CALCULATION OF REGISTRATION FEE
 
<TABLE>
<CAPTION>
==========================================================================================================
                                                                PROPOSED MAXIMUM
                   TITLE OF EACH CLASS OF                      AGGREGATE OFFERING         AMOUNT OF
                SECURITIES TO BE REGISTERED                       PRICE(1)(2)          REGISTRATION FEE
----------------------------------------------------------------------------------------------------------
<S>                                                          <C>                    <C>
Common Stock, par value $.01 per share......................      $46,000,000              $13,940
==========================================================================================================
</TABLE>
 
(1) In accordance with Rule 457(o) under the Securities Act of 1933, the number
    of shares being registered and the proposed maximum offering price per share
    are not included in this table.
(2) Estimated for purposes of calculating registration fee.
 
     THE REGISTRANT HEREBY AMENDS THIS REGISTRATION STATEMENT ON SUCH DATE OR
DATES AS MAY BE NECESSARY TO DELAY ITS EFFECTIVE DATE UNTIL THE REGISTRANT SHALL
FILE A FURTHER AMENDMENT WHICH SPECIFICALLY STATES THAT THIS REGISTRATION
STATEMENT SHALL THEREAFTER BECOME EFFECTIVE IN ACCORDANCE WITH SECTION 8(a) OF
THE SECURITIES ACT OF 1933 OR UNTIL THE REGISTRATION STATEMENT SHALL BECOME
EFFECTIVE ON SUCH DATE AS THE SECURITIES AND EXCHANGE COMMISSION, ACTING
PURSUANT TO SAID SECTION 8(a), MAY DETERMINE.
================================================================================
<PAGE>   2
 
INFORMATION CONTAINED HEREIN IS SUBJECT TO COMPLETION OR AMENDMENT. A
REGISTRATION STATEMENT RELATING TO THESE SECURITIES HAS BEEN FILED WITH THE
SECURITIES AND EXCHANGE COMMISSION. THESE SECURITIES MAY NOT BE SOLD NOR MAY
OFFERS TO BUY BE ACCEPTED PRIOR TO THE TIME THE REGISTRATION STATEMENT BECOMES
EFFECTIVE. THIS PROSPECTUS SHALL NOT CONSTITUTE AN OFFER TO SELL OR THE
SOLICITATION OF AN OFFER TO BUY NOR SHALL THERE BE ANY SALE OF THESE SECURITIES
IN ANY STATE IN WHICH SUCH OFFER, SOLICITATION OR SALE WOULD BE UNLAWFUL PRIOR
TO REGISTRATION OR QUALIFICATION UNDER THE SECURITIES LAWS OF ANY SUCH STATE.
 
                   SUBJECT TO COMPLETION, DATED MAY 29, 1998
PROSPECTUS
 
                                3,400,000 SHARES
 
                                     [LOGO]
 
                                  COMMON STOCK
                         ------------------------------
       The 3,400,000 shares of Common Stock, $.01 par value (the "Common
Stock"), offered hereby (the "Offering") are being sold by Brigham Exploration
Company, a Delaware corporation ("Brigham" or the "Company"). The Common Stock
is traded on The Nasdaq Stock Market(SM) under the trading symbol "BEXP." On May
27, 1998, the last reported sales price of the Common Stock on The Nasdaq Stock
Market(SM) was $11.75 per share. See "Price Range of Common Stock and Dividend
Policy."
                         ------------------------------
      ANY INVESTMENT IN THE SECURITIES OFFERED HEREIN INVOLVES A HIGH DEGREE OF
RISK. SEE "RISK FACTORS" BEGINNING ON PAGE 12.
                         ------------------------------
  THESE SECURITIES HAVE NOT BEEN APPROVED OR DISAPPROVED BY THE SECURITIES AND
 EXCHANGE COMMISSION OR ANY STATE SECURITIES COMMISSION NOR HAS THE SECURITIES
   AND EXCHANGE COMMISSION OR ANY STATE SECURITIES COMMISSION PASSED UPON THE
ACCURACY OR ADEQUACY OF THIS PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY IS A
                               CRIMINAL OFFENSE.
 
<TABLE>
<CAPTION>
=================================================================================================================
                                                                             UNDERWRITING
                                                           PRICE TO         DISCOUNTS AND         PROCEEDS TO
                                                            PUBLIC          COMMISSIONS(1)        COMPANY(2)
-----------------------------------------------------------------------------------------------------------------
<S>                                                    <C>               <C>                  <C>
Per Share.............................................         $                  $                    $
-----------------------------------------------------------------------------------------------------------------
Total(3)..............................................         $                  $                    $
=================================================================================================================
</TABLE>
 
(1) The Company and the Selling Stockholders have agreed to indemnify the
    several Underwriters against certain liabilities, including liabilities
    under the Securities Act of 1933. See "Underwriting."
 
(2) Before deducting expenses of the Offering payable by the Company estimated
    to be $          .
 
(3) The Selling Stockholders have granted the several Underwriters a 30-day
    over-allotment option to purchase up to an additional 510,000 shares of
    Common Stock on the same terms and conditions as the Common Stock offered
    hereby solely to cover over-allotments, if any, and the Company has granted
    the several Underwriters an option to purchase such additional shares in the
    event that a Selling Stockholder fails to meet its obligations to sell such
    shares. If the over-allotment option is exercised in full, the total Price
    to Public will be $       and the total Proceeds to Selling Stockholders
    will be $          . See "Underwriting."
                         ------------------------------
     The shares of Common Stock are offered subject to prior sale, when, as and
if delivered to and accepted by the Underwriters and subject to certain other
conditions. The Underwriters reserve the right to withdraw, cancel or modify
such offer and to reject orders in whole or in part. It is expected that
delivery of the shares of Common Stock will be made on or about        , 1998 at
the office of Bear, Stearns & Co. Inc., 245 Park Avenue, New York, New York
10167.
                         ------------------------------
BEAR, STEARNS & CO. INC.
                             DAIN RAUSCHER WESSELS
                    A DIVISION OF DAIN RAUSCHER INCORPORATED
 
                                             HOWARD, WEIL, LABOUISSE, FRIEDRICHS
                                                INCORPORATED
 
               The date of this Prospectus is             , 1998
<PAGE>   3
 
     [map depicting Brigham's core areas of exploration activity and table of
certain operational and financial statistics by region and in total]
 
                            ------------------------
 
     CERTAIN PERSONS PARTICIPATING IN THIS OFFERING MAY ENGAGE IN TRANSACTIONS
THAT STABILIZE, MAINTAIN OR OTHERWISE AFFECT THE PRICE OF THE COMMON STOCK,
INCLUDING OVER-ALLOTMENT, STABILIZING AND SHORT-COVERING TRANSACTIONS IN SUCH
COMMON STOCK, AND THE IMPOSITION OF A PENALTY BID, DURING AND AFTER THE
OFFERING. FOR A DESCRIPTION OF THESE ACTIVITIES, SEE "UNDERWRITING."
 
                                        2
<PAGE>   4
 
                               PROSPECTUS SUMMARY
 
     The following summary should be read in conjunction with, and is qualified
in its entirety by, the detailed information and the Financial Statements and
notes thereto included elsewhere in this Prospectus. All references in this
Prospectus to "Brigham" or the "Company" include Brigham Exploration Company,
its subsidiaries and its predecessors and their subsidiaries. Unless otherwise
indicated, the information in this Prospectus assumes no exercise of the
Underwriters' over-allotment option. Certain terms relating to the oil and gas
industry are defined in "Glossary of Certain Oil and Gas Terms."
 
                                  THE COMPANY
 
     Brigham is an independent exploration and production company that applies
3-D seismic imaging and other advanced technologies to systematically explore
and develop onshore domestic natural gas and oil provinces. The Company focuses
its 3-D seismic activity in provinces where it believes 3-D technology may be
effectively applied and which Brigham believes offer relatively large potential
reserve volumes per well and per field, high potential production rates and
multiple producing objectives. The Company's exploration activities are
concentrated primarily in three core provinces: the Anadarko Basin of western
Oklahoma and the Texas Panhandle; the onshore Gulf Coast of Texas and Louisiana;
and West Texas. Brigham is accelerating its 3-D seismic and drilling activities
in the Anadarko Basin and the Gulf Coast and will continue to focus its
activities in those geologic trends of West Texas where it has achieved its best
results historically.
 
     The Company pioneered the acquisition of large scale, onshore 3-D seismic
surveys for exploration, obtaining extensive 3-D seismic data and experience in
capturing undiscovered natural gas and oil reserves. Through December 31, 1997,
Brigham had acquired 4,005 square miles (2.6 million acres) of 3-D seismic and
identified 1,170 potential drilling locations, of which the Company had drilled
370. The Company generates most of its exploratory projects and, therefore, has
the ability to retain a sizeable working interest to the extent that it decides
not to place interests with industry participants.
 
     From inception in 1990 through December 31, 1997, Brigham had drilled 324
exploratory and 46 development wells on its 3-D seismic generated prospects with
an aggregate 63% success rate and an average working interest of 24%. Utilizing
the capital it raised in its May 1997 initial public offering, the Company
increased the average working interest it retained in its wells during the
second half of 1997, retaining a 45% average working interest in the 36 wells
that it drilled. As of December 31, 1997, the Company had added approximately 93
Bcfe of net proved reserves (excluding revisions) to its reserve base,
approximately 72 net Bcfe of which were discovered by Brigham through its
systematic 3-D seismic exploration drilling activities. The Company's estimated
net proved reserves as of December 31, 1997 were 72.3 Bcfe having an aggregate
Present Value of Future Net Revenues of $69.2 million, compared to estimated net
proved reserves as of December 31, 1996 of 21.9 Bcfe having an aggregate Present
Value of Future Net Revenues of $44.5 million. The Company's net proved reserve
volumes at December 31, 1997 were 74% natural gas and 65% categorized as proved
developed reserves.
 
                               BUSINESS STRATEGY
 
     Brigham's business strategy is to achieve superior growth in shareholder
value through the application of its systematic exploration approach, which
emphasizes the integrated use of 3-D seismic imaging and other advanced
technologies to reduce drilling risks and finding costs. Since its inception in
1990, the Company has consistently achieved rapid growth in its acquisition of
3-D seismic data, identification of potential drilling locations, discovery of
proved reserves and production volumes.
 
     Brigham completed its initial public offering of common stock in May 1997,
raising approximately $24 million to fund the Company's accelerated 3-D seismic
acquisition and exploration drilling activities. Key elements of the Company's
growth strategy at its initial public offering and continuing today include: (i)
accelerating the rate at which it acquires 3-D seismic and identifies potential
drilling locations; (ii) increasing the working interests it retains in
exploration projects to capture a greater share of the reserves
 
                                        3
<PAGE>   5
 
that the Company discovers; (iii) identifying higher potential, higher impact
prospects; and (iv) accelerating the rate at which its 3-D seismic defined
locations are drilled.
 
     During the second half of 1997, the Company employed the capital raised in
its initial public offering to attain significant growth in each of its core
strategic objectives:
 
          Accelerated 3-D Seismic Acquisition. During 1997, Brigham acquired
     approximately 1,250 square miles of 3-D seismic, which increased the
     Company's aggregate 3-D seismic inventory 45% to approximately 4,000 square
     miles as of December 31, 1997. The overall level of 3-D seismic acquisition
     in 1997 represents the most active year in the Company's history, and
     approximately 85% of this increased 3-D seismic was acquired in its higher
     potential Anadarko Basin and Gulf Coast provinces.
 
          Increased Working Interest. In an effort to retain a greater portion
     of the value generated by its 3-D seismic exploration efforts, Brigham
     increased the average working interests it retained in its 1997 3-D seismic
     projects to 68% as compared with its average project working interest of
     24% in 1990 through 1996. As a result of the higher working interests and
     the accelerated acquisition of 3-D seismic, the Company acquired 845 net
     square miles of 3-D seismic in 1997 as compared with 780 cumulative net
     square miles acquired from 1990 through 1996.
 
          Higher Potential, Higher Impact Prospects. By focusing an increasing
     portion of its exploration activities in the more prolific Anadarko Basin,
     Brigham increased its average proved reserves discovered per net well
     drilled (including dry holes) to 1.2 Bcfe in 1997 from 0.7 Bcfe in 1996 and
     0.4 Bcfe in 1992 through 1995. In the Anadarko Basin alone, Brigham's
     average proved reserves discovered per net well drilled was 3.4 Bcfe in
     1997 compared with 1.8 Bcfe in 1996 and 2 Bcfe in 1994 through 1995.
     Contributing to these increases, the Company's Anadarko Basin drilling in
     1997 produced the two largest field discoveries in Brigham's history, which
     resulted in the discovery of approximately 52 Bcfe of gross proved reserves
     and provided the Company with several development drilling opportunities.
 
          Accelerated Drilling. Through its strategy of retaining higher working
     interests in its 3-D seismic projects and subsequent drilling, Brigham
     participated in the drilling of 28 net wells in 1997, a 76% increase from
     the approximate 16 net wells drilled by the Company in 1996. The Company
     achieved a 63% success rate on the 73 wells in its 1997 drilling program,
     consistent with Brigham's historical average success rate. A key factor
     contributing to its increased level of drilling activity was the Company's
     addition of personnel in engineering, land and administrative functions
     during 1997. These staff additions provided Brigham with the additional
     infrastructure required to increase its operating capabilities, enabling
     the Company to operate 37% of its gross wells and 64% of its net wells
     drilled in 1997.
 
     As a result of the combined effects of the Company's multi-pronged growth
strategy, Brigham generated net proved reserve additions of approximately 38
Bcfe through drilling in 1997, which represents approximately 175% of the
Company's year-end 1996 net proved reserves of approximately 22 Bcfe. In
addition to its drilling efforts in 1997, the Company acquired 21.5 Bcfe of net
proved reserves at an implied cost of $0.63 per proved Mcfe in its November 1997
purchase of certain properties in and adjacent to its West Bradley project area
in its Anadarko Basin province. Brigham believes this acquisition will enable it
to further build its inventory of potential drilling locations over the
historically prolific Carter Knox anticline in the Anadarko Basin through a 3-D
seismic shoot planned for 1998.
 
     Primarily through its exploration efforts, the Company increased its net
production volumes 52% to 3.1 Bcfe in 1997 from 2.1 Bcfe in 1996. As further
evidence of the Company's acceleration efforts subsequent to its May 1997
initial public offering, Brigham increased its average net daily production
volumes from 6.6 MMcfe in the second quarter 1997 to 15.9 MMcfe in the first
quarter 1998 at a compound annual growth rate of 34% per quarter.
 
     Based on the results that the Company has achieved from its growth strategy
since its initial public offering, Brigham intends with the proceeds from the
Offering to increase its exploration activities in 1998 to take advantage of
opportunities currently available to further accelerate the Company's growth. As
a result, the Company has increased its 1998 capital budget for net seismic,
land and drilling expenditures to
 
                                        4
<PAGE>   6
 
approximately $68 million from the $52 million originally budgeted. The
Company's current 1998 capital budget contemplates additional expenditures for
3-D seismic acquisition due to increased working interests in its planned 1998
projects, an increase in budgeted drilling expenditures in the Anadarko Basin
and the Gulf Coast provinces and a reduction in planned drilling activity in
West Texas in part due to recent declines in oil prices. The Company intends to
continue to retain higher working interests in its 3-D seismic projects in the
Anadarko Basin and the onshore Gulf Coast. By increasing its working interests
to in excess of 75% in the majority of its current and planned seismic projects,
Brigham expects to further accelerate its growth not only by retaining a greater
portion of the reserves its discovers, but also by increasing its ability to
control the timing of the drilling of its exploration projects and therefore
helping to accelerate its drilling pace. The Company's current 1998 budget
consists of 106 gross (56 net) wells, compared with the 100 gross (42 net) wells
previously budgeted for 1998. This increase in anticipated 1998 drilling is the
result of an increase in planned drilling of higher working interest wells in
the Anadarko Basin and the Gulf Coast offset by a reduction in planned drilling
activity in West Texas.
 
                             COMPETITIVE ADVANTAGES
 
     Brigham believes that its knowledge base, personnel and technology provide
it with the following competitive advantages to capture undiscovered natural gas
and oil reserves.
 
          3-D Seismic Knowledge Base. From 1990 through 1997, the Company
     acquired 4,005 square miles of 3-D seismic and drilled 370 wells in over 20
     geologic trends in seven basins and seven states. With the resulting
     knowledge of the application of 3-D seismic to different geologic trends,
     the Company has refined its exploration techniques and identified
     exploration areas where it believes 3-D seismic can reduce risks and
     enhance returns on its investments.
 
          Technological Expertise. Brigham's 19 explorationists collectively
     have over 300 years of experience, including approximately 85 years of
     experience using computer aided exploration ("CAEX") workstations, and have
     expertise in many geologic trends.
 
          Project Generation and Control. Brigham is not dependent on third
     parties for its project flow, having generated approximately 90% of its 3-D
     seismic exploration projects. With the resulting project control, the
     Company is able to manage the predrilling exploration phases and can
     determine the level of working interest it retains and the extent to which
     it manages drilling and post-drilling operations.
 
          Numerous Potential Drilling Locations. As of December 31, 1997, the
     Company had identified 1,170 3-D defined potential drilling locations in
     historically productive geologic trends, of which 370 had been drilled. The
     Company currently anticipates drilling 106 of these locations (56 net) in
     1998 at an aggregate cost of approximately $47 million.
 
          Pioneering Innovations. In 1990 the Company pioneered the assemblage
     of large scale onshore 3-D seismic projects and the use of pre-seismic
     lease options for the systematic exploration of proven natural gas and oil
     provinces. Subsequent innovations include the Company's 3-D seismic
     acquisition and processing alliances and creative industry trade structures
     to financially leverage its drilling program.
 
                         PRIMARY EXPLORATION PROVINCES
 
     Brigham's exploration activities are concentrated primarily in three core
provinces: the Anadarko Basin of western Oklahoma and the Texas Panhandle; the
onshore Gulf Coast of Texas and Louisiana; and West Texas. Brigham is
accelerating 3-D seismic activity in the Anadarko Basin and the Gulf Coast and
will continue such activity in those geologic trends of the West Texas region
where it has achieved its best results historically. Brigham is focusing its 3-D
seismic exploration efforts in provinces where it believes 3-D seismic
technology may be effectively applied and which the Company believes offer
relatively large potential reserve volumes per well and per field, high
potential production rates and multiple producing objectives.
 
     Although the Company is acquiring 3-D seismic within the provinces listed
below and has identified approximately 800 potential drilling locations yet to
be drilled in those provinces, there can be no assurance
                                        5
<PAGE>   7
 
that any of the seismic will be acquired or will generate additional drilling
locations or that any potential drilling locations will be drilled at all or
within the expected time frame. The final determination with respect to the
drilling of any well, including those currently budgeted, will depend on a
number of factors, including (i) the results of exploration efforts and the
review and analysis of the seismic, (ii) the availability of sufficient capital
resources by the Company and other participants for drilling prospects, (iii)
economic and industry conditions at the time of drilling, including prevailing
and anticipated prices for natural gas and oil and the availability of drilling
rigs and crews, (iv) the financial resources and results of the Company and (v)
the availability of leases on reasonable terms and permitting for the potential
drilling location. There can be no assurance that the budgeted wells will, if
drilled, encounter reservoirs of commercial quantities of natural gas or oil.
 
<TABLE>
<CAPTION>
                                                                                             CURRENT 1998 CAPITAL BUDGET(1)
                                                                                      --------------------------------------------
                             3-D SEISMIC       3-D SEISMIC                UNDRILLED                      CAPITAL EXPENDITURES
                           DATA ACQUIRED/          DATA         GROSS     POTENTIAL                              ($MM)
                          INTERPRETED AS OF    BUDGETED TO      WELLS     DRILLING       WELLS       -----------------------------
                              12/31/97        BE ACQUIRED IN   DRILLED    LOCATIONS     BUDGETED       NET
                             (GROSS SQ.        1998 (GROSS     THROUGH      AS OF     ------------   SEISMIC     NET
PROVINCE                       MILES)           SQ. MILES)     12/31/97   12/31/97    GROSS   NET    & LAND    DRILLING   TOTAL(2)
--------                  -----------------   --------------   --------   ---------   -----   ----   -------   --------   --------
<S>                       <C>                 <C>              <C>        <C>         <C>     <C>    <C>       <C>        <C>
Anadarko Basin..........   1,515/1,195             550            55         364        62    32.0    $23.0     $27.5      $50.5
Gulf Coast..............     566/325               400            11         110        19    13.0     (3.0)     14.0       11.0
West Texas..............   1,649/1,600              30           287         302        24    11.0      1.5       5.0        6.5
Others(3)...............     275/275                --            17          24         1     0.2       --       0.2        0.2
                             -----------           ---           ---         ---       ---    ----    -----     -----      -----
        Total...........   4,005/3,395             980           370         800       106    56.2    $21.5     $46.7      $68.2
                             ===========           ===           ===         ===       ===    ====    =====     =====      =====
</TABLE>
 
---------------
 
(1) Prepared as of May 27, 1998.
 
(2) 3-D seismic and land acquisition costs and drilling expenditures.
 
(3) Colorado, Kansas and Montana.
 
     Anadarko Basin. The Anadarko Basin is a prolific natural gas province that
the Company believes has been relatively under explored, particularly with
regard to deep, high potential objectives. The Anadarko Basin contains numerous
historically elusive stratigraphic targets, such as the Red Fork, Morrow and
Springer channel sands, and structural targets, such as the Hunton and Arbuckle
carbonates, which are well-suited to 3-D seismic imaging. In some cases, these
objectives have produced in excess of 30 Bcf of natural gas from a single well
at rates up to 30 MMcf of natural gas per day.
 
     The Company has assembled an extensive digital data base in this province,
including geologic studies, basin wide geologic tops, production data, well
data, geographic data and over 8,400 miles of 2-D seismic. Working with its team
of in-house geologists and supplemented by consulting geologists, the Company's
explorationists integrate this data with their extensive expertise and knowledge
base to generate 3-D projects in the Anadarko Basin.
 
     As of December 31, 1997, the Company had acquired or was acquiring 1,515
square miles (969,600 acres) in 30 projects in the Anadarko Basin. The Company
anticipates acquiring 550 square miles (352,000 acres) of additional 3-D seismic
in this province in 1998. As of December 31, 1997, Brigham had completed 44
wells in 55 attempts (80% success rate) in the Anadarko Basin and had found
cumulative proved reserves of 44 net Bcfe. In 1997, the Company completed 19
wells in 23 attempts in the Anadarko Basin with an average working interest of
39%, adding 31 net Bcfe of proved reserves. In addition, the Company acquired
21.5 net Bcfe of proved reserves in this region in November 1997. As of December
31, 1997, the Company had 364 3-D seismic delineated potential drilling
locations in the Anadarko Basin, of which the Company intends to drill 62 gross
(32 net) wells in 1998.
 
     Gulf Coast. The onshore Gulf Coast region of Texas and Louisiana is a high
potential, multi-pay province that lends itself to 3-D seismic exploration due
to its substantial structural and stratigraphic complexity. The Company has
assembled a digital data base including geographical, production, geophysical
and geological information that the Company evaluates on its CAEX workstations.
Working with consulting regional geologists, the Company's explorationists
integrate this data with their extensive expertise and
 
                                        6
<PAGE>   8
 
knowledge base to generate 3-D seismic projects in the Gulf Coast. Brigham's
commitment to this province is evidenced by the Company's staff additions, the
opening of its Houston office and the addition of ten new 3-D seismic projects
in 1996 and 1997.
 
     The Company anticipates that its increased project assemblage and 3-D
seismic acquisition activity in the Gulf Coast will generate accelerated
drilling in this province in 1998 and 1999. The Company is currently assembling
projects in the Expanded Wilcox and Expanded Vicksburg trends in South Texas,
the Miocene trend in South Texas and South Louisiana, and the Lower and Middle
Frio trends of South Texas.
 
     As of December 31, 1997, the Company had acquired or was acquiring 566
square miles (362,400 acres) of 3-D seismic in seven projects in the onshore
Gulf Coast province. The Company anticipates acquiring 400 square miles (256,000
acres) of additional 3-D seismic in this province in 1998. As of December 31,
1997, Brigham had completed 8 wells in 11 attempts (73% success rate) in the
Gulf Coast and had found cumulative proved reserves of 3 net Bcfe. In 1997, the
Company completed seven wells in 10 attempts with an average working interest of
9% adding 3 net Bcfe of proved reserves. As of December 31, 1997, the Company
had 110 3-D seismic delineated potential drilling locations in the Gulf Coast
province, of which the Company intends to drill 19 gross (13 net) wells in 1998.
 
     West Texas. The Company's 3-D seismic drilling activity in the West Texas
region has been focused in the Horseshoe Atoll, the Midland Basin and the
Eastern Shelf of the Permian Basin and the Hardeman Basin. The Company plans to
continue drilling its locations in these areas. Recently the Company initiated
an exploration program in the Delaware Basin and increased its activity in
portions of geologic trends that the Company believes offer greater potential
for lower finding costs and higher returns, including the Ellenberger and
Devonian formations of the Delaware Basin and the Fusselman formation of the
Midland Basin.
 
     As of December 31, 1997, the Company had acquired or was acquiring 1,649
square miles (1,055,360 acres) in 74 projects in the West Texas region. The
Company anticipates acquiring 30 square miles (19,200 acres) of additional 3-D
seismic in this region in 1998. As of December 31, 1997, Brigham had completed
180 wells in 287 attempts (63% success rate) in the West Texas region and had
found cumulative proved reserves of 24 net Bcfe. In 1997, the Company completed
19 wells in 34 attempts with an average working interest of 45%, adding 4 net
Bcfe of proved reserves. As of December 31, 1997, the Company had 302 3-D
seismic delineated potential drilling locations in the West Texas region, of
which the Company intends to drill 24 gross (11 net) wells in 1998.
 
                                        7
<PAGE>   9
 
                                  THE OFFERING
 
<TABLE>
<CAPTION>
<S>                                                    <C>
Common Stock Offered by the Company..................  3,400,000 shares
Common Stock to be Outstanding after the Offering....  15,653,574 shares(1)
Use of Proceeds by the Company.......................  The net proceeds of the Offering will be used to fund
                                                       the Company's accelerated exploration and development
                                                       activities, and in the interim for repayment of
                                                       outstanding indebtedness of approximately $
                                                       million. See "Use of Proceeds."
The Nasdaq Stock Market(SM) Symbol...................  "BEXP"
</TABLE>
 
---------------
 
(1) Does not include 935,987 shares of Common Stock issuable, subject to
    vesting, upon exercise of outstanding employee stock options with an average
    exercise price of $7.61 per share. See
    "Management -- Executive Compensation" and "Capitalization."
 
                                  RISK FACTORS
 
     Any investment in the Common Stock involves a high degree of risk. For a
discussion of certain risks that a potential investor should carefully evaluate
prior to making an investment in the Common Stock, see "Risk Factors."
 
                                        8
<PAGE>   10
 
                             SUMMARY FINANCIAL DATA
                    (IN THOUSANDS, EXCEPT PER SHARE AMOUNTS)
 
     The following table sets forth selected financial data of the Company. The
data for the three years ended December 31, 1997 has been derived from the
financial statements appearing elsewhere in this Prospectus. The data for the
two years ended December 31, 1994 has been derived from financial statements not
appearing in this Prospectus. The consolidated financial data at March 31, 1998
and for the three months ended March 31, 1998 and March 31, 1997 have been
derived from the condensed consolidated financial statements of the Company
which, in the opinion of management, include all adjustments, consisting only of
normal adjustments, necessary for a fair presentation of the results for the
periods. The results for the three months ended March 31, 1998 are not
necessarily indicative of the results to be expected for the full year. The
information should be read in conjunction with the Management's Discussion and
Analysis of Financial Condition and Results of Operations and the Financial
Statements and notes thereto included elsewhere in this Prospectus.
 
<TABLE>
<CAPTION>
                                                                                                         THREE MONTHS
                                                                                                             ENDED
                                                             YEAR ENDED DECEMBER 31,                       MARCH 31,
                                                --------------------------------------------------    -------------------
                                                 1993       1994      1995       1996       1997       1997        1998
                                                -------    -------   -------   --------   --------    -------    --------
<S>                                             <C>        <C>       <C>       <C>        <C>         <C>        <C>
STATEMENT OF OPERATIONS DATA:
  Revenues:
    Natural gas and oil sales.................  $   937    $ 2,565   $ 3,578   $  6,141   $  9,184    $ 2,136    $  3,143
    Workstation revenue.......................      467        815       635        627        637        164         114
                                                -------    -------   -------   --------   --------    -------    --------
        Total revenues........................    1,404      3,380     4,213      6,768      9,821      2,300       3,257
  Costs and expenses:
    Lease operating...........................      111        491       761        726      1,151        206         414
    Production taxes..........................       47        126       165        362        549        127         188
    General and administrative................    1,433      1,785     1,897      2,199      3,570        702       1,154
    Depletion of natural gas and oil
      properties..............................    4,371(1)   1,104     1,626      2,323      2,732        687       1,267
    Depreciation and amortization.............      406        561       533        487        582        137         178
                                                -------    -------   -------   --------   --------    -------    --------
        Total costs and expenses..............    6,368      4,067     4,982      6,097      8,584      1,859       3,201
                                                -------    -------   -------   --------   --------    -------    --------
  Operating income (loss).....................   (4,964)      (687)     (769)       671      1,237        441          56
  Other income (expense):
    Interest income...........................        6         56       128         52        145         18          37
    Interest expense..........................     (105)      (668)     (936)    (1,173)    (1,190)      (390)     (1,022)
                                                -------    -------   -------   --------   --------    -------    --------
        Total other income (expense)..........      (99)      (612)     (808)    (1,121)    (1,045)      (372)       (985)
                                                -------    -------   -------   --------   --------    -------    --------
  Net income (loss) before income taxes.......   (5,063)    (1,299)   (1,577)      (450)       192         69        (929)
  Income tax (expense) benefit, net...........       --         --        --         --     (1,228)(2)  (4,964)(2)      314
                                                -------    -------   -------   --------   --------    -------    --------
        Net loss..............................  $(5,063)   $(1,299)  $(1,577)  $   (450)  $ (1,036)   $(4,895)   $   (615)
                                                =======    =======   =======   ========   ========    =======    ========
  Net loss per share -- basic/diluted.........  $ (0.57)   $ (0.15)  $ (0.18)  $  (0.05)  $  (0.09)   $ (0.55)   $  (0.05)
  Weighted average shares outstanding --
    basic/diluted.............................    8,929      8,929     8,929      8,929     11,081      8,929      12,254
STATEMENT OF CASH FLOWS DATA:
  Net cash provided by (used in) operating
    activities................................  $  (730)   $   626   $ 1,383   $  3,710   $  9,806    $ 4,224    $ (2,796)
  Net cash used in investing activities.......   (6,983)    (5,463)   (8,005)   (11,796)   (57,300)    (7,301)    (13,136)
  Net cash provided by financing activities...    7,839      4,634     7,724      7,731     47,748      2,794      16,031
OTHER FINANCIAL DATA:
  Capital expenditures........................  $ 6,632    $ 5,445   $ 7,935   $ 13,612   $ 57,170    $ 6,830    $ 12,993
  EBITDA(3)...................................     (187)       978     1,390      3,481      4,551      1,265       1,501
  Operating cash flow(4)......................     (286)       366       582      2,360      3,506        893         622
</TABLE>
 
<TABLE>
<CAPTION>
                                                                AS OF MARCH 31, 1998
                                                              -------------------------
                                                               ACTUAL    AS ADJUSTED(5)
                                                              --------   --------------
<S>                                                           <C>        <C>
BALANCE SHEET DATA:
  Cash and cash equivalents.................................  $  1,800      $
  Natural gas and oil properties, at cost, net..............    96,676
  Total assets..............................................   107,508
  Notes payable.............................................    50,000
  Stockholders' equity......................................    42,742
</TABLE>
 
---------------
 
(1) Includes a capitalized ceiling impairment charge of $3.3 million in 1993.
 
(2) 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 February 27, 1997, the date of the Exchange. During the
    fourth quarter of
 
                                        9
<PAGE>   11
 
    1997, the Company elected to record a step-up in basis of its assets for tax
    purposes as a result of the Exchange. Related to this election, the Company
    recorded a $3.8 million deferred income tax benefit, resulting in a net $1.2
    million ($.10 per share) non-cash deferred income tax charge for the year
    ended December 31, 1997. See Note 2 of Notes to the December 31, 1997
    Consolidated Financial Statements. See "The Company."
 
(3) EBITDA represents net income (loss) plus income taxes, net interest expense
    and depreciation, depletion and amortization expense. EBITDA should not be
    considered in isolation or as a substitute for net income, cash flows from
    operating activities or any other measure of financial performance prepared
    in accordance with generally accepted accounting principles or as a measure
    of a company's profitability or liquidity.
 
(4) Operating cash flow represents net income (loss) plus depreciation,
    depletion and amortization ("DD&A") expenses, deferred income taxes and
    other non-cash items. Operating cash flow should not be considered in
    isolation or as a substitute for net income, cash flows from operating
    activities or any other measure of financial performance prepared in
    accordance with generally accepted accounting principles or as a measure of
    a company's profitability or liquidity.
 
(5) As adjusted to give effect to the Offering and the application of the
    estimated $     million net proceeds therefrom to the Company. See "Use of
    Proceeds" and "Capitalization."
 
                                       10
<PAGE>   12
 
                       SUMMARY RESERVE AND OPERATING DATA
                  (Dollars in thousands, except per Mcfe data)
 
<TABLE>
<CAPTION>
                                                                                        THREE MONTHS
                                                                                           ENDED
                                             YEAR ENDED DECEMBER 31,                     MARCH 31,
                                --------------------------------------------------    ----------------
                                 1993      1994       1995      1996(1)     1997       1997      1998
                                ------    -------    -------    -------    -------    ------    ------
<S>                             <C>       <C>        <C>        <C>        <C>        <C>       <C>
3-D SEISMIC ACQUIRED:
  Gross square miles..........     908        423        311        655      1,243       458       196
  Net square miles............     272        114         90        241        845       255       175
  Average project working
    interest..................      30%        27%        29%        37%        68%       56%       89%
WELLS DRILLED:
  Gross wells drilled.........      52         73         78         68         73        13        13
  Net wells drilled...........     9.2       16.8       18.5       16.0       28.0       2.6       6.0
  Average drilling working
    interest..................      18%        23%        24%        24%        38%       20%       46%
ESTIMATED PROVED RESERVES (AT
  YEAR END)(2):
  Natural gas (MMcf)..........     227      3,579      4,257     10,257     53,230
  Oil (MBbls).................     336      1,022      1,672      1,940      3,181
  Natural gas equivalent
    (MMcfe)...................   2,243      9,711     14,289     21,897     72,316
  Present Value of Future Net
    Revenues..................  $3,158    $10,240    $18,222    $44,506    $69,249
  Percent natural gas(3)......      10%        37%        30%        47%        74%
  Percent proved
    developed(3)..............     100%        76%        80%        67%        65%
NET PROVED RESERVE
  ADDITIONS(4):
  All sources (MMcfe).........   1,987      8,527      8,885     13,996     59,313
  Excluding acquisitions
    (MMcfe)...................   1,987      8,527      8,885     13,718     38,131
RESERVE REPLACEMENT RATIO(5):
  All sources.................     553%       851%       667%       679%     1,897%
  Excluding acquisitions......     553%       851%       667%       666%     1,220%
NET PRODUCTION VOLUMES:
  Natural gas (MMcf)..........      59        165        272        698      1,382       243       740
  Oil (MBbls).................      50        140        177        227        291        63       115
  Natural gas equivalent
    (MMcfe)...................     359      1,002      1,332      2,060      3,126       623     1,431
  Percent natural gas.........      16%        16%        20%        34%        44%       39%       52%
PER MCFE DATA:
  Natural gas and oil sales...  $ 2.61    $  2.56    $  2.69    $  2.98    $  2.94    $ 3.43    $ 2.20
  Workstation revenue.........    1.30        .81        .48        .30        .20       .26       .08
  Lease operating expenses....    (.31)      (.49)      (.57)      (.35)      (.37)     (.33)     (.29)
  Production taxes............    (.13)      (.13)      (.12)      (.18)      (.18)     (.20)     (.13)
  General and administrative
    expenses..................   (3.99)     (1.78)     (1.42)     (1.07)     (1.14)    (1.13)     (.81)
                                ------    -------    -------    -------    -------    ------    ------
    Operating margin..........  $ (.52)   $   .97    $  1.06    $  1.68    $  1.45    $ 2.03    $ 1.05
                                ======    =======    =======    =======    =======    ======    ======
</TABLE>
 
---------------
 
(1) Net of a sale by the Company in January 1996 of its interest in certain
    properties that accounted for 299 MMcf of natural gas and 272 MBbls of oil
    (1,931 MMcfe of proved reserves) as of December 31, 1995.
 
(2) The estimates of reserve and present value data have been prepared in
    accordance with the SEC's guidelines by Cawley, Gillespie & Associates,
    Inc., the Company's independent petroleum consultants ("Cawley Gillespie").
    Cawley Gillespie's letter summarizing its December 31, 1997 reserve report
    is attached hereto as Appendix A to this Prospectus.
 
(3) Based on volumes.
 
(4) Excludes revisions of previous estimates.
 
(5) Net proved reserve additions divided by the Company's net production volumes
    for the period.
 
                                       11
<PAGE>   13
 
                DISCLOSURE REGARDING FORWARD-LOOKING STATEMENTS
 
     This Prospectus includes statements that are "forward-looking statements"
within the meaning of Section 27A of the Securities Act of 1933 (the "Securities
Act") and Section 21E of the Securities Exchange Act of 1934, including
statements regarding estimated future net revenues from natural gas and oil
reserves and the present value thereof, planned capital expenditures (including
the amount and nature thereof), increases in natural gas and oil production, the
number of wells the Company anticipates drilling through 1998 and the Company's
financial position, business strategy and other plans and objectives for future
operations. Although the Company believes that the expectations reflected in
these forward-looking statements are reasonable, there can be no assurance that
the actual results or developments anticipated by the Company will be realized
or, even if substantially realized, that they will have the expected effects on
its business or operations. Among the factors that could cause actual results to
differ materially from the Company's expectations are general economic
conditions, inherent uncertainties in interpreting engineering data, operating
hazards, delays or cancellations of drilling operations for a variety of
reasons, competition, fluctuations in natural gas and oil prices, the ability of
the Company to successfully integrate the business and operations of acquired
companies, government regulations and other factors disclosed under "Risk
Factors" and elsewhere in this Prospectus. All subsequent oral and written
forward looking statements attributable to the Company or persons acting on its
behalf are expressly qualified in their entirety by these factors. The Company
assumes no obligation to update any of these statements.
 
                                  RISK FACTORS
 
     Any investment in the Common Stock involves a high degree of risk.
Prospective purchasers of the Common Stock should carefully consider the risk
factors set forth below, as well as the other information contained in this
Prospectus.
 
DEPENDENCE ON EXPLORATORY DRILLING ACTIVITIES
 
     The Company's revenues, operating results and future rate of growth are
highly dependent upon the success of its exploratory drilling program, which
will be funded in part with the proceeds of the Offering. Exploratory drilling
involves numerous risks, including the risk that no commercially productive
natural gas or oil reservoirs will be encountered. The cost of drilling,
completing and operating wells is often uncertain, and drilling operations may
be curtailed, delayed or canceled as a result of a variety of factors, including
unexpected drilling conditions, pressure or irregularities in formations,
equipment failures or accidents, adverse weather conditions, compliance with
governmental requirements and shortages or delays in the availability of
drilling rigs and the delivery of equipment. Despite the use of 3-D seismic and
other advanced technologies, exploratory drilling remains a speculative
activity. Even when fully utilized and properly interpreted, 3-D seismic and
other advanced technologies only assist geoscientists in identifying subsurface
structures and do not enable the interpreter to know whether hydrocarbons are in
fact present in those structures. In addition, the use of 3-D seismic and other
advanced technologies requires greater predrilling expenditures than traditional
drilling strategies, and the Company could incur losses as a result of such
expenditures. The Company's future drilling activities may not be successful.
There can be no assurance that the Company's overall drilling success rate or
its drilling success rate for activity within a particular province will not
decline. Unsuccessful drilling activities could have a material adverse effect
on the Company's results of operations and financial condition. The Company
often gathers 3-D seismic over large areas. The Company's interpretation of data
delineates those portions of an area desirable for drilling. Therefore, the
Company may choose not to acquire option and lease rights prior to acquiring
seismic and, in many cases, the Company may identify a drilling location before
seeking option or lease rights in the location. Although the Company has
identified numerous potential drilling locations, there can be no assurance that
they will ever be leased or drilled or that natural gas or oil will be produced
from these or any other potential drilling locations.
 
                                       12
<PAGE>   14
 
VOLATILITY OF NATURAL GAS AND OIL PRICES
 
     The Company's revenues, operating results and future rate of growth are
highly dependent upon the prices received for the Company's natural gas and oil.
Historically, the markets for natural gas and oil have been volatile and are
likely to continue to be volatile in the future. Various factors beyond the
control of the Company will affect sales prices of its natural gas and oil,
including worldwide and domestic supplies of natural gas and oil, the ability of
the members of the Organization of Petroleum Exporting Countries to agree to and
maintain oil price and production controls, political instability or armed
conflict in oil-producing regions, the price and level of foreign imports, the
level of consumer demand, the price and availability of alternative fuels, the
availability of pipeline capacity, the availability and cost of drilling rigs,
weather conditions, domestic and foreign governmental regulations and taxes, and
the overall economic environment. During 1997, the high and low prices for
natural gas on the NYMEX were $3.79 per MMBtu and $1.78 per MMBtu and the high
and low prices for oil on the NYMEX were $26.26 per Bbl and $17.60 per Bbl. From
January 1, 1998 through May 22, 1998, the high and low prices for natural gas on
the NYMEX were $2.64 per MMBtu and $2.00 per MMBtu and the high and low prices
for oil on the NYMEX were $17.82 per Bbl and $13.21 per Bbl. It is impossible to
predict future natural gas and oil price movements with certainty. Declines in
natural gas and oil prices may materially adversely affect the Company's
business, financial condition and results of operations. Lower natural gas and
oil prices also may reduce the amount of natural gas and oil that the Company
can produce economically. Any significant decline in the price of oil or natural
gas would adversely affect the Company's revenues and operating income and may
require a reduction in the carrying value of the Company's natural gas and oil
properties. See "Risk Factors -- Uncertainty of Reserve Information and Future
Net Revenue Estimates," "Management's Discussion and Analysis of Financial
Condition and Results of Operations -- Other Matters" and "Business and
Properties -- Competition."
 
     During the quarter ended March 31, 1998, the NYMEX crude oil price ranged
from $17.82 to $13.21 per barrel. This decline in prices is generally thought to
be caused primarily by an oversupply of crude oil inventory created, in part, by
an unusually warm winter in the United States and Europe, an announced increase
in crude oil production quotas for OPEC countries and a possible decline in
demand in certain Asian markets. If such a decline in the NYMEX crude oil price
worsens or persists for a protracted period, it would adversely affect the
Company's revenues, net income and cash flows from operations. Also, if these
prices maintain their present level for an extended time period or decline
further, the Company may delay or postpone certain of its capital projects.
 
RISKS ASSOCIATED WITH MANAGEMENT OF GROWTH AND IMPLEMENTATION OF GROWTH STRATEGY
 
     The Company's rapid growth has placed, and is expected to continue to
place, a significant strain on the Company's financial, technical, operational
and administrative resources. As the Company increases the number of projects it
is evaluating or in which it is participating, there will be additional demands
on the Company's financial, technical, operational and administrative resources.
In addition, the Company has only limited experience operating and managing
field operations, including drilling, and there can be no assurances that the
Company will be successful in doing so. Any increase in the Company's activities
as an operator will increase its exposure to operating hazards. See "Risk
Factors -- Operating Hazards and Uninsured Risks." The failure to continue to
upgrade the Company's technical, administrative, operating and financial control
systems or the occurrence of unexpected expansion difficulties, including
difficulties in recruiting and retaining geophysicists, geologists, engineers
and sufficient numbers of qualified personnel to enable the Company to expand
its role in the drilling and production phase, or the reduced availability
and/or increased costs of seismic gathering, drilling or other services in the
face of growing demand, could have a material adverse effect on the Company's
business, financial condition and results of operations.
 
SUBSTANTIAL CAPITAL REQUIREMENTS
 
     The Company makes and will continue to make substantial capital
expenditures in its exploration and development projects. The Company intends to
finance these capital expenditures with the net proceeds from the Offering, cash
flow from operations and its existing financing arrangements. Additional
financing may be required in the future to fund the Company's developmental and
exploratory drilling and 3-D seismic
                                       13
<PAGE>   15
 
acquisition activities. No assurance can be given as to the availability or
terms of any such additional financing that may be required or that financing
will continue to be available under the existing or new financing arrangements.
If additional capital resources are not available to the Company, its drilling
and other activities may be curtailed and its business, financial condition and
results of operations could be materially adversely affected. See "Use of
Proceeds" and "Management's Discussion and Analysis of Financial Condition and
Results of Operations -- Liquidity and Capital Resources."
 
HISTORICAL OPERATING LOSSES AND VARIABILITY OF OPERATING RESULTS
 
     The Company had net losses of approximately $5.1 million in 1993, $1.3
million in 1994, $1.6 million in 1995, $450,000 in 1996, $1.0 million (including
a net $1.2 million non-cash deferred income tax charge incurred in connection
with the Company's conversion from a partnership to a corporation) in 1997 and
$615,000 in the first three months of 1998. The Company has incurred net losses
in each year of operation, and there can be no assurance that the Company will
be profitable in the future. At March 31, 1998, the Company's accumulated
deficit was $589,000 and its total stockholders' equity was $42.7 million. In
addition, the Company's future operating results may fluctuate significantly
depending upon a number of factors, including industry conditions, prices of
natural gas and oil, rates of drilling success, rates of production from
completed wells and the timing of capital expenditures. This variability could
have a material adverse effect on the Company's business, financial condition
and results of operations. In addition, any failure or delay in the realization
of expected cash flows from operating activities could limit the Company's
ability to invest and participate in economically attractive projects. See
"Selected Financial Data" and "Management's Discussion and Analysis of Financial
Condition and Results of Operations."
 
RESERVE REPLACEMENT RISK
 
     In general, production from natural gas and oil properties declines as
reserves are depleted, with the rate of decline depending on reservoir
characteristics. Except to the extent the Company conducts successful
exploration and development activities or acquires properties containing proved
reserves, or both, the proved reserves of the Company will decline as reserves
are produced. The Company's future natural gas and oil production is highly
dependent upon its ability to economically find, develop or acquire reserves in
commercial quantities. The business of exploring for or developing reserves is
capital intensive. To the extent cash flow from operations is reduced and
external sources of capital become limited or unavailable, the Company's ability
to make the necessary capital investment to maintain or expand its asset base of
natural gas and oil reserves would be impaired. The Company participates in a
substantial percentage of its wells as a non-operator. The failure of an
operator of the Company's wells to adequately perform operations, or an
operator's breach of the applicable agreements, could adversely impact the
Company. In addition, there can be no assurance that the Company's future
exploration and development activities will result in additional proved reserves
or that the Company will be able to drill productive wells at acceptable costs.
Furthermore, although the Company's revenues could increase if prevailing prices
for natural gas and oil increase significantly, the Company's finding and
development costs could also increase. See "Management's Discussion and Analysis
of Financial Condition and Results of Operations."
 
OPERATING HAZARDS AND UNINSURED RISKS
 
     The Company's operations are subject to hazards and risks inherent in
drilling for and producing and transporting natural gas and oil, such as fires,
natural disasters, explosions, encountering formations with abnormal pressures,
blowouts, cratering, pipeline ruptures and spills, any of which can result in
the loss of hydrocarbons, environmental pollution, personal injury claims and
other damage to properties of the Company and others. As protection against
operating hazards, the Company maintains insurance coverage against some, but
not all, potential losses. The Company may elect to self-insure if management
believes that the cost of insurance, although available, is excessive relative
to the risks presented. The Company generally maintains insurance for the
hazards and risks inherent in drilling for and producing and transporting
natural gas and oil and believes this insurance is adequate. Nevertheless, the
occurrence of an event that is not covered, or not fully covered, by insurance
could have a material adverse effect on the Company's business, financial
condition
 
                                       14
<PAGE>   16
 
and results of operations. In addition, pollution and environmental risks
generally are not fully insurable. See "Business and Properties -- Operating
Hazards and Uninsured Risks."
 
UNCERTAINTY OF RESERVE INFORMATION AND FUTURE NET REVENUE ESTIMATES
 
     Numerous uncertainties are inherent in estimating quantities of proved
reserves and their values, including many factors beyond the Company's control.
The reserve information in this Prospectus is an estimate only. Although the
Company believes these estimates are reasonable, reserve estimates are imprecise
and are expected to change as additional information becomes available.
Estimates of natural gas and oil reserves by necessity are projections based on
engineering data, and uncertainties are inherent in the interpretation of this
data, the projection of future rates of production and the timing of development
expenditures. Reserve engineering is a subjective process of estimating
underground accumulations of natural gas and oil that are difficult to measure.
The accuracy of any reserve estimate is a function of the quality of available
data, engineering and geologic interpretation, and judgment. Estimates of
economically recoverable natural gas and oil reserves and of future net cash
flows depend upon a number of variable factors and assumptions, such as
historical production from the area compared with production from other
producing areas, the assumed effects of regulations by governmental agencies,
and assumptions concerning future natural gas and oil prices, future operating
costs, severance and excise taxes, development costs and workover and remedial
costs, all of which may in fact vary considerably from actual results. For these
reasons, estimates of the economically recoverable quantities of natural gas and
oil attributable to any particular group of properties, classifications of
reserves based on risk of recovery, and estimates of the future net cash flows
may vary substantially. Moreover, there can be no assurance that the Company's
reserves will ultimately be produced or that the Company's proved undeveloped
reserves will be developed within the periods anticipated. Any significant
variance in the assumptions could materially affect the estimated quantity and
value of the Company's reserves. Actual production, revenues and expenditures
with respect to the Company's reserves will likely vary from estimates, and such
variances may be material. See "Business and Properties -- Natural Gas and Oil
Reserves."
 
     The Present Value of Future Net Revenues referred to in this Prospectus
should not be construed as the current market value of the estimated natural gas
and oil reserves attributable to the Company's properties. In accordance with
applicable requirements of the SEC, the estimated discounted future net cash
flows from proved reserves are generally based on prices and costs as of the
date of the estimate, whereas actual future prices and costs may be materially
higher or lower. At December 31, 1997, the date of the estimate of the Company's
reserves and present value data, the prices of natural gas and oil on the NYMEX
were $2.26 per MMBtu and $17.64 per Bbl, respectively. At May 22, 1998, the
prices were $2.18 per MMBtu and $14.47 per Bbl, respectively. Actual future net
cash flows also will be affected by factors such as the amount and timing of
actual production, supply and demand for natural gas and oil, curtailments or
increases in consumption by gas purchasers, and changes in governmental
regulations or taxation. The timing of actual future net cash flows from proved
reserves, and thus their actual present value, will be affected by the timing of
both the production and the incurrence of expenses in connection with
development and production of natural gas and oil properties. In addition, the
10% discount factor, which must be used to calculate discounted future net cash
flows for SEC reporting purposes, is not necessarily the most appropriate
discount factor based on interest rates in effect from time to time and risks
associated with the Company or the oil and gas industry in general.
 
COMPETITION
 
     The Company operates in the highly competitive areas of natural gas and oil
exploration, exploitation, acquisition and production with other companies. In
seeking to acquire desirable producing properties or new leases for future
exploration and in marketing its natural gas and oil production, as well as in
seeking to acquire the equipment and expertise necessary to operate and develop
those properties, the Company faces intense competition from a large number of
independent, technology-driven companies as well as both major and other
independent natural gas and oil companies. Many of these competitors have
financial and other resources substantially in excess of those available to the
Company. The effects of this highly competitive
 
                                       15
<PAGE>   17
 
environment could have a material adverse effect on the Company's business,
financial condition and results of operations. See "Business and
Properties -- Competition."
 
COMPLIANCE WITH GOVERNMENT REGULATIONS
 
     The Company's business is subject to federal, state and local laws and
regulations relating to the exploration for, and the development, production and
transportation of, natural gas and oil, as well as safety matters. Although the
Company believes it is in substantial compliance with all applicable laws and
regulations, legal requirements are frequently changed and subject to
interpretation, and the Company is unable to predict the ultimate cost of
compliance with these requirements or their effect on its operations.
Significant expenditures may be required to comply with governmental laws and
regulations. See "Business and Properties -- Governmental Regulation."
 
COMPLIANCE WITH ENVIRONMENTAL REGULATIONS
 
     The Company's operations are subject to complex environmental laws and
regulations adopted by federal, state and local governmental authorities.
Environmental laws and regulations are frequently changed. The implementation of
new, or the modification of existing, laws or regulations could have a material
adverse effect on the Company. The discharge of natural gas, oil, or other
pollutants into the air, soil or water may give rise to significant liabilities
on the part of the Company to the government and third parties and may require
the Company to incur substantial costs of remediation. No assurance can be given
that existing environmental laws or regulations, as currently interpreted or
reinterpreted in the future, or future laws or regulations will not materially
adversely affect the Company's results of operations and financial condition.
See "Business and Properties -- Environmental Matters."
 
RISK OF HEDGING ACTIVITIES
 
     In an attempt to reduce its sensitivity to energy price volatility, the
Company has in the past and may continue in the future to enter into hedging
transactions that generally result in a fixed price over a fixed period. If the
Company's reserves are not produced at rates equivalent to the hedged position,
the Company would be required to satisfy its obligations under hedging contracts
on potentially unfavorable terms without the ability to hedge that risk through
sales of comparable quantities of its own production. Further, the terms under
which the Company enters into hedging contracts are based on assumptions and
estimates of numerous factors such as cost of production and pipeline and other
transportation costs to delivery points. Substantial variations between the
assumptions and estimates used by the Company and actual results experienced
could materially adversely affect the Company's anticipated profit margins and
its ability to manage the risk associated with fluctuations in natural gas and
oil prices. Additionally, hedging contracts limit the benefits the Company will
realize if actual prices rise above the contract prices. In addition, hedging
contracts are subject to the risk that the other party may prove unable or
unwilling to perform its obligations under such contracts. Any significant
nonperformance could have a material adverse financial effect on the Company.
For the year ended December 31, 1997, the Company realized a reduction in
revenues attributable to oil hedges of $6,191. In 1997 the Company did not hedge
any of its natural gas production. In February 1998, the Company entered into a
hedging contract whereby 10,000 MMBtu per day of natural gas is purchased and
sold subject to a fixed price swap agreement for monthly periods from April 1998
through October 1999. Pursuant to these arrangements the Company exchanges a
floating market price for a fixed contract price. See "Management's Discussion
and Analysis of Financial Condition and Results of Operations -- Other Matters."
 
MARKETABILITY OF PRODUCTION
 
     The marketability of the Company's production depends in part upon the
availability, proximity and capacity of natural gas gathering systems, pipelines
and processing facilities. The Company delivers natural gas through gas
transportation systems that it generally does not own. Federal and state
regulation of natural gas and oil production and transportation, tax and energy
policies, changes in supply and demand and general economic conditions all could
adversely affect the Company's ability to produce and market its natural gas and
 
                                       16
<PAGE>   18
 
oil. Any dramatic change in market factors could have a material adverse effect
on the Company's business, financial condition and results of operations.
 
DEPENDENCE ON KEY PERSONNEL
 
     The Company has assembled a team of geologists, geophysicists and engineers
having considerable experience applying 3-D imaging technology. The Company is
dependent upon the knowledge, skills and experience of these experts to provide
3-D imaging and assist the Company in reducing the risks associated with its
participation in natural gas and oil exploration projects. In addition, the
success of the Company's business also depends to a significant extent upon the
abilities and continued efforts of its management, particularly Ben M. Brigham,
the Company's President, Chief Executive Officer and Chairman of the Board. The
Company has an employment agreement with Ben M. Brigham, but does not have an
employment agreement with any of its other employees. The Company has key man
life insurance on Mr. Brigham in the amount of $2.0 million. The loss of
services of key management personnel or the Company's technical experts, or the
inability to attract additional qualified personnel, could have a material
adverse effect on the Company's business, financial condition and results of
operations. There can be no assurance that the Company will be successful in
attracting and retaining such executives, geophysicists, geologists and
engineers. See "Management -- Directors and Executive Officers" and "Business
and Properties -- Exploration Staff."
 
CONTROL BY EXISTING STOCKHOLDERS
 
     Upon completion of the Offering, directors, executive officers and
principal stockholders of the Company, and certain of their affiliates, will
beneficially own approximately 60.36% of the Company's outstanding Common Stock.
Accordingly, these stockholders, as a group, will be able to control the outcome
of stockholder votes, including votes concerning the election of directors, the
adoption or amendment of provisions in the Company's Certificate of
Incorporation or Bylaws and the approval of mergers and other significant
corporate transactions. The existence of these levels of ownership concentrated
in a few persons makes it unlikely that any other holder of Common Stock will be
able to affect the management or direction of the Company. These factors may
also have the effect of delaying or preventing a change in the management or
voting control of the Company. See "Principal and Selling Stockholders."
 
YEAR 2000 COMPLIANCE
 
     Many currently installed computer systems and software products are coded
to accept only two digit entries in the date code field. These date code fields
will need to accept four digit entries to distinguish the 21st century dates
from 20th century dates. As a result, computer systems and software used by many
companies may need to be upgraded to comply with such "Year 2000" requirements.
Although the Company believes that its software products are Year 2000
compliant, there can be no assurance that the Company's software products
contain all necessary software routines and programs necessary for the accurate
calculation, display, storage and manipulation of data involving dates.
Moreover, the Company cannot determine what effect, if any, the Year 2000
requirements will have on its vendors, customers, other businesses with which
its conducts business and the numerous local, state, federal, and other U.S. and
foreign governmental entities by which it is regulated, governed or taxed. No
assurance can be given that the computer systems and software of such entities
will be Year 2000 compliant or that compliance costs or the impact of the
Company's failure to achieve substantial Year 2000 compliance will not have a
material adverse effect on the Company's business, financial position and
results of operations.
 
CERTAIN ANTITAKEOVER CONSIDERATIONS
 
     The Company's Certificate of Incorporation authorizes the Board of
Directors of the Company to issue up to 10.0 million shares of preferred stock
without stockholder approval and to set the rights, preferences and other
designations, including voting rights, of those shares as the Board of Directors
may determine. These provisions, alone or in combination with the matters
described in "Risk Factors -- Control by Existing Stockholders," may discourage
transactions involving actual or potential changes of control of the Company,
 
                                       17
<PAGE>   19
 
including transactions that otherwise could involve payment of a premium over
prevailing market prices to holders of Common Stock. The Company also is subject
to provisions of the Delaware General Corporation Law that may make some
business combinations more difficult. See "Description of Capital Stock --
Delaware Law Provisions."
 
SHARES ELIGIBLE FOR FUTURE SALE; REGISTRATION RIGHTS
 
     Sales of a substantial number of shares of Common Stock in the public
market following the Offering could adversely affect the market price for the
Common Stock. Upon completion of the Offering the Company will have 15,653,574
shares of Common Stock outstanding. 8,928,574 shares of Common Stock that were
issued in reliance on exemptions from the registration requirements of the
Securities Act are now eligible for sale under Rule 144, subject to compliance
with the volume and other limitations of Rule 144, and 6,850,000 shares of
Common Stock that will be issued in the Offering or were sold in the Company's
initial public offering are freely tradeable, except to the extent that they are
held by affiliates of the Company. Investors holding 8,421,431 shares have the
right to require the Company to register the public resale of their shares.
Holders of 8,928,574 shares are entitled to "piggyback" registration rights.
     shares are subject to "lock-up" agreements from which they will be released
90 days after the date of this Prospectus. Options covering 935,987 shares of
Common Stock are outstanding, with an average exercise price of $7.61 per share,
subject to vesting. See "Shares Eligible for Future Sale" and "Description of
Capital Stock -- Registration Rights."
 
POSSIBLE STOCK PRICE VOLATILITY
 
     The trading price of the Common Stock and the price at which the Company
may sell securities in the future could be subject to large fluctuations in
response to limited trading volume in the Company's stock and changes in
government regulations, quarterly variations in operating results, litigation,
general market conditions, the prices of natural gas and oil, announcements by
the Company and its competitors, the liquidity of the Company, the Company's
ability to raise additional funds and other events.
 
                                       18
<PAGE>   20
 
                                  THE COMPANY
 
     Brigham Exploration Company was formed in February 1997 as a Delaware
corporation and is the holding company for Brigham Oil & Gas, L.P. (the
"Partnership"). The Partnership was formed in May 1992 by contribution of assets
of Brigham, Inc., and its general partners were General Atlantic Partners III,
L.P., a Delaware limited partnership ("GAP III"), and Brigham, Inc. Under the
Exchange Agreement (the "Exchange Agreement"), effective February 27, 1997, the
following transactions occurred: (i) GAP III and the limited partners of the
Partnership transferred all their partnership interests to the Company in
exchange for an aggregate of 3,314,286 shares of Common Stock, (ii) the
stockholders of Brigham, Inc. transferred all the issued and outstanding stock
of Brigham, Inc. to the Company in exchange for an aggregate of 3,859,821 shares
of Common Stock and (iii) Resource Investors Management Company Limited
Partnership ("RIMCO") exchanged all of the Partnership's subordinated
convertible notes for 1,754,464 shares of Common Stock. These transactions are
referred to in this Prospectus as the "Exchange." The stockholders of Brigham,
Inc. were Ben M. Brigham, President, Chief Executive Officer and Chairman of the
Board of the Company, and Anne L. Brigham, Executive Vice President and a
Director of the Company. The limited partners of the Partnership included the
following officers and/or directors of the Company, who received shares of
Common Stock in the Exchange as indicated: Jon L. Glass, Vice
President -- Exploration and a Director (66,964 shares); Craig M. Fleming, Chief
Financial Officer (44,643 shares); David T. Brigham, Vice President -- Land and
Administration and Corporate Secretary (44,643 shares); and Harold D. Carter, a
Director (350,893 shares). As a result of the Exchange, Brigham Exploration
Company owns, directly or indirectly, all the partnership interests in the
Partnership and no instruments, agreements or rights exist which may be
converted, exchanged into, or otherwise become interests in the Partnership. The
Company conducts its active business operations through the Partnership.
References to the "Company" or to "Brigham" are to Brigham Exploration Company
and its predecessors and subsidiaries, including the Partnership and Brigham,
Inc.
 
     Brigham's principal executive offices are located at 6300 Bridge Point
Parkway, Building 2, Suite 500, Austin, Texas 78730 and its telephone number is
(512) 427-3300.
 
                                       19
<PAGE>   21
 
                                USE OF PROCEEDS
 
     The net proceeds to the Company from the sale of the shares of Common Stock
offered by the Company are estimated to be approximately $37 million, after
deducting the estimated underwriting discounts and commissions and estimated
expenses of the Offering.
 
     The Company intends to use the net proceeds of the Offering to fund the
Company's accelerated exploration and development activities and in the interim
for repayment of outstanding indebtedness under the Credit Facility (as defined)
($61 million was outstanding at May 22, 1998). The interest rate for borrowings
under the Credit Facility is either the lender's base rate or LIBOR plus 2.25%,
at the Company's option. Borrowings under the facility, which matures on January
26, 2001, currently bear interest at an annual rate of approximately 7.9%. See
"Management's Discussion and Analysis of Financial Condition and Results of
Operations -- Liquidity and Capital Resources -- Revolving Credit Facilities"
for a description of the Credit Facility. The Company will not receive any of
the proceeds from the sale of Common Stock by the Selling Stockholders.
 
                PRICE RANGE OF COMMON STOCK AND DIVIDEND POLICY
 
     The Company's Common Stock is traded on The Nasdaq Stock Market(SM) under
the symbol "BEXP." The following table sets forth, for the periods indicated,
the reported high and low closing prices of the Company's Common Stock, as
reported on The Nasdaq Stock Market(SM):
 
<TABLE>
<CAPTION>
                                                               HIGH          LOW
                                                              ------        ------
<S>                                                           <C>           <C>
FISCAL 1997:
Second Quarter (from May 9, 1997)...........................  $ 8.75        $ 7.08
Third Quarter...............................................   14.31          8.25
Fourth Quarter..............................................   17.13         12.00
FISCAL 1998:
First Quarter...............................................  $14.00        $10.50
Second Quarter (through May 27, 1998).......................   15.50         11.50
</TABLE>
 
     On May 27, 1998, the last reported sale price of the Common Stock as
reported on The Nasdaq Stock Market(SM) was $11.75 per share. As of May 27, 1998
there were 65 holders of record of the Common Stock.
 
     The Company has never declared or paid cash dividends on its Common Stock
and anticipates that all future earnings will be retained for use in its
business. In addition, the Credit Facility prohibits the payment of cash
dividends on Common Stock. The Board of Directors of the Company may review the
Company's dividend policy from time to time in light of, among other things, the
Company's earnings and financial position. See "Management's Discussion and
Analysis of Financial Condition and Results of Operations -- Liquidity and
Capital Resources."
 
                                       20
<PAGE>   22
 
                                 CAPITALIZATION
 
     The following table sets forth the capitalization of the Company (i) as of
March 31, 1998 and (ii) pro forma as adjusted for the Offering and the
application of the net proceeds therefrom. The table should be read with
"Management's Discussion and Analysis of Financial Condition and Results of
Operations" and the Financial Statements and notes thereto in this Prospectus.
 
<TABLE>
<CAPTION>
                                                              AS OF MARCH 31, 1998
                                                              ---------------------
                                                              ACTUAL    AS ADJUSTED
                                                              -------   -----------
                                                                 (IN THOUSANDS)
<S>                                                           <C>       <C>
Total debt:
  Credit Facility...........................................  $50,000     $
Stockholders' equity:
  Preferred Stock, $.01 par value, 10 million shares
     authorized; no shares outstanding actual, and as
     adjusted...............................................       --          --
  Common Stock, $.01 par value, 30 million shares
     authorized; 12,253,574 shares issued and outstanding
     actual and           as adjusted(1)....................      123
  Additional paid-in capital................................   44,344
  Unearned stock compensation...............................   (1,136)
  Accumulated deficit.......................................     (589)
                                                              -------     -------
          Total stockholders' equity........................   42,742
                                                              -------     -------
Total capitalization........................................  $92,742     $
                                                              =======     =======
</TABLE>
 
---------------
 
(1) Excludes 1,588,169 shares of Common Stock the Company has reserved for
    future issuance under the Company's 1997 Incentive Plan and 25,000 shares of
    Common Stock reserved for issuance under the Company's 1997 Director Stock
    Option Plan, of which options to purchase 935,987 shares, subject to
    vesting, with an average exercise price of $7.61 per share are outstanding.
    See "Management -- Employee Benefit Plans -- 1997 Incentive Plan" and Note
    11 of Notes to the December 31, 1997 Consolidated Financial Statements.
 
                                       21
<PAGE>   23
 
                            SELECTED FINANCIAL DATA
                    (IN THOUSANDS, EXCEPT PER SHARE AMOUNTS)
 
     The following table sets forth selected financial data of the Company. The
data for the three years ended December 31, 1997 has been derived from the
financial statements appearing in this Prospectus. The data for the two years
ended December 31, 1994 has been derived from financial statements not appearing
in this Prospectus. The consolidated financial data at March 31, 1998 and for
the three months ended March 31, 1998 and March 31, 1997 have been derived from
the condensed consolidated financial statements of the Company which, in the
opinion of management, include all adjustments, consisting only of normal
adjustments, necessary for a fair presentation of the results for the periods.
The results for the three months ended March 31, 1998 are not necessarily
indicative of the results to be expected for the full year. The information
should be read in conjunction with the Management's Discussion and Analysis of
Financial Condition and Results of Operations and the Financial Statements and
notes thereto included elsewhere in this Prospectus.
 
<TABLE>
<CAPTION>
                                                                                                         THREE MONTHS
                                                                                                            ENDED
                                                           YEAR ENDED DECEMBER 31,                        MARCH 31,
                                              --------------------------------------------------     --------------------
                                               1993       1994      1995       1996       1997        1997         1998
                                              -------    -------   -------   --------   --------     -------     --------
<S>                                           <C>        <C>       <C>       <C>        <C>          <C>         <C>
STATEMENT OF OPERATIONS DATA:
  Revenues:
    Natural gas and oil sales...............  $   937    $ 2,565   $ 3,578   $  6,141   $  9,184     $ 2,136     $  3,143
    Workstation revenue.....................      467        815       635        627        637         164          114
                                              -------    -------   -------   --------   --------     -------     --------
        Total revenues......................    1,404      3,380     4,213      6,768      9,821       2,300        3,257
  Costs and expenses:
    Lease operating.........................      111        491       761        726      1,151         206          414
    Production taxes........................       47        126       165        362        549         127          188
    General and administrative..............    1,433      1,785     1,897      2,199      3,570         702        1,154
    Depletion of natural gas and oil
      properties............................    4,371(1)   1,104     1,626      2,323      2,732         687        1,267
    Depreciation and amortization...........      406        561       533        487        582         137          178
                                              -------    -------   -------   --------   --------     -------     --------
        Total costs and expenses............    6,368      4,067     4,982      6,097      8,584       1,859        3,201
                                              -------    -------   -------   --------   --------     -------     --------
  Operating income (loss)...................   (4,964)      (687)     (769)       671      1,237         441           56
  Other income (expense):
    Interest income.........................        6         56       128         52        145          18           37
    Interest expense........................     (105)      (668)     (936)    (1,173)    (1,190)       (390)      (1,022)
                                              -------    -------   -------   --------   --------     -------     --------
        Total other income (expense)........      (99)      (612)     (808)    (1,121)    (1,045)       (372)        (985)
                                              -------    -------   -------   --------   --------     -------     --------
  Net income (loss) before income taxes.....   (5,063)    (1,299)   (1,577)      (450)       192          69         (929)
  Income tax (expense) benefit, net.........       --         --        --         --     (1,228)(2)  (4,964)(2)      314
                                              -------    -------   -------   --------   --------     -------     --------
        Net loss............................  $(5,063)   $(1,299)  $(1,577)  $   (450)  $ (1,036)    $(4,895)    $   (615)
                                              =======    =======   =======   ========   ========     =======     ========
  Net loss per share -- basic/diluted.......  $ (0.57)   $ (0.15)  $ (0.18)  $  (0.05)  $  (0.09)    $ (0.55)    $  (0.05)
  Weighted average shares outstanding --
    basic/diluted...........................    8,929      8,929     8,929      8,929     11,081       8,929       12,254
STATEMENT OF CASH FLOWS DATA:
  Net cash provided by (used in) operating
    activities..............................  $  (730)   $   626   $ 1,383   $  3,710   $  9,806     $ 4,224     $ (2,796)
  Net cash used in investing activities.....   (6,983)    (5,463)   (8,005)   (11,796)   (57,300)     (7,301)     (13,136)
  Net cash provided by financing
    activities..............................    7,839      4,634     7,724      7,731     47,748       2,794       16,031
OTHER FINANCIAL DATA:
  Capital expenditures......................  $ 6,632    $ 5,445   $ 7,935   $ 13,612   $ 57,170     $ 6,830     $ 12,993
  EBITDA(3).................................     (187)       978     1,390      3,481      4,551       1,265        1,501
  Operating cash flow(4)....................     (286)       366       582      2,360      3,506         893          622
</TABLE>
 
<TABLE>
<CAPTION>
                                                              AS OF DECEMBER 31,                       AS OF MARCH 31,
                                              --------------------------------------------------     --------------------
                                               1993       1994      1995       1996       1997        1997         1998
                                              -------    -------   -------   --------   --------     -------     --------
<S>                                           <C>        <C>       <C>       <C>        <C>          <C>         <C>
BALANCE SHEET DATA:
  Cash and cash equivalents.................  $   903    $   700   $ 1,802   $  1,447   $  1,701     $ 1,164     $  1,800
  Natural gas and oil properties, at cost,
    net.....................................    7,803     11,970    18,538     28,005     84,176      33,897       96,676
  Total assets..............................   14,003     15,781    22,916     33,614     92,401      39,949      107,508
  Notes payable.............................    3,000      7,950    16,000     24,000     32,000          --       50,000
  Stockholders' equity......................    6,570      5,271     3,694      3,244     43,153      14,897       42,742
</TABLE>
 
---------------
 
(1) Includes a capitalized ceiling impairment charge of $3.3 million in 1993.
 
(2) 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 February 27, 1997, the date of the Exchange date. During the
    fourth
 
                                       22
<PAGE>   24
 
    quarter of 1997, the Company elected to record a step-up in basis of its
    assets for tax purposes as a result of the Exchange. Related to this
    election, the Company recorded a $3.8 million deferred income tax benefit,
    resulting in a net $1.2 million ($.10 per share) non-cash deferred income
    tax charge for the year ended December 31, 1997. See Note 2 of Notes to the
    December 31, 1997 Consolidated Financial Statements.
 
(3) EBITDA represents net income (loss) plus income taxes, net interest expense
    and depreciation, depletion and amortization expense. EBITDA should not be
    considered in isolation or as a substitute for net income, cash flows from
    operating activities or any other measure of financial performance prepared
    in accordance with generally accepted accounting principles or as a measure
    of a company's profitability or liquidity.
 
(4) Operating cash flow represents net income (loss) plus DD&A expenses,
    deferred income taxes and other non-cash items. Operating cash flow should
    not be considered in isolation or as a substitute for net income, cash flows
    from operating activities or any other measure of financial performance
    prepared in accordance with generally accepted accounting principles or as a
    measure of a company's profitability or liquidity.
 
                                       23
<PAGE>   25
 
                    MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITION AND RESULTS OF OPERATIONS
 
OVERVIEW
 
     The Company is an independent exploration and production company that
applies 3-D seismic imaging and other advanced technologies to systematically
explore and develop onshore domestic natural gas and oil provinces. From
inception in 1990 through December 31, 1997, Brigham had acquired 4,005 square
miles of 3-D seismic, identified 1,170 potential drilling locations and drilled
370 wells delineated by 3-D seismic analysis. The Company believes this
performance demonstrates a systematic methodology for finding natural gas and
oil in onshore domestic natural gas and oil provinces.
 
     Combining its geologic and geophysical expertise with a sophisticated land
effort, the Company manages the majority of its projects from conception through
3-D acquisition, processing and interpretation and leasing. Because it generates
most of its projects, the Company can control the size of the working interest
that it retains as well as the selection of the operator and the non-operating
participants. Additionally, the Company manages the negotiation and drafting of
most of its geophysical exploration agreements, resulting in reduced contract
risk and more consistent deal terms. In 1995, the Company began to manage
operations, on a limited basis, through the drilling and production phases. The
Company had discovered an aggregate of approximately 72 Bcfe of net proved
reserves as of December 31, 1997. Brigham continues to increase the working
interest it retains in its projects, based on capital availability and perceived
risk. The Company's average working interest in its wells drilled during 1995,
1996 and 1997 was 24%, 24% and 38%, respectively.
 
     Expenditures made in natural gas and oil exploration vary from project to
project depending primarily on the costs related to land, seismic acquisition,
drilling costs and the working interest retained by the Company. Historically,
the Company's participants have borne a disproportionate share of the costs of
optioning available acreage and acquiring, processing and interpreting the 3-D
seismic, and the Company and its participants each bear leasing, drilling and
completion costs in proportion to their ownership interests. Brigham currently
intends to retain working interests of between 75% and 100% in its current 3-D
seismic projects, thereby reducing the financial leverage it has historically
received on the costs of optioning available acreage and acquiring, processing
and interpreting the 3-D seismic and increasing its working interests during the
drilling phase.
 
     From inception through 1996, the Company acquired 2,762 square miles of 3-D
seismic in 104 projects. Initially, the Company focused its efforts in West
Texas. In 1995, the Company began to devote substantial attention to the
Anadarko Basin, and since 1996 the Company has devoted the majority of its
resources to the Anadarko Basin and Gulf Coast. With this shift in regional
focus, the majority of the Company's production volumes has shifted from oil to
natural gas. To finance these project generation and drilling activities, the
Company has supplemented cash flow from operations with private placements of
debt and equity, commercial bank credit facilities and placements of working
interests in projects with industry participants. As the Company's cash flows
from operations and other sources of capital have increased, it has retained
larger average working interests in its projects.
 
     In 1997, the Company acquired 1,243 square miles of 3-D seismic and
continued to focus the majority of its 3-D exploration efforts in the Anadarko
Basin and the Gulf Coast. The Company acquired 648 square miles (52%) of 3-D
seismic in nine projects in the Anadarko Basin, making this basin the most
active 3-D seismic acquisition province for the Company again in 1997. Brigham
also significantly increased its Gulf Coast activity, acquiring 412 square miles
(33%) of 3-D seismic in four projects. During 1997, the Company drilled
seventy-three 3-D seismic delineated wells, increasing its revenues from natural
gas and oil production to $9.1 million. The Company's production volumes
consisted of 44% natural gas on an equivalent basis. The Company's average
working interest in wells drilled in 1997 was 38%. The Company's fourth quarter
1997 revenue from natural gas and oil production increased to $3.2 million from
$1.9 million in the fourth quarter of 1996, while its production volumes
consisted of 53% natural gas during the fourth quarter 1997 as compared with 36%
during the prior year period. The Company supplemented cash flow from operations
with borrowings under the credit facility it had in place at the time, $24
million raised in its initial public offering of common
 
                                       24
<PAGE>   26
 
stock in May 1997 and the placement of working interests in projects to industry
participants to finance its project generation, property acquisition and
drilling activities.
 
     The Company uses the full-cost method of accounting for its natural gas and
oil properties. Under this method, all acquisition, exploration and development
costs, including certain internal costs that are directly attributable to the
Company's acquisition, exploration and development activities, are capitalized
in the amortizable base of the "full-cost pool" as incurred. Upon the
interpretation by the Company of the 3-D seismic associated with unproved
properties, the geological and geophysical costs of acreage that is not
specifically identified as prospective are transferred to the amortizable base.
Geological and geophysical costs associated with prospective acreage, as well as
leasehold costs, are transferred to the amortizable base when the prospects are
drilled. The Company records depletion of its full-cost pool using the unit of
production method. To the extent that the costs capitalized in the full-cost
pool (net of depreciation, depletion and amortization and related deferred
taxes) exceed the present value (using a 10% discount rate) of estimated future
net after-tax cash flows from proved natural gas and oil reserves plus the
capitalized cost of unproved properties, such costs are charged to operations.
Once incurred, a write-down of natural gas and oil properties is not reversed at
a later date. See Note 2 of Notes to the December 31, 1997 Consolidated
Financial Statements.
 
     In connection with the Exchange in 1997, the Company issued options to
purchase 644,097 shares of Common Stock to certain of its officers and
employees. The Company recorded an unearned stock compensation balance of $1.9
million in the first quarter 1997, of which approximately one-half will be added
to the amortizable base of the full-cost pool over the vesting period of the
options and the balance will be recorded as a noncash compensation expense over
the vesting period of the options. As a result, the Company expects to incur
unearned stock compensation amortization expenses of approximately $290,000 in
1998, $140,000 in 1999 and an aggregate of $170,000 in the four years
thereafter.
 
     The Company's predecessor was classified as a partnership for federal
income tax purposes. Therefore, no income taxes were paid or provided for by the
Company prior to the Exchange. The Company is a taxable entity. In connection
with the Exchange on February 27, 1997, the Company incurred a $5 million charge
to record a deferred income tax liability to recognize the differences between
the financial statement basis and tax basis of the Company's predecessor
partnership's natural gas and oil properties at the Exchange date, given the
provisions of enacted tax laws. During the fourth quarter 1997, the Company
elected to record a step-up in the basis of its assets for tax purposes as a
result of the Exchange. Due to this election, the Company recorded a $3.8
million non-cash deferred income tax benefit during the fourth quarter 1997,
which resulted in a net $1.2 million non-cash deferred income tax charge for the
year ended December 31, 1997.
 
                                       25
<PAGE>   27
 
RESULTS OF OPERATIONS
 
     The following table sets forth certain operating data for the periods
presented.
 
<TABLE>
<CAPTION>
                                                                              THREE MONTHS ENDED
                                                 YEAR ENDED DECEMBER 31,           MARCH 31,
                                                --------------------------    -------------------
                                                 1995      1996      1997      1997        1998
                                                ------    ------    ------    -------     -------
<S>                                             <C>       <C>       <C>       <C>         <C>
Production:
  Natural gas (MMcf)..........................     272       698     1,382       243         740
  Oil (MBbls).................................     177       227       291        63         115
  Natural gas equivalent (MMcfe)..............   1,332     2,060     3,126       623       1,431
Average sales prices per unit (1):
  Natural gas (per Mcf).......................  $ 1.62    $ 2.30    $ 2.56    $ 3.10      $ 2.05
  Oil (per Bbl)...............................   17.76     19.98     19.40     21.82       14.15
  Natural gas equivalent (per Mcfe)...........    2.69      2.98      2.94      3.43        2.20
Costs and expenses per Mcfe:
  Lease operating.............................  $ 0.57    $ 0.35    $ 0.37    $ 0.33      $ 0.29
  Production taxes............................    0.12      0.18      0.18      0.20        0.13
  General and administrative..................    1.42      1.07      1.14      1.13        0.81
  Depletion of natural gas and oil
     properties...............................    1.22      1.13      0.87      1.10        0.89
</TABLE>
 
---------------
 
(1) Reflects the effects of the Company's hedging activities. See "Management's
    Discussion and Analysis of Financial Condition and Results of
    Operations -- Other Matters."
 
  Three Months Ended March 31, 1998 Compared to Three Months Ended March 31,
1997
 
     Natural gas and oil sales. Natural gas and oil sales increased 47% from
$2.1 million in the first quarter of 1997 to $3.1 million in the first quarter
of 1998. Of this net increase, $2.8 million was attributable to an increase in
production, offset by $1.8 million attributable to a decrease in the average
sales price for natural gas and oil. Production volumes for natural gas
increased 205% from 243 MMcf in the first quarter of 1997 to 740 MMcf in the
first quarter of 1998. The average price received for natural gas decreased 34%
from $3.10 per Mcf in the first quarter of 1997 to $2.05 per Mcf in the first
quarter of 1998. Production volumes for oil increased 82% from 63 MBbls in the
first quarter of 1997 to 115 MBbls in the first quarter of 1998. The average
price received for oil decreased 35% from $21.82 per Bbl in the first quarter of
1997 to $14.15 per Bbl in the first quarter of 1998. Natural gas and oil sales
were increased by production from wells completed during the first quarter of
1998, partially offset by the natural decline of existing production.
 
     Lease operating expenses. Lease operating expense increased 101% from
$206,000 for the first quarter of 1997 to $414,000 for the first quarter of
1998, while on a per unit of production basis, lease operating expenses for the
same periods decreased 12% from $.33 per Mcfe to $.29 per Mcfe. The increase in
lease operating expenses was primarily due to an increase in the number of
producing wells in the first 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 (39% and
52% for the first 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 47% from $127,000 ($.20 per
Mcfe) for the first quarter of 1997 to $188,000 ($.13 per Mcfe) for the first
quarter 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 each period.
 
     General and administrative expenses. General and administrative expenses
increased 64% from $702,000 for the first quarter of 1997 to $1.2 million for
the first 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
 
                                       26
<PAGE>   28
 
corporation increased for the first quarter of 1998 as compared to the same
period for 1997. On a per unit of production basis, general and administrative
expenses decreased 28% from $1.13 per Mcfe for the first quarter of 1997 to $.81
per Mcfe for the first quarter of 1998.
 
     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 84% from $687,000 ($1.10 per Mcfe) in the first quarter
of 1997 to $1.3 million ($.89 per Mcfe) in the first quarter of 1998. Of this
net increase, $892,000 was due to the increase in production volumes which was
offset by $312,000 due to a 19% 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 165% from $372,000 in the
first quarter of 1997 to $985,000 in the first quarter of 1998. This increase
was due to a higher average outstanding debt balance in the first quarter of
1998 partially offset by a decreased effective interest rate. The weighted
average outstanding debt balance increased 179% from $15.3 million in the first
quarter of 1997 to $42.8 million in the first quarter of 1998. The effective
annual interest rate including the non-cash amortization of deferred loan fees
decreased 6% from 10% in the first quarter of 1997 to 9.5% in the first quarter
of 1998. The increase in the average outstanding debt balance was primarily a
result of increased capital expenditures related to the Company's exploration
activities. At March 31, 1998, the Company had $50 million in borrowings
outstanding under the Credit Facility which had an annual interest rate of 7.9%.
Interest expense increased an additional $106,000 in the first 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.
 
  Year Ended December 31, 1997 Compared to Year Ended December 31, 1996
 
     Natural gas and oil sales. Natural gas and oil sales increased 50% from
$6.1 million in 1996 to $9.2 million in 1997. Production volume increases
accounted for $3.2 million (104%) of this increase and were offset by $134,000
(4%) from a decrease in the average sales price received for natural gas and oil
sales. Production volumes for natural gas increased 98% from 698,036 Mcf in 1996
to 1,381,996 Mcf in 1997. The average price received for natural gas increased
11% from $2.30 per Mcf in 1996 to $2.56 per Mcf in 1997. Production volumes for
oil increased 28% from 226,925 Bbls in 1996 to 290,624 Bbls in 1997. The average
price received for oil decreased 3% from $19.98 per Bbl in 1996 to $19.40 per
Bbl in 1997. Natural gas and oil sales were increased by production from 46
wells completed in 1997, which was partially offset by the natural decline of
existing production. Hedging activities in 1997 reduced the amount by which oil
revenues increased by $6,191, compared to a decrease in oil revenues of $301,280
as a result of hedging activities in 1996.
 
     Workstation revenue. Workstation revenue increased 2% from $627,255 in 1996
to $636,702 in 1997. Workstation revenue is recognized by Brigham as industry
participants in the Company's seismic programs are charged an hourly rate for
the work performed by the Company on its 3-D seismic interpretation
workstations. The Company expects workstation revenue to decline in 1998 due to
the Company increasing its working interest in the square miles of 3-D seismic
acquired beginning in 1997, reducing the net hours billed to its participants.
 
     Lease operating expenses. Lease operating expenses increased 59% from
$725,785 ($.35 per Mcfe) in 1996 to $1,151,238 ($.37 per Mcfe) in 1997. The
increase was primarily due to an increase in producing wells during the year.
 
     Production taxes. Production taxes increased 52% from $362,000 ($.18 per
Mcfe) in 1996 to $549,000 ($.18 per Mcfe) in 1997 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 each period.
 
     General and administrative expenses. General and administrative expenses
increased 62% from $2.2 million ($1.07 per Mcfe) in 1996 to $3.6 million ($1.14
per Mcfe) in 1997. Approximately $300,000 of the increase in 1997 resulted from
nonrecurring expenses related to the Company's relocation of its corporate
headquarters from Dallas, Texas to Austin, Texas, and the balance was primarily
attributable to the hiring of
 
                                       27
<PAGE>   29
 
additional personnel and related expenses necessary to manage the Company's
growing operations. The increase in the per unit rate was a result of a greater
increase in aggregate general and administrative expenses than natural gas and
oil production volumes from 1996 to 1997 due to the aforementioned factors.
 
     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 18% from $2.3 million ($1.13 per Mcfe) in 1996 to $2.7
million ($0.87 per Mcfe) in 1997 as a result of higher production volumes. The
per unit amount decreased due to the addition of proved reserves during 1997.
 
     Interest expense. Interest expense was essentially unchanged from 1996 to
1997 as the Company's lower average outstanding debt balance in 1997 was offset
by a higher effective average interest rate. The weighted average outstanding
debt balance decreased 45% from $19.7 million in 1996 to $10.8 million in 1997.
The effective interest rate increased 83% from 5.7% in 1996 to 10.5% in 1997.
The decrease in the weighted average outstanding debt balance and increase in
the effective average interest rate resulted primarily from the conversion to
equity of privately placed 5% notes (the "5% Notes") in February 1997, the
retirement of $13.3 million of borrowings under its previous credit facility in
connection with the Company's May 1997 initial public offering, and $32 million
of borrowings incurred under its previous credit facility subsequent to the
Company's initial public offering to fund the Company's increased exploration
activity and its $13.5 million acquisition of properties from Mobil adjacent to
its West Bradley 3-D Project area. The Company's previous credit facility had an
effective interest rate of 8.8% at December 31, 1997.
 
  Year Ended December 31, 1996 Compared to Year Ended December 31, 1995
 
     Natural gas and oil sales. Natural gas and oil sales increased 72% from
$3.6 million in 1995 to $6.1 million in 1996. Of this increase, $2.0 million or
76% was attributable to an increase in production, and $607,894 or 24% was
attributable to an increase in the average sales price received for natural gas
and oil. Production volumes for natural gas increased 157% from 271,707 Mcf in
1995 to 698,036 Mcf in 1996. The average price received for natural gas
increased 42% from $1.62 per Mcf in 1995 to $2.30 per Mcf in 1996. Production
volumes for oil increased 28% from 176,693 Bbls in 1995 to 226,925 Bbls in 1996.
The average price received for oil increased 13% from $17.76 per Bbl in 1995 to
$19.98 per Bbl in 1996. Natural gas and oil sales were increased by production
from 42 wells completed in 1996, which was partially offset by the sale of
certain producing properties in January 1996 and the natural decline of existing
production. Hedging activities in 1996 reduced the amount by which oil revenues
increased by $301,280, compared to an increase in oil revenues of $40,849 as a
result of hedging activities in 1995.
 
     Workstation revenue. Workstation revenue decreased 1% from $635,401 in 1995
to $627,255 in 1996, primarily as a result of a decrease in the rate at which
3-D seismic was acquired in 1995 and interpreted in 1996.
 
     Lease operating expenses. Lease operating expenses decreased 5% from
$760,784 ($.57 per Mcfe) in 1995 to $725,785 ($.35 per Mcfe) in 1996. The
decrease was primarily due to the sale of certain producing properties in
January 1996 partially offset by an increase in producing wells. The decrease in
the per unit rate was a result of the sale of higher cost oil wells in January
1996 and an increase in the percentage of production from natural gas wells.
 
     Production taxes. Production taxes increased 119% from $165,000 ($.12 per
Mcfe) in 1995 to $362,000 ($.18 per Mcfe) in 1996 primarily as a result of
increased production volumes. The effective average production tax rate
increased from 4.6% in 1995 to 6% in 1996, reflecting the increased percentage
of total production attributable to natural gas, which is taxed at a higher
effective rate than oil.
 
     General and administrative expenses. General and administrative expenses
increased 16% from $1.9 million ($1.42 per Mcfe) in 1995 to $2.2 million ($1.07
per Mcfe) in 1996. Approximately $110,000 of the increase in 1996 resulted from
salary increases for employees, and the remainder was primarily attributable to
an increase in third-party consulting fees. The decrease in the per unit rate
was a result of the increase in natural gas and oil production from 1995 to
1996.
 
                                       28
<PAGE>   30
 
     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 43% from $1.6 million ($1.22 per Mcfe) in 1995 to $2.3
million ($1.13 per Mcfe) in 1996 as a result of higher production volumes.
 
     Interest expense. Interest expense increased 25% from $936,266 in 1995 to
$1.2 million in 1996. This increase was due to a higher average outstanding debt
balance in 1996, which was partially offset by a lower effective interest rate.
The weighted average outstanding debt balance increased 71% from approximately
$11.5 million in 1995 to $19.7 million in 1996. The effective interest rate
decreased 25% from 7.6% in 1995 to 5.7% in 1996. The increase in the weighted
average outstanding debt balance and decrease in the effective interest rate
resulted primarily from the retirement of privately placed 10% notes (the "10%
Notes") and the issuance of $16 million in principal amount of 5% Notes in
August 1995.
 
LIQUIDITY AND CAPITAL RESOURCES
 
     The Company's primary sources of capital have been its revolving credit
facility and other debt borrowings, public and private equity financing, the
sale of interests in projects and funds generated by operations. The Company's
primary capital requirements are 3-D seismic and land acquisition costs and
drilling expenditures.
 
     Revolving Credit Facilities. In April 1996, the Company entered into a
revolving credit facility. This facility had a three-year term and was subject
to certain borrowing base limitations. The Company had borrowings outstanding
under this credit facility of $32 million as of December 31, 1997. The Company
retired this credit facility in January 1998 with borrowings under its Credit
Facility (as defined).
 
     In January 1998, Brigham entered into a new reserve-based credit agreement
(the "Credit Facility"), providing for current borrowing availability of $75
million. The current borrowing base of $75 million will be available to the
Company until January 31, 1999, when the availability under the facility will be
redetermined by the bank based on the Company's then proved reserve value. The
Company, at its option, can have the availability under the facility
redetermined based on its current proved reserve value at any time prior to
January 31, 1999. Principal outstanding under the Credit Facility is due at
maturity on January 26, 2001 with interest due monthly. The interest rate for
borrowings under the Credit Facility is either the lender's base rate or LIBOR
plus 2.25%, at the Company's option. Borrowings under the facility currently
bear interest at an annual rate of approximately 7.9%. The Company's obligations
under the Credit Facility are secured by substantially all of the natural gas
and oil properties of the Company. See Note 5 of Notes to the December 31, 1997
Consolidated Financial Statements. The Company used a portion of the funds
available under Credit Facility to repay the $32 million in borrowings
outstanding at December 31, 1997 under its previous credit facility.
 
     The Company believes that through the foreseeable future -- including
through the remainder of 1998 -- 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 recently amended 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 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.
 
  Cash Flow Analysis
 
     Cash Flows from Operating Activities. Cash flows provided by operating
activities were $9.8 million in 1997, $3.7 million in 1996, and $1.4 million in
1995. The increase in cash flows for 1997 compared to 1996 was due primarily to
an increase in natural gas and oil revenues, net of lease operating expenses,
production taxes and general and administrative expenses, and changes in balance
sheet items. The increase in cash flows for 1996 compared to 1995 was due
primarily to an increase in natural gas and oil revenues, net of lease operating
expenses, production taxes and general and administrative expenses. In the first
quarter of 1998, cash flow used by operations was $2.8 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.
                                       29
<PAGE>   31
 
     Cash Flows from Investing Activities. Cash flows used in investing
activities increased to $57.3 million in 1997 compared to $11.8 million in 1996
and $8.0 million in 1995. These increases are directly related to an increase in
capital expenditures. Capital expenditures were $57.2 million in 1997, $13.6
million in 1996 and $7.9 million in 1995. The Company acquired 1,243 gross (845
net) square miles of 3-D seismic in 1997, 655 gross (241 net) square miles in
1996, and 311 gross (90 net) square miles in 1995. The Company's drilling
efforts resulted in the successful completion of 46 wells (17.6 net) in 1997, 42
wells (8.7 net) in 1996 and 46 wells (9.9 net) in 1995, which resulted in
aggregate net increases in proved reserve volumes of 32.4 Bcfe in 1997, 11.3
Bcfe in 1996 and 6.0 Bcfe in 1995. In addition, the Company sold certain
producing properties in 1996 for $2.1 million and acquired certain producing
properties and related interests in 1997 for $13.5 million. Cash flow used in
investing activities was $13.1 million in the first quarter of 1998 primarily as
a result of capital expenditures related to exploration activities.
 
     Cash Flows from Financing Activities. Cash flows from financing activities
for 1997 were $47.7 million, primarily as a result of borrowings under the
Company's previous credit facility and proceeds from the common stock sold in
the Company's initial public offering. Cash flows from financing activities for
1996 were $7.7 million, primarily as a result of borrowings under the Company's
previous credit facility. Cash flows from financing activities for 1995 were
$7.7 million, primarily as a result of the issuance of the 5% Notes offset by
the net repayment of the $7.9 million outstanding balance on the 10% Notes. Cash
flows from financing activities for the first quarter of 1998 were $16 million,
net of deferred loan fees of $1.9 million, in the first three 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.
 
  Capital Expenditures
 
     The Company currently estimates capital expenditures in 1998 will be
approximately $73 million. The Company expects to incur these capital
expenditures primarily to drill 106 gross (56 net) planned wells, to acquire
approximately 970 gross (735 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. See "Business and Properties --
Primary Exploration Provinces."
 
     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 requirements. While the Company believes that the net proceeds
of the Offering, cash flow from operations and borrowings under the Credit
Facility should allow the Company to finance its operations at least through
1998 based on current conditions, additional financing may be required in the
future to fund the Company's 3-D seismic acquisition and drilling programs. In
the event additional financing is not available, the Company may be required to
curtail these activities.
 
OTHER MATTERS
 
  Hedging Activities
 
     The Company believes that hedging, although not free of risk, allows the
Company to reduce its exposure to natural gas and oil sales price fluctuations
and thereby to achieve more predictable cash flows. However, hedging
arrangements, when utilized, limit the benefit to the Company of increases in
the prices of the hedged commodity. Moreover, the Company's hedging arrangements
apply only to a portion of its production and provide only partial price
protection against declines in commodity prices. The Company expects that the
amount of its hedges will vary from time to time. See "Risk Factors -- Risk of
Hedging Activities."
 
     In 1995 the Company, in an attempt to reduce its sensitivity to volatile
commodity prices, began using crude oil swap arrangements resulting in a fixed
price over a period of six months. Total oil purchased and sold subject to swap
arrangements entered into by the Company was 118,150 Bbls in 1996 and 54,900
Bbls in 1995. The Company accounts for all these transactions as hedging
activities and, accordingly, adjusts the price received for natural gas and oil
production during the period the hedged transactions occur. Adjustments to the
price received for oil under these swap arrangements resulted in an increase in
oil revenues of $40,849 in
 
                                       30
<PAGE>   32
 
1995 and decreases in oil revenues of $301,280 in 1996 and $6,191 in 1997. As of
December 31, 1997, the Company had no hedging contracts outstanding.
 
     In February 1998, the Company entered into a hedging contract whereby
10,000 MMBtu per day of natural gas is purchased and sold subject to a fixed
price swap agreement for monthly periods from April 1998 through October 1999.
Pursuant to these arrangements the Company exchanges a floating market price for
a fixed contract price. Payments are made by the Company when the floating price
exceeds the fixed price for a contract month and payments are received when the
fixed price exceeds the floating price. Settlements on these swaps are based on
the difference between the ANR Pipeline Co.-Oklahoma index price (as published
in Inside FERC's Gas Market Report) for a contract month and the fixed contract
price for the same month. Total natural gas subject to this hedging contract is
2,750,000 MMBtu in 1998 and 3,040,000 MMBtu in 1999.
 
  Effects of Inflation and Changes in Prices
 
     The Company's results of operations and cash flows are affected by changing
natural gas and oil prices. If the price of natural gas and oil increases
(decreases), there could be a corresponding increase (decrease) in revenues as
well as the operating costs that the Company is required to bear for operations.
Inflation has had a minimal effect on the Company.
 
  Environmental and Other Regulatory Matters
 
     The Company's business is subject to certain federal, state and local laws
and regulations relating to the exploration for and the development, production
and marketing of natural gas and oil, as well as environmental and safety
matters. Many of these laws and regulations have become more stringent in recent
years, often imposing greater liability on a larger number of potentially
responsible parties. Although the Company believes it is in substantial
compliance with all applicable laws and regulations, the requirements imposed by
laws and regulations are frequently changed and subject to interpretation, and
the Company is unable to predict the ultimate cost of compliance with these
requirements or their effect on its operations. Any suspensions, terminations or
inability to meet applicable bonding requirements could materially adversely
affect the Company's financial condition and operations. Although significant
expenditures may be required to comply with governmental laws and regulations
applicable to the Company, compliance has not had a material adverse effect on
the earnings or competitive position of the Company. Future regulations may add
to the cost of, or significantly limit, drilling activity. See "Risk
Factors -- Compliance with Environmental Regulations," "Business and
Properties -- Governmental Regulation" and "Business and
Properties -- Environmental Matters."
 
  Year 2000 Issues
 
     The Company has reviewed the effect of the Year 2000 issues 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 nor its financial position. 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
U.S. and foreign 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.
 
  Recent Accounting Pronouncements
 
     In June 1997, the Financial Accounting Standards Board issued SFAS 130,
"Reporting Comprehensive Income," and SFAS 131, "Disclosure about Segments of an
Enterprise and Related Information." Neither SFAS will have a material impact on
the Company.
 
                                       31
<PAGE>   33
 
                            BUSINESS AND PROPERTIES
 
     Brigham is an independent exploration and production company that applies
3-D seismic imaging and other advanced technologies to systematically explore
and develop onshore domestic natural gas and oil provinces. The Company focuses
its 3-D seismic activity in provinces where it believes 3-D technology may be
effectively applied and which Brigham believes offer relatively large potential
reserve volumes per well and per field, high potential production rates and
multiple producing objectives. The Company's exploration activities are
concentrated primarily in three core provinces: the Anadarko Basin of western
Oklahoma and the Texas Panhandle; the onshore Gulf Coast of Texas and Louisiana;
and West Texas. Brigham is accelerating its 3-D seismic and drilling activities
in the Anadarko Basin and the Gulf Coast and will continue to focus its
activities in those geologic trends of West Texas where it has achieved its best
historical results.
 
     The Company pioneered the acquisition of large scale, onshore 3-D seismic
surveys for exploration, obtaining extensive 3-D seismic data and experience in
capturing undiscovered natural gas and oil reserves. Through December 31, 1997,
Brigham had acquired 4,005 square miles (2.6 million acres) of 3-D seismic and
identified 1,170 potential drilling locations, of which the Company had drilled
370. The Company generates most of its exploratory projects and, therefore, has
the ability to retain a sizeable working interest to the extent that it decides
not to place interests with industry participants.
 
     From inception in 1990 through 1997, Brigham had drilled 324 exploratory
and 46 development wells on its 3-D seismic generated prospects with an
aggregate 63% success rate and an average working interest of 24%. Utilizing the
capital it raised in its May 1997 initial public offering, the Company increased
the average working interest it retained in its wells during the second half of
1997, retaining a 45% average working interest in the 36 wells that it drilled.
As of December 31, 1997, the Company had added approximately 93 Bcfe of net
proved reserves (excluding revisions) to its reserve base, approximately 72 net
Bcfe of which were discovered by Brigham through its systematic 3-D seismic
exploration drilling activities. The Company's estimated net proved reserves as
of December 31, 1997 were 72.3 Bcfe having an aggregate Present Value of Future
Net Revenues of $69.2 million, compared to estimated net proved reserves as of
December 31, 1996 of 21.9 Bcfe having an aggregate Present Value of Future Net
Revenues of $44.5 million. The Company's net proved reserve volumes at December
31, 1997 were 74% natural gas and 65% categorized as proved developed reserves.
 
BUSINESS STRATEGY
 
     Brigham's business strategy is to achieve superior growth in shareholder
value through the application of its systematic exploration approach, which
emphasizes the integrated use of 3-D seismic imaging and other advanced
technologies to reduce drilling risks and finding costs. Since its inception in
1990, the Company has consistently achieved rapid growth in its acquisition of
3-D seismic data, identification of potential drilling locations, discovery of
proved reserves and production volumes.
 
     Brigham completed its initial public offering of common stock in May 1997,
raising approximately $24 million to fund the Company's accelerated 3-D seismic
acquisition and exploration drilling activities. Key elements of the Company's
growth strategy at its initial public offering and continuing today include: (i)
accelerating the rate at which it acquires 3-D seismic and identifies potential
drilling locations; (ii) increasing the working interests it retains in
exploration projects to capture a greater share of the reserves that the Company
discovers; (iii) identifying higher potential, higher impact prospects; and (iv)
accelerating the rate at which its 3-D seismic defined locations are drilled.
 
     During the second half of 1997, the Company employed the capital raised in
its initial public offering to attain significant growth in each of its core
strategic objectives:
 
          Accelerated 3-D Seismic Acquisition. During 1997, Brigham acquired
     approximately 1,250 square miles of 3-D seismic, which increased the
     Company's aggregate 3-D seismic inventory 45% to approximately 4,000 square
     miles as of December 31, 1997. The overall level of 3-D seismic acquisition
     in 1997 represents the most active year in the Company's history, and
     approximately 85% of this increased 3-D seismic was acquired in its higher
     potential Anadarko Basin and Gulf Coast provinces.
 
                                       32
<PAGE>   34
 
          Increased Working Interest. In an effort to retain a greater portion
     of the value generated by its 3-D seismic exploration efforts, Brigham
     increased the average working interest it retained in its 1997 3-D seismic
     projects to 68% as compared with its average project working interest of
     24% in 1990 through 1996. As a result of the higher working interests and
     the accelerated acquisition of 3-D seismic, the Company acquired 845 net
     square miles of 3-D seismic in 1997 as compared with 780 cumulative net
     square miles acquired from 1990 through 1996.
 
          Higher Potential, Higher Impact Prospects. By focusing an increasing
     portion of its exploration activities in the more prolific Anadarko Basin,
     Brigham increased its average proved reserves discovered per net well
     drilled (including dry holes) to 1.2 Bcfe in 1997 from 0.7 Bcfe in 1996 and
     0.4 Bcfe in 1992 through 1995. In the Anadarko Basin alone, Brigham's
     average proved reserves discovered per net well drilled was 3.4 Bcfe in
     1997 compared with 1.8 Bcfe in 1996 and 2 Bcfe in 1994 through 1995.
     Contributing to these increases, the Company's Anadarko Basin drilling in
     1997 produced the two largest field discoveries in Brigham's history, which
     resulted in the discovery of approximately 52 Bcfe of gross proved reserves
     and provided the Company with several development drilling opportunities.
 
          Accelerated Drilling. Through its strategy of retaining higher working
     interests in its 3-D projects and subsequent drilling, Brigham participated
     in the drilling of 28 net wells in 1997, a 76% increase from the
     approximate 16 net wells drilled by the Company in 1996. The Company
     achieved a 63% success rate on the 73 wells in its 1997 drilling program,
     consistent with Brigham's historical average success rate. A key factor
     contributing to its increased level of drilling activity was the Company's
     addition of personnel in engineering, land and administrative functions
     during 1997. These staff additions provided Brigham with the additional
     infrastructure required to increase its operating capabilities, enabling
     the Company operate 37% of its gross wells and 64% of its net wells drilled
     in 1997.
 
     As a result of the combined effects of the Company's multi-pronged growth
strategy, Brigham generated net proved reserve additions of approximately 38
Bcfe through drilling in 1997, which represents approximately 175% of the
Company's year-end 1996 net proved reserves of approximately 22 Bcfe. In
addition to its drilling efforts in 1997, the Company acquired 21.5 Bcfe of net
proved reserves at an implied cost of $0.63 per proved Mcfe in its November 1997
purchase of certain properties in and adjacent to its West Bradley project area
in its Anadarko Basin province. Brigham believes this acquisition will enable it
to further build its inventory of potential drilling locations over the
historically prolific Carter Knox anticline in the Anadarko Basin through a 3-D
seismic shoot planned for 1998.
 
     Primarily through its exploration efforts, the Company increased its net
production volumes 52% to 3.1 Bcfe in 1997 from 2.1 Bcfe in 1996. As further
evidence of the Company's acceleration efforts subsequent to its May 1997
initial public offering, Brigham increased its average net daily production
volumes from 6.6 MMcfe in the second quarter 1997 to 15.9 MMcfe in the first
quarter 1998 at a compound annual growth rate of 34% per quarter.
 
     Based on the results that the Company has achieved from its growth strategy
since its initial public offering, Brigham intends with the proceeds from the
Offering to increase its exploration activities in 1998 to take advantage of
opportunities currently available to further accelerate the Company's growth. As
a result, the Company has increased its 1998 capital budget for net seismic,
land and drilling expenditures to approximately $68 million from the $52 million
originally budgeted. The Company's current 1998 capital budget contemplates
additional expenditures for 3-D seismic acquisition due to increased working
interests in its planned 1998 projects, an increase in budgeted drilling
expenditures in the Anadarko Basin and the Gulf Coast provinces and a reduction
in planned drilling activity in West Texas in part due to recent declines in oil
prices. The Company intends to continue to retain higher working interests in
its 3-D seismic projects in the Anadarko Basin and the onshore Gulf Coast. By
increasing its working interests to in excess of 75% in the majority of its
current and planned seismic projects, Brigham expects to further accelerate its
growth not only by retaining a greater portion of the reserves its discovers,
but also by increasing its ability to control the timing of the drilling of its
exploration projects and therefore helping to accelerate its drilling pace. The
Company's current 1998 budget consists of 106 gross (56 net) wells, compared
with the 100 gross (42 net) wells previously budgeted for 1998. This increase in
anticipated 1998 drilling is the result of an increase in planned
                                       33
<PAGE>   35
 
drilling of higher working interest wells in the Anadarko Basin and the Gulf
Coast offset by a reduction in planned drilling activity in West Texas.
 
COMPETITIVE ADVANTAGES
 
     Brigham believes that its knowledge base, personnel and technology provide
it with the following competitive advantages to capture undiscovered natural gas
and oil reserves.
 
          3-D Seismic Knowledge Base. The Company began acquiring 3-D seismic in
     1990 and drilled its first 3-D delineated well, which was a discovery, in
     February 1991. From inception through 1997, the Company has acquired 4,005
     square miles of 3-D seismic and drilled 370 wells in over 20 geologic
     trends in seven basins and seven states. As a result, the Company has
     gained extensive technological and economic knowledge relating to the
     application of 3-D seismic to different geologic trends. This experience
     and knowledge enable the Company to refine its exploration techniques and
     identify exploration areas where Brigham believes 3-D seismic can be
     applied to reduce risks and enhance returns on its investments.
 
          Technological Expertise. Led by its CEO, who is an experienced,
     practicing geophysicist, the Company has built an exploration staff that
     includes nine other geophysicists and ten geologists. Brigham's
     explorationists collectively have over 300 years of experience, including
     approximately 85 years of experience using CAEX workstations, and have
     expertise in many geologic trends. The Company makes extensive use of
     advanced technologies, including 3-D seismic imaging and CAEX and in-house
     analytical and processing capabilities, to define drilling prospects. To
     support the efforts of its explorationists, Brigham has invested in
     advanced hardware and software, including 19 UNIX-based CAEX workstations.
 
          Project Generation and Control. Brigham is not dependent on third
     parties for its project flow, having generated approximately 90% of its 3-D
     seismic exploration projects through the acquisition of proprietary
     seismic. Therefore, the Company is able to manage the predrilling
     exploration phases, from project conception and assemblage through 3-D
     seismic acquisition, processing and interpretation and subsequent leasing.
     Brigham believes that its management of the exploration process enhances
     project quality and compresses the cycle time, contributing to lower
     finding and development costs and an enhanced project rate of return.
     Furthermore, the Company can determine the level of working interest it
     retains and the extent to which it manages drilling and post-drilling
     operations and continues to expand its efforts in these areas.
 
          Numerous Potential Drilling Locations. As of December 31, 1997, the
     Company had identified 1,170 3-D defined potential drilling locations in
     historically productive geologic trends, of which 370 had been drilled. The
     Company currently anticipates drilling 106 of these locations (56 net) in
     1998 at an aggregate drilling cost of approximately $47 million. The
     Company also anticipates acquiring approximately 970 gross (735 net) square
     miles of 3-D seismic in 1998 at a net cost to the Company of approximately
     $17 million. The Company continually evaluates and prioritizes potential
     drilling locations to determine whether to drill them, farm them out or
     replace them with higher quality locations.
 
          Pioneering Innovations.  In 1990 the Company pioneered the assemblage
     of large scale onshore 3-D seismic projects and the use of preseismic lease
     options for the systematic exploration of proven natural gas and oil
     provinces. The Company believes it was one of the first to form alliances
     and joint participation arrangements with companies and individuals
     possessing extensive local geologic or operating expertise to complement
     its 3-D seismic exploration expertise. Subsequent innovations include the
     Company's 3-D seismic acquisition and processing alliances and its creative
     industry trade structures to financially leverage its drilling program.
 
EXPLORATION AND OPERATING APPROACH
 
     From inception through December 31, 1997, the Company had acquired 3-D
seismic in 119 projects covering 4,005 square miles (2.6 million acres) in 20
geologic trends in seven basins and seven states. Through
 
                                       34
<PAGE>   36
 
this activity, the Company has developed expertise in the selection of geologic
trends that are suitable for 3-D seismic exploration. Brigham uses experience
that it gains within a trend to enhance the quality of subsequent projects in
the same trend and other analogous trends, contributing to lower finding and
development costs, compressing project cycle times and increasing project rates
of return.
 
     The Company typically acquires 3-D seismic in and around existing
production where the Company can benefit from the imaging of producing analogs.
These 3-D seismic defined analogs, combined with the Company's experience in
drilling 370 wells, provide the Company with a knowledge base to evaluate other
potential geologic trends, 3-D seismic projects within trends and 3-D seismic
delineated potential drilling locations. The Company's knowledge base assists in
identifying geologic trends where Brigham believes it can find and develop
economic volumes of natural gas and oil.
 
     The Company has experience exploring with 3-D seismic in a wide range of
reservoir types and geologic trapping styles, both stratigraphic and structural
(including reefs, salt domes, channel sands, complex faulted and fractured
reservoirs and pinchout plays). The Company seeks to supplement its knowledge
base with local geologic expertise for a particular geologic trend by hiring new
explorationists, engaging consultants and entering into joint ventures with
industry participants. In addition, if the targeted geologic trend is extensive,
the Company typically acquires a digital data base for integration on the
Company's CAEX workstations, including digital land grids, well information, log
curves, production information, geologic studies, geologic top data bases and
existing 2-D seismic.
 
     The Company uses its knowledge base, local geological expertise and
acquired digital data bases, integrated with 3-D seismic, to create maps of
producing reservoirs. The Company believes its 3-D generated maps are more
accurate than previous reservoir maps used by the industry (which generally were
based on subsurface geological information and 2-D seismic surveys), enabling
the Company to better evaluate recoverable reserves and the economic feasibility
of projects and drilling locations.
 
     Brigham acquires most of its raw 3-D seismic on a proprietary basis using
seismic acquisition vendors. Additionally, the Company acquires data through
alliances affording it the exclusive right to interpret and use data for
extended periods of time. Occasionally the Company participates in
non-proprietary group shoots of 3-D seismic. In its proprietary acquisitions and
alliances, Brigham selects the sites of projects, primarily guided by its
knowledge and experience in the core provinces it explores; establishes and
monitors the seismic parameters of each project for which data is shot; and
typically selects the equipment that will be used. Data is generally priced on
the basis of square miles shot. See "Business and Properties -- Industry
Alliances."
 
PRIMARY EXPLORATION PROVINCES
 
     Brigham's exploration activities are concentrated primarily in three core
provinces: the Anadarko Basin of western Oklahoma and the Texas Panhandle; the
onshore Gulf Coast of Texas and Louisiana; and West Texas. Brigham is
accelerating 3-D seismic activity in the Anadarko Basin and the Gulf Coast and
will continue such activity in those geologic trends of the West Texas region
where it has achieved its best results historically. Brigham is focusing its 3-D
seismic exploration efforts in provinces where it believes 3-D technology may be
effectively applied and which the Company believes offer relatively large
potential reserve volumes per well and per field, high potential production
rates and multiple producing objectives.
 
     Although the Company is acquiring 3-D seismic within the provinces listed
below and has identified approximately 800 potential drilling locations yet to
be drilled in those provinces, there can be no assurance that any of the seismic
will be acquired or will generate additional drilling locations or that any
potential drilling locations will be drilled at all or within the expected time
frame. The final determination with respect to the drilling of any well,
including those currently budgeted, will depend on a number of factors,
including (i) the results of exploration efforts and the review and analysis of
the seismic, (ii) the availability of sufficient capital resources by the
Company and other participants for drilling prospects, (iii) economic and
industry conditions at the time of drilling, including prevailing and
anticipated prices for natural gas and oil and the availability of drilling rigs
and crews, (iv) the financial resources and results of the Company and (v) the
availability of leases on reasonable terms and permitting for the potential
drilling location. There can be no
 
                                       35
<PAGE>   37
 
assurance that the budgeted wells will, if drilled, encounter reservoirs of
commercial quantities of natural gas or oil.
 
<TABLE>
<CAPTION>
                              3-D SEISMIC                                                   CURRENT 1998 CAPITAL BUDGET(1)
                                 DATA                                                --------------------------------------------
                               ACQUIRED/      3-D SEISMIC                UNDRILLED                             CAPITAL
                              INTERPRETED         DATA         GROSS     POTENTIAL                        EXPENDITURES($MM)
                                 AS OF        BUDGETED TO      WELLS     DRILLING       WELLS       -----------------------------
                               12/31/97      BE ACQUIRED IN   DRILLED    LOCATIONS     BUDGETED       NET
                              (GROSS SQ.      1998 (GROSS     THROUGH      AS OF     ------------   SEISMIC     NET
PROVINCE                        MILES)         SQ. MILES)     12/31/97   12/31/97    GROSS   NET    & LAND    DRILLING   TOTAL(2)
--------                     -------------   --------------   --------   ---------   -----   ----   -------   --------   --------
<S>                          <C>    <C>      <C>              <C>        <C>         <C>     <C>    <C>       <C>        <C>
Anadarko Basin.............  1,515/  1,195        550            55         364        62    32.0    $23.0     $27.5      $50.5
Gulf Coast.................    566/    325        400            11         110        19    13.0     (3.0)     14.0       11.0
West Texas.................  1,649/  1,600         30           287         302        24    11.0      1.5       5.0        6.5
Others(3)..................    275/    275         --            17          24         1     0.2       --       0.2        0.2
                             ------ ------        ---           ---         ---       ---    ----    -----     -----      -----
        Total..............  4,005/  3,395        980           370         800       106    56.2    $21.5     $46.7      $68.2
                             ====== ======        ===           ===         ===       ===    ====    =====     =====      =====
</TABLE>
 
---------------
 
(1) Prepared as of May 12, 1998.
 
(2) 3-D seismic and land acquisition costs and drilling expenditures.
 
(3) Colorado, Kansas and Montana.
 
     Anadarko Basin. The Anadarko Basin is a prolific natural gas province that
the Company believes has been relatively under explored, particularly with
regard to deep, high potential objectives. The Anadarko Basin contains numerous
historically elusive stratigraphic targets, such as the Red Fork, Morrow and
Springer channel sands, and structural targets, such as the Hunton and Arbuckle
carbonates, which are well-suited to 3-D seismic imaging. In some cases, these
objectives have produced in excess of 30 Bcf of natural gas from a single well
at rates up to 30 MMcf of natural gas per day.
 
     The Company has assembled an extensive digital data base in this province,
including geologic studies, basin wide geologic tops, production data, well
data, geographic data and over 8,400 miles of 2-D seismic. Working with its team
of in-house geologists and supplemented by consulting geologists, the Company's
explorationists integrate this data with their extensive expertise and knowledge
base to generate 3-D seismic projects in the Anadarko Basin.
 
     Over the last several years the Company has accelerated its activity in the
Anadarko Basin, acquiring 195 square miles in 1995, 457 square miles in 1996 and
648 square miles in 1997. The Company retained a 66% average working interest in
the 3-D seismic it acquired in this province in 1997. The Company believes its
increased level of activity in the Anadarko Basin will be a significant factor
in the Company's growth. As of December 31, 1997, the Company had acquired or
was acquiring 1,515 square miles (969,600 acres) in 30 projects in the Anadarko
Basin. The Company anticipates acquiring 550 square miles (352,000 acres) of
additional 3-D seismic in this province in 1998.
 
     As of December 31, 1997, Brigham had completed 44 wells in 55 attempts (80%
success rate) in the Anadarko Basin and had found cumulative proved reserves of
44 net Bcfe. In 1997, the Company completed 19 wells in 23 attempts in its
Anadarko Basin province with an average working interest of 39%, adding 31 net
Bcfe of proved reserves. In addition, the Company acquired 21.5 net Bcfe of
proved reserves in this region in November 1997. As of December 31, 1997, the
Company had 364 3-D delineated potential drilling locations in the Anadarko
Basin, of which the Company intends to drill 62 gross (32 net) wells in 1998.
 
     Brigham's Anadarko Basin activity provides a blend of intermediate depth,
moderate risk objectives and deeper, higher potential but somewhat higher risk
objectives. The intermediate depth targets at 9,000 to 13,000 feet have provided
Brigham with good drilling results to date. These include the Upper Morrow
channel sands and the Lower Morrow shallow marine sands of the Texas Panhandle,
the Springer channels of the Watonga Chikasha trend of western Oklahoma, and
structural traps in the Hunton carbonates of the northeastern portion of the
Anadarko Basin.
 
     Intermediate depth objectives in the Anadarko Basin can provide significant
reserve additions, as evidenced by Brigham's Lower Morrow discovery in its
Pistol Pete 3-D Seismic Project. The Company's
 
                                       36
<PAGE>   38
 
largest discovery to date, the Brigham-operated Christopher 84 #1, was completed
in one of four apparently productive Lower Morrow zones at approximately 12,000
feet, and initially tested at 2.65 MMcfe per day with a flowing tubing pressure
of 1,800 pounds per square inch. This well is currently producing approximately
4.5 MMcfe per day with a flowing tubing pressure of 4,275 pounds per square
inch. Brigham owns a 36% working interest in the well and plans to drill two
development wells in 1998. The Company is completing the first offset well to
the Christopher 84 #1, in which Brigham has a 36% working interest, and is
currently drilling the second offset well, in which Brigham has a 91% working
interest. Estimated reserves for this discovery and the two development wells
are 35.6 gross Bcfe, or 16.1 Bcfe net to Brigham.
 
     The deeper Anadarko Basin objectives provided Brigham's second largest
discovery to date, the Brigham operated Weise 28 #1 in its Jayhawk 3-D Seismic
Project in Wheeler County, Texas. This well represents Brigham's first
significant Hunton formation discovery. Drilled to a total depth of
approximately 14,800 feet, the Weise 28 #1 tested an initial production rate of
6.1 MMcfe per day. This well is currently producing approximately 3 MMcfe per
day with a flowing tubing pressure of 1,600 pounds per square inch. A
development well will be drilled on this discovery in 1998. The Weise 28 #1 and
its offset are estimated to contain proved reserves of approximately 16 gross
Bcfe, or 4.3 Bcfe net to Brigham. Brigham plans to drill several higher
potential tests in the deeper portions of the Anadarko Basin primarily in the
Texas Panhandle and far western Oklahoma in 1998.
 
     On November 12, 1997, Brigham acquired an interest in producing properties
and undeveloped acreage at the northern end of the Carter Knox anticline in
Grady County, Oklahoma (the "Chitwood Acquisition"). For $13.5 million, Brigham
acquired estimated net proved reserves totaling 21.3 Bcfe and received a 50%
working interest in 3,600 net acres of leasehold and 750 net mineral acres in
the Chitwood Acquisition. The properties were acquired from Mobil Oil
Corporation through Ward Petroleum Corporation ("Ward"), and Ward will act as
drilling operator. In 1998, Brigham and Ward plan to participate in a 20 square
mile 3-D seismic project in this area to delineate opportunities in the
Springer, Big Four, Bromide and Arbuckle formations. The Chitwood Acquisition
overlaps and is adjacent to Brigham's West Bradley 3-D Seismic Project, where
Ward operates the majority of the drilling operations.
 
     Gulf Coast. The onshore Gulf Coast region of South Texas and South
Louisiana is a high potential, multi-pay province that lends itself to 3-D
seismic exploration due to its substantial structural and stratigraphic
complexity. The Company has assembled a digital data base including
geographical, production, geophysical and geological information that the
Company evaluates on its CAEX workstations. Working with consulting regional
geologists, the Company's explorationists integrate this data with their
extensive expertise and knowledge base to generate and evaluate 3-D seismic and
projects in the Gulf Coast. Brigham's commitment to this province is evidenced
by the Company's staff additions, the opening of its Houston office and the
addition of ten new 3-D seismic projects in 1996 and 1997.
 
     The Company anticipates that its increased project assemblage and 3-D
seismic acquisition activity in the Gulf Coast will generate accelerated
drilling in this province in 1998 and 1999. The Company is currently assembling
projects in the Expanded Wilcox and Expanded Vicksburg trends in South Texas,
the Miocene trend in South Texas and South Louisiana, and the Lower and Middle
Frio trends of South Texas.
 
     As of December 31, 1997, the Company had acquired or was acquiring 566
square miles (362,240 acres) of 3-D seismic in seven projects in the onshore
Gulf Coast province. The Company anticipates acquiring 400 square miles (256,000
acres) of additional 3-D seismic in this province in 1998. As of December 31,
1997, Brigham had completed 8 wells in 11 attempts (73% success rate) in the
Gulf Coast and had found cumulative proved reserves of 3 net Bcfe. In 1997, the
Company completed seven wells in 10 attempts with an average working interest of
9% adding 3 net Bcfe of proved reserves. As of December 31, 1997, the Company
had 110 3-D delineated potential drilling locations in the Gulf Coast province,
of which the Company intends to drill 19 gross (13 net) wells in 1998.
 
     Brigham initiated its Gulf Coast effort in 1995 with the Esperson Dome
Project in Liberty County, Texas where the Company and its participants
currently control approximately 9,600 gross (7,500 net) acres through leases and
farmouts and have acquired 39 square miles of 3-D seismic. The Esperson Dome
Project targets structurally trapped sands in the Miocene, Vicksburg and
Yegua/Cook Mountain series ranging in depth from
 
                                       37
<PAGE>   39
 
1,200 feet to 10,000 feet on a complexly faulted salt dome feature. Ten wells
have been drilled in the project to date (one Miocene, three Yegua/Cook Mountain
and six Vicksburg), yielding seven discoveries. Brigham currently maintains a
small net profits interest in the Esperson Dome Project that will convert to a
variable back-in working interest of 12% to 20% in the project after payout.
 
     Brigham's Welder Ranch and Caliente projects encompass an area covering
more than 400 square miles within a non-proprietary 3-D seismic program
currently being conducted in Duval and Webb counties, Texas. Initially Brigham
acquired 48 square miles of 3-D seismic over the Welder Cabeza Ranch, where the
Company controls a 100% working interest in a seismic option on approximately
17,000 acres. The first well in the project, the Brigham-operated Welder-State
212 #1, in which Brigham owns an 80% working interest, was completed in February
1998, and tested naturally at a rate of 2.75 MMcf per day from the Lower Wilcox
formation at 13,350 feet. This well is currently producing approximately 500 Mcf
per day. The Company plans to add perforations and stimulate additional pay
zones in an attempt to increase production from this well. Brigham has
interpreted virtually all of the data covering the Welder Ranch Project and
approximately 25% of the data covering the Caliente Project, and has eight
exploratory wells budgeted in these projects for 1998.
 
     Another project in South Texas is Brigham's Diablo Project covering
approximately 12,000 acres in Brooks County, Texas. The Company acquired 25
square miles of proprietary 3-D seismic in 1997 and plans to shoot an additional
33 square miles in 1998. Brigham recently teamed up with Exxon Company, USA,
which controls adjoining acreage to jointly explore the combined acreage for
potential below 10,000 feet in the Vicksburg formation. Brigham has retained a
33% working interest in this deep joint exploration project. In prospective
zones above 10,000 feet, primarily the Frio, Brigham has retained a 100% working
interest in its original 4,000 acre lease block. The Company plans to drill a
number of wells in this project in 1998 to test the shallow Frio and deeper
Vicksburg objectives.
 
     In its Southwest Danbury Project in Brazoria County, Texas, Brigham is the
operator of a 13,000 foot Frio test that commenced drilling late in the first
quarter of 1998. Brigham has retained a 46% working interest in this test, and
plans to drill several additional wells in this project in 1998.
 
     In May 1997, Brigham initiated its El Sauz Project with a seismic option
covering approximately 94,000 acres in Willacy and Kennedy counties, Texas. The
El Sauz Project is an underexplored area due north of the Willamar Field, which
has produced a cumulative 350 Bcf from the Miocene and Frio sands. Brigham
expects to define Miocene and Frio sands at 6,000 to 10,000 feet, with
additional potential as deep as 18,000 feet. Reserve targets range from 5 to 20
Bcf per well. The Company initiated a 200 square mile 3-D seismic program over
this acreage in 1998, with initial drilling anticipated for early 1999. Brigham
has retained a 55% working interest in the El Sauz Project after it brought in
two industry participants to leverage preseismic land and 3-D seismic
acquisition costs of this project.
 
     Also in the Miocene/Frio trend of South Texas, Brigham acquired a seismic
option covering approximately 28,000 acres in the Hawkins Ranch located in
Matagorda County, Texas. The region has potential in the shallow, nonpressured
Miocene and Frio sands as well as the deeper, pressured Frio sands. The Company
has acquired approximately 94 square miles of new proprietary 3-D seismic to
merge with 65 square miles of non-proprietary 3-D seismic already in inventory.
The Company is currently negotiating a transaction pursuant to which the above
described 94 square miles of proprietary 3-D seismic would, if the transaction
is consummated, become non-proprietary after an exclusivity period benefiting
the Company, allowing the Company to acquire the 3-D seismic at a substantial
cost savings. Brigham has retained working interests ranging from 69% to 75% in
this project.
 
     Brigham's first significant venture into South Louisiana, its Tigre Point
Project, is located in six feet of water in the transition zone off Vermilion
Parish. The project consists of 44 square miles of 3-D seismic covering a 7,200
acre lease block in Louisiana State waters, where Brigham currently controls a
75% working interest. The project has targeted the same series of sands that
produce in the prolific Freshwater Bayou field, located five miles to the north.
An 18,000 foot Lower Miocene test is scheduled for late 1998. Currently, Brigham
plans to retain a 30% to 40% working interest in this project following the sale
of a portion of its interest to an industry participant.
 
                                       38
<PAGE>   40
 
     West Texas. The Company's 3-D seismic drilling activity in the West Texas
region has been focused in the Horseshoe Atoll, the Midland Basin and the
Eastern Shelf of the Permian Basin and the Hardeman Basin. The Company plans to
continue drilling its locations in these areas. Recently the Company initiated
an exploration program in the Delaware Basin and increased its activity in
portions of geologic trends that the Company believes offer greater potential
for lower finding costs and higher returns, including the Ellenberger and
Devonian formations of the Delaware Basin and the Fusselman formation of the
Midland Basin.
 
     As of December 31, 1997, the Company had acquired or was acquiring 1,649
square miles (1,055,360 acres) in 74 projects in the West Texas region. The
Company anticipates acquiring 30 square miles (19,200 acres) of additional 3-D
seismic in this province in 1998. As of December 31, 1997, Brigham had completed
180 wells in 287 attempts (63% success rate) in the West Texas province and had
found cumulative proved reserves of 24 net Bcfe. In 1997, the Company completed
19 wells in 34 attempts with an average working interest of 45% adding 4 net
Bcfe of proved reserves. As of December 31, 1997, the Company had 302 3-D
delineated potential drilling locations in the West Texas region, of which the
Company intends to drill 24 gross (11 net) wells in 1998.
 
     The Company has recently experienced success in the deeper portions of the
Midland Basin, where it has drilled five Fusselman discoveries to date.
Currently the most significant of these discoveries is the Elizabeth Rose field,
with gross proved reserves estimated by the Company's independent petroleum
consultants at December 31, 1997 of 1.5 MMBbls of oil. The Company has drilled
five wells in this Fusselman field that were producing an aggregate of
approximately 890 Bbls of oil per day in February 1998. Brigham's working
interest in its five Fusselman discoveries ranges from 19% to 91%. In 1998 the
Company has acquired 27 square miles of 3-D seismic in three additional 3-D
seismic projects adjacent to the Elizabeth Rose field and currently retains
working interests of 100% in these projects.
 
     The Company completed three Canyon Reef discoveries during 1997 in its
Discovery Project located in the Horseshoe Atoll Trend. This project, in which
Brigham currently retains a working interest of 75%, targets oil producing
Canyon-age reef objectives at depths of approximately 9,500 feet. The Company's
three 1997 discoveries in its Discovery Project were producing an aggregate of
approximately 200 Bbls of oil and 900 Mcf of natural gas per day in February
1998. Brigham plans to drill three additional wells in its Discovery Project
during 1998.
 
     Among Brigham's higher potential, higher risk projects in its West Texas
province are its Buffalo and Longhorn projects, located in the Delaware Basin,
in which the Company owns a 25% working interest. From two 3-D seismic programs
covering approximately 137 square miles acquired in 1996 and 1997, the Company
has identified numerous potential 3-D seismic delineated drilling locations and
has leased over 23,000 gross (5,780 net) acres. These projects are surrounded by
prolific production from the Devonian and Ellenberger formations at depths of
15,000 to 21,000 feet, in fields such as Evetts (approximately 600 Bcf of
natural gas to date from 16 wells) and War Wink South (approximately 295 Bcf of
natural gas to date from eight wells).
 
                                       39
<PAGE>   41
 
NATURAL GAS AND OIL RESERVES
 
     The Company's estimated total net proved reserves of natural gas and oil as
of December 31, 1995, 1996 and 1997 and the present values attributable to these
reserves as of those dates were as follows:
 
<TABLE>
<CAPTION>
                                                              AS OF DECEMBER 31,
                                                          ---------------------------
                                                           1995     1996(1)    1997
                                                          -------   -------   -------
<S>                                                       <C>       <C>       <C>
Estimated net proved reserves:
  Natural gas (MMcf)....................................    4,257    10,257    53,230
  Oil (MBbls)...........................................    1,672     1,940     3,181
  Natural gas equivalent (MMcfe)........................   14,289    21,897    72,316
Proved developed reserves as a percentage of proved
  reserves..............................................      80%       67%       65%
Present Value of Future Net Revenues(2) (in
  thousands)............................................  $18,222   $44,506   $69,249
Standardized Measure of Discounted Future Net Cash
  Flows(3) (in thousands)...............................  $18,222   $44,506   $64,274
</TABLE>
 
---------------
 
(1) Net of a sale by the Company in January 1996 of its interest in certain
    properties that accounted for 299 MMcf of natural gas and 272 MBbls of oil
    (1,931 MMcfe of proved reserves) as of December 31, 1995.
 
(2) The Present Value of Future Net Revenues attributable to the Company's
    reserves was prepared using prices in effect at the end of the respective
    periods presented, discounted at 10% per annum on a pre-tax basis. These
    amounts reflect the effects of the Company's hedging activities in the
    periods presented.
 
(3) The Standardized Measure of Discounted Future Net Cash Flows prepared by the
    Company represents the present value of future net revenues after income
    taxes discounted at 10%. These amounts reflect the effects of the Company's
    hedging activities in the periods presented.
 
     The average prices for the Company's reserves were $1.85 per Mcf of natural
gas and $18.22 per Bbl of oil as of December 31, 1995, $3.62 per Mcf of natural
gas and $24.66 per Bbl of oil as of December 31, 1996 and $2.11 per Mcf of
natural gas and $16.64 per Bbl of oil as of December 31, 1997.
 
     In accordance with applicable requirements of the SEC, estimates of the
Company's proved reserves and future net revenues are made using sales prices
estimated to be in effect as of the date of such reserve estimates and are held
constant throughout the life of the properties (except to the extent a contract
specifically provides for escalation). Estimated quantities of proved reserves
and future net revenues therefrom are affected by natural gas and oil prices,
which have fluctuated widely in recent years. At December 31, 1997, the date the
Company's reserves and present value were estimated, the prices of natural gas
and oil on the NYMEX were $2.26 per MMBtu and $17.64 per Bbl, respectively. From
January 1, 1998 through May 22, 1998, the price of natural gas on the NYMEX
ranged from $2.64 per MMBtu to $2.00 per MMBtu and the price of oil on the NYMEX
ranged from $17.82 per Bbl to $13.21 per Bbl. There are numerous uncertainties
inherent in estimating natural gas and oil reserves and their estimated values,
including many factors beyond the control of the Company. The reserve data set
forth herein represents only estimates. Reservoir engineering is a subjective
process of estimating underground accumulations of natural gas and oil that
cannot be measured in an exact manner. The accuracy of any reserve estimate is a
function of the quality of available data and of engineering and geologic
interpretation and judgment. As a result, estimates of different engineers,
including those used by the Company, may vary. In addition, estimates of
reserves are subject to revision based upon actual production, results of future
development and exploration activities, prevailing natural gas and oil prices,
operating costs and other factors. The revisions may be material. Accordingly,
reserve estimates are often different from the quantities of natural gas and oil
that are ultimately recovered and are highly dependent upon the accuracy of the
assumptions upon which they are based. The Company's estimated proved reserves
have not been filed with or included in reports to any federal agency. See "Risk
Factors -- Uncertainty of Reserve Information and Future Net Revenue Estimates."
 
     Estimates with respect to proved reserves that may be developed and
produced in the future are often based upon volumetric calculations and upon
analogy to similar types of reserves rather than actual production
 
                                       40
<PAGE>   42
 
history. Estimates based on these methods are generally less reliable than those
based on actual production history. Subsequent evaluation of the same reserves
based upon production history will result in variations in the estimated
reserves that may be substantial.
 
DRILLING ACTIVITIES
 
     The Company drilled, or participated in the drilling of, the following
number of wells during the periods indicated.
 
<TABLE>
<CAPTION>
                                                                                                THREE
                                                                                                MONTHS
                                                         YEAR ENDED DECEMBER 31,                ENDED
                                                ------------------------------------------    MARCH 31,
                                                    1995           1996           1997         1998(1)
                                                ------------   ------------   ------------   ------------
                                                GROSS   NET    GROSS   NET    GROSS   NET    GROSS   NET
                                                -----   ----   -----   ----   -----   ----   -----   ----
<S>                                             <C>     <C>    <C>     <C>    <C>     <C>    <C>     <C>
Exploratory Wells:
  Natural gas.................................    5      1.2     5      1.2    15      6.3     6      1.7
  Oil.........................................   37      8.1    22      5.2    21      7.9     2      1.6
  Non-productive..............................   32      8.7    24      7.0    26      9.8     1      0.7
                                                 --     ----    --     ----    --     ----    --     ----
          Total...............................   74     18.0    51     13.4    62     24.0     9      4.0
                                                 ==     ====    ==     ====    ==     ====    ==     ====
Development Wells:
  Natural gas.................................   --       --    10      1.3     4      1.6    --       --
  Oil.........................................    4      0.5     5      1.0     6      1.8     1      0.2
  Non-productive..............................   --       --     1      0.2     1      0.6     1      0.9
                                                 --     ----    --     ----    --     ----    --     ----
          Total...............................    4      0.5    16      2.5    11      4.0     2      1.1
                                                 ==     ====    ==     ====    ==     ====    ==     ====
</TABLE>
 
---------------
 
(1) At March 31, 1998, the Company was in the process of drilling 2 gross (0.8
    net) wells that are not reflected in the table.
 
     The Company does not own any drilling rigs, and the majority of its
drilling activities have been conducted by industry participant operators or
independent contractors under standard drilling contracts. Consistent with its
business strategy, the Company has chosen to retain operations of an increasing
number of the wells it drills and expects to continue to operate more wells in
1998.
 
PRODUCTIVE WELLS AND ACREAGE
 
  Productive Wells
 
     The following table sets forth the Company's ownership interest as of
December 31, 1997 in productive natural gas and oil wells in the areas
indicated.
 
<TABLE>
<CAPTION>
                                                    NATURAL GAS        OIL           TOTAL
                                                    ------------   ------------   ------------
PROVINCE                                            GROSS   NET    GROSS   NET    GROSS   NET
--------                                            -----   ----   -----   ----   -----   ----
<S>                                                 <C>     <C>    <C>     <C>    <C>     <C>
Anadarko Basin....................................   43     13.0      5     1.2     48    14.2
Gulf Coast........................................    1      0.0      5     0.1      6     0.1
West Texas........................................    2      0.7     91    24.5     93    25.2
Other.............................................   --       --      1     0.5      1     0.5
                                                     --     ----    ---    ----    ---    ----
          Total...................................   46     13.7    102    26.3    148    40.0
                                                     ==     ====    ===    ====    ===    ====
</TABLE>
 
     Productive wells consist of producing wells and wells capable of
production, including wells waiting on pipeline connection. Wells that are
completed in more than one producing horizon are counted as one well. Of the
gross wells reported above, none had multiple completions.
 
                                       41
<PAGE>   43
 
  Acreage
 
     Undeveloped acreage includes leased acres on which wells have not been
drilled or completed to a point that would permit the production of commercial
quantities of natural gas and oil, regardless of whether or not such acreage
contains proved reserves. A gross acre is an acre in which an interest is owned.
A net acre is deemed to exist when the sum of fractional ownership interests in
gross acres equals one. The number of net acres is the sum of the fractional
interests owned in gross acres expressed as whole numbers and fractions thereof.
The following table sets forth the approximate developed and undeveloped acreage
in which the Company held a leasehold, mineral or other interest at December 31,
1997:
 
<TABLE>
<CAPTION>
                                                DEVELOPED         UNDEVELOPED            TOTAL
                                              --------------   -----------------   -----------------
PROVINCE                                      GROSS     NET     GROSS      NET      GROSS      NET
--------                                      ------   -----   -------   -------   -------   -------
<S>                                           <C>      <C>     <C>       <C>       <C>       <C>
Anadarko Basin..............................  16,600   7,716    75,377    32,181    91,977    39,897
Gulf Coast..................................      --      --    18,588    14,902    18,588    14,902
West Texas..................................   6,035   1,794    19,957    11,517    25,992    13,311
Other.......................................     160      80   145,295    51,546   145,455    51,626
                                              ------   -----   -------   -------   -------   -------
          Total.............................  22,795   9,590   259,217   110,146   282,012   119,736
                                              ======   =====   =======   =======   =======   =======
</TABLE>
 
     All the leases for the undeveloped acreage summarized in the preceding
table will expire at the end of their respective primary terms unless the
existing leases are renewed, production has been obtained from the acreage
subject to the lease prior to that date, or some other "savings clause" is
implicated. The following table sets forth the minimum remaining terms of leases
for the gross and net undeveloped acreage:
 
<TABLE>
<CAPTION>
                                                               ACRES EXPIRING
                                                              -----------------
                                                               GROSS      NET
                                                              -------   -------
<S>                                                           <C>       <C>
Twelve Months Ending:
  December 31, 1998.........................................  120,186    46,491
  December 31, 1999.........................................   65,254    30,857
  December 31, 2000.........................................   51,984    24,263
  Thereafter................................................   21,793     8,535
                                                              -------   -------
          Total.............................................  259,217   110,146
                                                              =======   =======
</TABLE>
 
     In addition, the Company had lease options as of December 31, 1997 to
acquire an additional 254,699 acres, substantially all of which expire within
one year.
 
VOLUMES, PRICES AND PRODUCTION COSTS
 
     The following table sets forth the production volumes, average prices
received and average production costs associated with the Company's sale of
natural gas and oil for the periods indicated.
 
<TABLE>
<CAPTION>
                                                                                THREE MONTHS
                                                           YEAR ENDED               ENDED
                                                          DECEMBER 31,            MARCH 31,
                                                    ------------------------   ---------------
                                                     1995     1996     1997     1997     1998
                                                    ------   ------   ------   ------   ------
<S>                                                 <C>      <C>      <C>      <C>      <C>
Production:
  Natural gas (MMcf)..............................     272      698    1,382      243      740
  Oil (MBbls).....................................     177      227      291       63      115
  Natural gas equivalent (MMcfe)..................   1,332    2,060    3,126      623    1,431
Average sales price(1):
  Natural gas (per Mcf)...........................  $ 1.62   $ 2.30   $ 2.56   $ 3.10   $ 2.05
  Oil (per Bbl)...................................   17.76    19.98    19.40    21.82    14.15
Average production expenses and taxes (per
  Mcfe)...........................................  $  .69   $  .53   $  .55   $ 0.53   $ 0.42
</TABLE>
 
                                       42
<PAGE>   44
 
---------------
 
(1) Reflects the results of hedging activities in the periods presented.
 
COSTS INCURRED
 
     The costs incurred in natural gas and oil acquisition, exploration and
development activities are as follows (in thousands):
 
<TABLE>
<CAPTION>
                                                            YEAR ENDED DECEMBER 31,
                                                          ---------------------------
                                                           1995      1996      1997
                                                          -------   -------   -------
<S>                                                       <C>       <C>       <C>
Cost incurred for the year:
  Exploration...........................................  $ 6,893   $10,527   $29,421
  Property acquisition..................................    1,885     6,195    26,922
  Development...........................................      713     1,328     2,953
  Proceeds from participants............................   (1,296)   (4,111)     (319)
                                                          -------   -------   -------
                                                          $ 8,195   $13,939   $58,977
                                                          =======   =======   =======
</TABLE>
 
     Costs incurred represent amounts incurred by the Company for exploration,
property acquisition and development activities. Periodically, the Company will
receive reimbursement of certain costs from participants in its projects
subsequent to project initiation in return for an interest in the project. These
payments are described as "Proceeds from participants" in the table above.
 
EXPLORATION STAFF
 
     Over the last seven years the Company has assembled an exploration staff
that includes nine geophysicists, ten geologists, four petroleum engineers, four
computer applications specialists, three geophysical/geological/engineering
technicians, five landmen and six lease and division order analysts. Brigham's
nine geophysicists have different but complementary backgrounds, and their
diversity of experience in varied geological and geophysical settings, combined
with various technical specializations (from hardware and systems to software
and seismic data processing), provide the Company with valuable technical
intellectual resources. The Company's team of explorationists has over 300 years
of exploration experience and approximately 85 years of 3-D CAEX workstation
experience, most of which was acquired at Brigham and various major and large
independent oil companies. Occasionally, the Company complements and leverages
its exploration staff by seeking out alliances or retainer relationships with
geologists having extensive experience in a particular area of interest.
 
3-D SEISMIC TECHNOLOGY
 
     The Company's strategy is to use 3-D seismic and other advanced
technologies, including CAEX, to systematically explore and develop domestic
onshore natural gas and oil provinces. In general, 3-D seismic is the process of
acquiring seismic data along multiple lines and grids. The primary advantage of
3-D seismic over 2-D seismic is that it provides information with respect to
multiple horizontal and vertical points within a geologic formation instead of
information on a single vertical line or multiple vertical lines within the
formation. Acquiring larger amounts of data relating to a geologic formation
allows a user to better correlate the data and, in some cases, obtain a greater
understanding and image of the formation. Although it is impossible to predict
with certainty the specific configuration or composition of any underground
geologic formation, the use of 3-D seismic provides clearer and more accurate
projected images of complex geologic formations, which can assist a user in
evaluating whether to drill for natural gas and oil reserves. If a decision to
drill is made, 3-D seismic can also help in determining the optimal location to
drill.
 
     CAEX is the process of accumulating and analyzing the various seismic,
production and other data obtained relating to a geographic area. In general,
CAEX involves accumulating various 2-D and 3-D seismic with respect to a
potential drilling location, correlating that data with historical well control
and production data from similar properties and analyzing the available data
through computer programs and modeling
 
                                       43
<PAGE>   45
 
techniques to project the likely geologic composition of a potential drilling
location and potential locations of undiscovered natural gas and oil reserves.
This process relies on a comparison of data with respect to the potential
drilling location and historical data with respect to the density and sonic
characteristics of different types of rock formations, hydrocarbons and other
subsurface minerals, resulting in a projected three dimensional image of the
subsurface. This modeling is performed through the use of advanced interactive
computer workstations and various combinations of available computer programs
that have been developed solely for this application.
 
     Brigham has invested extensively in the advanced computer hardware and
software necessary for 3-D seismic exploration. The Company has both Landmark
and Geoquest CAEX workstations. This workstation flexibility provides the
Company the opportunity to interpret a project on the particular CAEX
workstation that it believes is best suited for defining those particular
geologic objectives. Brigham's explorationists can access a diverse software
tool kit including SeisWorks, StratWorks, SeisCube, SurfCube, ZAP, Zmap+, ARIES,
SynTool, Poststack, Continuity Cube, TDQ, AutoPix, MapView, GeoViz, Voxels,
SynView, CSA (Computed Seismic Attributes), Surface Slice, Hampson -- Russell
AVO Analysis and Modeling and ZEH Graphics CGMage Builder (graphics montage
tool).
 
     The Company believes that its use of 3-D seismic technology provides it
with a number of benefits in the exploration, delineation and development
process that are not generally available to those who only use 2-D seismic and
conventional processing methods. In particular, the Company believes that it
obtains clearer and more accurate projected images of underground formations
through computer modeling, and is therefore better able to identify potential
locations of hydrocarbon accumulations based on the characteristics of the
formations and analogies made with nearby fields and formations where
hydrocarbons have been found. This enhanced data has been used to assist the
Company in eliminating potential drilling locations that might otherwise have
been drilled had the Company relied solely on 2-D seismic. This data has also
been used to assist the Company in attempting to identify the most desirable
location for the wellbore to increase the prospects of a successful exploratory
or development well and production from the reservoir.
 
INDUSTRY ALLIANCES
 
     Pursuant to certain alliances with Veritas DGC Land Ltd.("Veritas"),
Brigham had acquired approximately 850 square miles of 3-D seismic in the
Anadarko Basin through December 31, 1997 and had agreed to acquire from 775 to
875 additional square miles of data to be divided among numerous projects in
that province. In exchange for the Company's commitment to Veritas, the Company
and its assignees only pay a portion of the 3-D seismic acquisition costs as the
data is acquired. As the Company leases acreage or drills wells, it pays Veritas
the balance of the costs in the form of leasing and drilling fees. In addition,
in the event that the outstanding balance of deferred seismic acquisition costs
exceeds certain threshold amounts, the Company must pre-pay part of the leasing
and drilling fees to cause the outstanding balance to fall below the current
threshold amount. Under these arrangements, Veritas has agreed to make a
designated 3-D seismic crew available to the Company on a continuous basis and,
as long as the Company has a project area ready for surveying and field seismic
acquisition, to send the crew from one project area to the next without
interruption. If the Company does not have a project area designated upon
completion of one project, and Veritas has not been able to secure an
intervening project from a third party, the Company is obligated to pay Veritas
a stand-by fee. The Company has never incurred a stand-by fee to Veritas. These
arrangements afford the Company access to 3-D seismic acquisition in a
compressed cycle time, providing the Company with operational efficiencies.
 
     In addition, Veritas Geoservices, Ltd. provides three employees that
maintain and operate four seismic data processing workstations in Brigham's
offices. Supervised by Brigham's geophysicists, the vendor's employees process
most of the Company's 3-D seismic. The associated improvement in communication
and integration, from field data acquisition to processing, reduces project
cycle times, and therefore costs, while improving the quality of the data for
Brigham's subsequent interpretation.
 
     The Company has entered into alliances with Vintage Petroleum, Inc.
("Vintage") and Stephens Production Company ("Stephens") providing for their
participation with Brigham in all projects that the
 
                                       44
<PAGE>   46
 
Company conducts within a 625 square mile 3-D seismic program that was completed
in 1997 with Veritas in the Anadarko Basin. Vintage and Stephens bear a
disproportionate share of all pre-seismic and certain seismic costs on all
projects in the program. Net of the interests of Vintage and Stephens, the
Company holds a 37.5% interest in the program. The Company believes that this
leveraging of its costs is possible because of the expertise and knowledge that
the Company has developed, enabling the Company to build its revenue and cash
flow base at a time when it has been capital constrained.
 
     Brigham is currently acquiring 3-D seismic under a second alliance with
Veritas in the Anadarko Basin. From August through December 1997, the Company
acquired approximately 225 square miles of 3-D seismic under this alliance and
expects to acquire an additional 775 to 875 square miles in various
Brigham-generated projects by early 1999. The Company plans to retain a 100%
working interest in the projects under its second alliance with Veritas.
 
     In order to participate in wells drilled by the Company between April 1,
1996 and March 31, 1997, each of Gasco Limited Partnership ("Gasco") and Middle
Bay Oil Company, Inc. ("Middle Bay") agreed to fund 25% of the Company's
drilling costs and 12.5% of its completion costs for each well drilled. In
return, the Company assigned to each an undivided 12.5% of the Company's
interest in the leasehold allocated to the proration unit for each completed
well. As a result, the Company paid for 50% of costs attributable to its working
interest to casing point, and 75% of its completion costs, for 75% of its
original working interest for each well funded during the term of the agreement.
 
     The Company renewed its agreement with Gasco in early 1997. In order to
participate in wells drilled by the Company between April 1, 1997 and March 31,
1998, Gasco agreed to fund 18% of the Company's drilling costs and 9% of its
completion cost for each well. In return, the Company has agreed to assign to
Gasco an undivided 9% of the Company's interest in the leasehold allocated to
the production unit for each completed well. As a result, the Company pays for
82% of costs attributable to its working interest to casing point, and 91% of
its completion costs, for 91% of its original working interest for each well
funded during the term of the agreement.
 
     In order to participate in wells drilled by the Company between April 1,
1998 and March 31, 1999, Gasco agreed to fund 8% of the Company's drilling costs
and 4% of its completion cost for each well. In return, the Company has agreed
to assign to Gasco an undivided 4% of the Company's interest in the leasehold
allocated to the production unit for each completed well. As a result, the
Company pays for 92% of costs attributable to its working interest to casing
point, and 96% of its completion costs, for 96% of its original working interest
for each well funded during the term of the agreement.
 
     The Company believes that its agreements with Middle Bay and Gasco have
been beneficial because they have allowed the Company to leverage its working
interests in its properties by requiring it to bear a disproportionately smaller
share of drilling costs. Depending on future conditions, the Company may seek to
enter into similar types of arrangements with industry or financial
participants. To the extent that the Company does seek to enter into such future
arrangements, the terms of these arrangements, including the percentages of
costs borne and interests assigned, may vary from those in the Company's past
and present arrangements.
 
NATURAL GAS AND OIL MARKETING AND MAJOR CUSTOMERS
 
     Most of the Company's natural gas and oil production is sold through
various marketing arrangements under price sensitive or spot market contracts.
The revenues generated by the Company's operations are highly dependent upon the
prices of and demand for natural gas and oil. The price received by the Company
for its natural gas and oil production depends on numerous factors beyond the
Company's control, including seasonality, competition, the condition of the
United States economy, foreign imports, political conditions in other
oil-producing and natural gas-producing countries, the actions of the
Organization of Petroleum Exporting Countries, and domestic government
regulation, legislation and policies. Decreases in the prices of natural gas and
oil could have an adverse effect on the carrying value of the Company's proved
reserves and the Company's revenues, profitability and cash flow. Although the
Company is not currently experiencing any significant involuntary curtailment of
its natural gas or oil production, market, economic and regulatory factors
 
                                       45
<PAGE>   47
 
may in the future materially affect the Company's ability to sell its natural
gas or oil production. See "Management's Discussion and Analysis of Financial
Condition and Results of Operations," "Risk Factors -- Volatility of Natural Gas
and Oil Prices" and "Risk Factors -- Marketability of Production." For the year
ended December 31, 1997, sales to Cobra Oil & Gas Corporation and Pride Pipeline
Company were approximately 14% and 12%, respectively, of the Company's natural
gas and oil revenues. Due to the availability of other markets and pipeline
connections, the Company does not believe that the loss of any single natural
gas or oil customer would have a material adverse effect on the Company's
results of operations.
 
COMPETITION
 
     The oil and gas industry is highly competitive in all of its phases. The
Company encounters competition from other oil and gas companies in all areas of
its operations, including the acquisition of seismic and leasing options and
natural gas and oil leases on properties. The Company's competitors include
major integrated natural gas and oil companies and numerous independent natural
gas and oil companies, individuals and drilling and income programs. Many of its
competitors are large, well established companies with substantially larger
operating staffs and greater capital resources than the Company's. Such
companies may be able to pay more for seismic and lease options on natural gas
and oil properties and exploratory prospects and to define, evaluate, bid for
and purchase a greater number of properties and prospects than the Company's
financial or human resources permit. The Company's ability to acquire additional
properties and to discover reserves in the future will be dependent upon its
ability to evaluate and select suitable properties and to consummate
transactions in a highly competitive environment. See "Risk
Factors -- Competition" and "Risk Factors -- Substantial Capital Requirements."
 
OPERATING HAZARDS AND UNINSURED RISKS
 
     Drilling activities are subject to many risks, including the risk that no
commercially productive reservoirs will be encountered. There can be no
assurance that new wells drilled by the Company will be productive or that the
Company will recover all or any portion of its investment. Drilling for natural
gas and oil may involve unprofitable efforts, not only from dry wells, but also
from wells that are productive but do not produce sufficient net revenues to
return a profit after drilling, operating and other costs. The cost of drilling,
completing and operating wells is often uncertain. The Company's drilling
operations may be curtailed, delayed or canceled as a result of numerous
factors, many of which are beyond the Company's control, including title
problems, weather conditions, compliance with governmental requirements and
shortages or delays in the delivery of equipment and services. The Company's
future drilling activities may not be successful and, if unsuccessful, such
failure may have a material adverse effect on the Company's business, financial
condition or results of operations. See "Risk Factors -- Dependence on
Exploratory Drilling Activities." In addition, use of 3-D seismic technology
requires greater pre-drilling expenditures than traditional drilling strategies.
Although the Company believes that its use of 3-D seismic technology will
increase the probability of success, some unsuccessful wells are likely, and
there can be no assurance unsuccessful drilling efforts will not have a material
adverse effect on the Company's business, financial condition or results of
operations.
 
     The Company's operations are subject to hazards and risks inherent in
drilling for and producing and transporting natural gas and oil, such as fires,
natural disasters, explosions, encountering formations with abnormal pressures,
blowouts, cratering, pipeline ruptures and spills, any of which can result in
the loss of hydrocarbons, environmental pollution, personal injury claims and
other damage to properties of the Company and others. The Company maintains
insurance against some but not all of the risks described above. In particular,
the insurance maintained by the Company does not cover claims relating to
failure of title to natural gas and oil leases, trespass during 3-D survey
acquisition or surface change attributable to seismic operations, business
interruption or loss of revenues due to well failure. In certain circumstances
in which insurance is available the Company may not purchase it. The occurrence
of an event that is not covered, or not fully covered, by insurance could have a
material adverse effect on the Company's business, financial condition and
results of operations.
 
                                       46
<PAGE>   48
 
EMPLOYEES
 
     On May 22, 1998, the Company had 65 full-time employees. None is
represented by any labor union. The Company believes its relations with its
employees are good. The Company also relies on several regional consulting
service companies to provide field landmen to support the Company on a
project-by-project basis. One of these companies, Brigham Land Management, is
owned by Vincent M. Brigham, who is the brother of Ben M. Brigham, the Company's
Chief Executive Officer, President and Chairman of the Board. See "Certain
Transactions."
 
FACILITIES
 
     The Company's principal executive offices are located in Austin, Texas,
where it leases approximately 28,000 square feet of office space at 6300 Bridge
Point Parkway, Building 2, Suite 500, Austin, Texas 78730. In the fall of 1998,
the Company expects to lease an additional 5,000 square feet of office space
adjacent to its principal executive offices. The Company also leases a 4,100
square foot office at 450 Gears Road, Suite 240, Houston, Texas 77067.
 
TITLE TO PROPERTIES
 
     The Company believes it has satisfactory title, in all material respects,
to substantially all of its producing properties in accordance with standards
generally accepted in the oil and gas industry. The Company's properties are
subject to royalty interests, standard liens incident to operating agreements,
liens for current taxes and other inchoate burdens which the Company believes do
not materially interfere with the use of or affect the value of such properties.
The Company's revolving credit facility is secured by substantially all of the
Company's natural gas and oil properties. See "Management's Discussion and
Analysis of Financial Condition and Results of Operations."
 
GOVERNMENTAL REGULATION
 
     The Company's natural gas and oil exploration, production and marketing
activities are subject to extensive laws, rules and regulations promulgated by
federal and state legislatures and agencies. Failure to comply with such laws,
rules and regulations can result in substantial penalties. The legislative and
regulatory burden on the oil and gas industry increases the Company's cost of
doing business and affects its profitability. Although the Company believes it
is in substantial compliance with all applicable laws and regulations, because
those laws and regulations are frequently amended, interpreted and
reinterpreted, the Company is unable to predict the future cost or impact of
complying with such laws and regulations.
 
     The State of Texas and many other states require permits for drilling
operations, drilling bonds and reports concerning operations and impose other
requirements relating to the exploration and production of natural gas and oil.
These states also have statutes or regulations addressing conservation matters,
including provisions for the unitization or pooling of natural gas and oil
properties, the establishment of maximum rates of production from wells and the
regulation of spacing, plugging and abandonment of such wells.
 
     The Federal Energy Regulatory Commission ("FERC") regulates interstate
natural gas transportation rates and service conditions, which affect the
marketing of gas produced by the Company, as well as the revenues received by
the Company for sales of such production. Since the mid-1980s, FERC has issued a
series of orders, culminating in Order Nos. 636, 636-A 636-B and 636-C ("Order
636"), that have significantly altered the marketing and transportation of gas.
Order 636 mandates a fundamental restructuring of interstate pipeline sales and
transportation service, including the unbundling by interstate pipelines of the
sale, transportation, storage and other components of the city-gate sales
services such pipelines previously performed and the provision of open-access
transportation on a nondiscriminatory basis. One of FERC's purposes in issuing
the order was to increase competition within all phases of the natural gas
industry. Numerous parties have filed petitions for review of Order 636, as well
as orders in individual pipeline restructuring proceedings. In July 1996, Order
636 was generally upheld on appeal, and the portions remanded for further action
do not appear to materially affect the Company. Because Order 636 may be
modified as a result of the appeals, it is difficult to predict the ultimate
impact of the orders on the Company and its gas
 
                                       47
<PAGE>   49
 
marketing efforts. Generally, Order 636 has eliminated or substantially reduced
the interstate pipelines' traditional role as wholesalers of natural gas and has
substantially increased competition and volatility in natural gas markets.
 
     The FERC frequently reexamines its transportation-related policies,
including the terms and conditions under which interstate pipeline shippers may
release interstate pipeline capacity for resale in the secondary market, the
appropriateness of the use of negotiated and market-based rates, and the
implementation of additional standardized terms and conditions for interstate
gas transmission. In April 1998, the FERC issued a new rule to further
standardize pipeline transportation tariffs that could adversely affect the
reliability of scheduled interruptible transportation service on some pipelines.
While any resulting FERC action would affect the Company only indirectly, any
new rules and policy statements may have the effect of enhancing competition in
natural gas markets or affecting the cost or availability of pipeline
transportation.
 
     The price the Company receives from the sale of natural gas liquids and oil
is affected by the cost of transporting products to markets. Effective January
1, 1995, FERC implemented regulations establishing an indexing system for
transportation rates for oil pipelines, which, generally, would index such rates
to inflation, subject to certain conditions and limitations. The Company is not
able to predict with certainty the effect, if any, of these regulations on its
operations. However, the regulations may increase transportation costs or reduce
well head prices for natural gas liquids and oil. See "Risk
Factors -- Compliance with Government Regulations."
 
ENVIRONMENTAL MATTERS
 
     The Company's operations and properties are, like the oil and gas industry
in general, subject to extensive and changing federal, state and local laws and
regulations relating to environmental protection, including the generation,
storage, handling, emission, transportation and discharge of materials into the
environment, and relating to safety and health. The recent trend in
environmental legislation and regulation generally is toward stricter standards,
and this trend will likely continue. These laws and regulations may require the
acquisition of a permit or other authorization before construction or drilling
commences and for certain other activities; limit or prohibit seismic
acquisition, construction, drilling and other activities on certain lands lying
within wilderness and other protected areas; and impose substantial liabilities
for pollution resulting from the Company's operations. The permits required for
various of the Company's operations are subject to revocation, modification and
renewal by issuing authorities. Governmental authorities have the power to
enforce compliance with their regulations, and violations are subject to fines
or injunction, or both. In the opinion of management, the Company is in
substantial compliance with current applicable environmental laws and
regulations, and the Company has no material commitments for capital
expenditures to comply with existing environmental requirements. Nevertheless,
changes in existing environmental laws and regulations or in interpretations
thereof could have a significant impact on the Company, as well as the oil and
gas industry in general. The Comprehensive Environmental Response, Compensation
and Liability Act and comparable state statutes impose strict and arguably joint
and several liability on owners and operators of certain sites and on persons
who disposed of or arranged for the disposal of "hazardous substances" found at
such sites. It is not uncommon for the neighboring land owners and other third
parties to file claims for personal injury and property damage allegedly caused
by the hazardous substances released into the environment. The Resource
Conservation and Recovery Act and comparable state statutes govern the disposal
of "solid waste" and "hazardous waste" and authorize imposition of substantial
fines and penalties for noncompliance. Although CERCLA currently excludes
petroleum from its definition of "hazardous substance," state laws affecting the
Company's operations impose clean-up liability relating to petroleum and
petroleum related products. In addition, although RCRA classifies certain oil
field wastes as "non-hazardous," such exploration and production wastes could be
reclassified as hazardous wastes thereby making such wastes subject to more
stringent handling and disposal requirements.
 
     Federal regulations require certain owners or operators of facilities that
store or otherwise handle oil, such as the Company, to prepare and implement
spill prevention, control countermeasure and response plans relating to the
possible discharge of oil into surface waters. The Oil Pollution Act of 1990
contains numerous requirements relating to the prevention of and response to oil
spills into waters of the United States. For
 
                                       48
<PAGE>   50
 
onshore and offshore facilities that may affect waters of the United States, the
OPA requires an operator to demonstrate financial responsibility. Regulations
are currently being developed under federal and state laws concerning oil
pollution prevention and other matters that may impose additional regulatory
burdens on the Company. In addition, the Clean Water Act and analogous state
laws require permits to be obtained to authorize discharge into surface waters
or to construct facilities in wetland areas. With respect to certain of its
operations, the Company is required to maintain such permits or meet general
permit requirements. The EPA recently adopted regulations concerning discharges
of storm water runoff. This program requires covered facilities to obtain
individual permits, participate in a group or seek coverage under an EPA general
permit. The Company believes that it will be able to obtain, or be included
under, such permits, where necessary, and to make minor modifications to
existing facilities and operations that would not have a material effect on the
Company.
 
     The Company has acquired leasehold interests in numerous properties that
for many years have produced natural gas and oil. Although the previous owners
of these interests have used operating and disposal practices that were standard
in the industry at the time, hydrocarbons or other wastes may have been disposed
of or released on or under the properties. In addition, some of the Company's
properties are operated by third parties over whom the Company has no control.
Notwithstanding the Company's lack of control over properties operated by
others, the failure of the operator to comply with applicable environmental
regulations may, in certain circumstances, adversely impact the Company. See
"Risk Factors -- Compliance with Environmental Regulations" and "Management's
Discussion and Analysis of Financial Condition and Results of
Operations -- Other Matters."
 
LEGAL PROCEEDINGS
 
     The Company is not a party to any material legal proceedings.
 
                                   MANAGEMENT
 
DIRECTORS AND EXECUTIVE OFFICERS
 
     The following table sets forth certain information regarding the executive
officers and directors of the Company:
 
<TABLE>
<CAPTION>
                 NAME                    AGE                  POSITION
                 ----                    ---                  --------
<S>                                      <C>   <C>
Ben M. Brigham........................   38    President, Chief Executive Officer and
                                               Chairman of the Board
Anne L. Brigham.......................   36    Executive Vice President and Director
Jon L. Glass..........................   42    Vice President -- Exploration and
                                               Director
Craig M. Fleming......................   40    Chief Financial Officer
David T. Brigham......................   37    Vice President -- Land and
                                               Administration, Corporate Secretary
A. Lance Langford.....................   36    Vice President -- Operations
Karen E. Lynch........................   36    Vice President and General Counsel
Harold D. Carter......................   59    Director
Alexis M. Cranberg....................   42    Director
Gary J. Milavec.......................   36    Director
Stephen P. Reynolds...................   46    Director
</TABLE>
 
     Set forth below is a description of the backgrounds of the executive
officers and directors of the Company.
 
     Ben M. "Bud" Brigham has served as Chief Executive Officer, President and
Chairman of the Board of the Company since founding the Company in 1990. From
1984 to 1990, Mr. Brigham served as an exploration geophysicist with Rosewood
Resources, an independent oil and gas exploration and production company.
 
                                       49
<PAGE>   51
 
Mr. Brigham began his career in Houston as a seismic data processing
geophysicist for Western Geophysical, a provider of 3-D seismic services, after
earning his B.S. in Geophysics from the University of Texas.
 
     Anne L. Brigham has served as Executive Vice President and a Director of
the Company since its inception in 1990 and as Corporate Secretary from 1990 to
February 1998. Before joining the Company full-time in 1991, Ms. Brigham
practiced law in the oil and gas and real estate sections of Thompson & Knight,
P.C. Ms. Brigham worked as a geologist for Hunt Petroleum Corporation, an
independent oil and gas exploration and production company, for over two years
before attending law school. Ms. Brigham holds a B.S. in Geology from the
University of Texas and a J.D. from Southern Methodist University.
 
     Jon L. Glass joined the Company in 1992 and has served as Vice
President -- Exploration since 1994 and a Director of the Company since 1995.
From 1984 to 1992, Mr. Glass served in various capacities with Santa Fe
Minerals, an oil and gas exploration company, in a variety of staff and
managerial positions mainly focused on Santa Fe Minerals' exploration activities
in the midcontinent and Gulf of Mexico (onshore and offshore). During this time
Mr. Glass also assisted in the development of exploration and acquisition
opportunities for Santa Fe Minerals in Canada and South America. Mr. Glass'
early geological experience includes three years with Mid-America Pipeline
Company and two years with Texaco USA, serving mainly as a midcontinent
exploration geologist. Mr. Glass holds a B.S. and an M.S. in Geology from
Oklahoma State University and an M.B.A. from the University of Tulsa.
 
     Craig M. Fleming has served as the Chief Financial Officer of the Company
since 1993. From 1990 to 1993, Mr. Fleming served as Controller of Odyssey
Petroleum Co., Ltd., an independent energy company. From 1988 to 1990, Mr.
Fleming served as Controller and Treasurer for Harken Exploration Company, an
independent energy company. Mr. Fleming began his career with Arthur Anderson &
Co. in the Oil and Gas Audit Division and is a Certified Public Accountant. Mr.
Fleming holds a B.B.A. in Accounting from Texas A&M University.
 
     David T. Brigham joined the Company in 1992 and has served as Vice
President -- Land and Administration and Corporate Secretary of the Company
since February 1998. Mr. Brigham served as Vice President -- Legal of the
Company from 1994 until February 1998. From 1987 to 1992, Mr. Brigham was an oil
and gas attorney with Worsham, Forsythe, Sampels & Wooldridge. Before attending
law school, Mr. Brigham was a landman for Wagner & Brown Oil and Gas Producers,
an independent oil and gas exploration and production company. Mr. Brigham holds
a B.B.A. in Petroleum Land Management from the University of Texas and a J.D.
from Texas Tech School of Law.
 
     A. Lance Langford joined the Company as Manager of Operations in 1995 and
has served as Vice President -- Operations since January 1997. From 1987 to
1995, Mr. Langford served in various engineering capacities with Meridian Oil
Inc., handling a variety of reservoir, production and drilling responsibilities.
Mr. Langford holds a B.S. in Petroleum Engineering from Texas Tech University.
 
     Karen E. Lynch joined the Company in October 1997 as General Counsel and
has served as Vice President and General Counsel of the Company since February
1998. Prior to joining the Company, Ms. Lynch was a shareholder in the
Dallas-based law firm of Thompson & Knight, P.C., where she practiced in the
energy area since joining the firm in 1987. Ms. Lynch holds a B.B.A. in
Petroleum Land Management from the University of Texas and a J.D. from the
University of Oklahoma.
 
     Harold D. Carter has served as a Director of and consultant to the Company
since 1992. Mr. Carter has more than 30 years experience in the oil and gas
industry and has been an independent consultant since 1990. Prior to consulting,
Mr. Carter served as Executive Vice President of Pacific Enterprises Oil Company
(USA). Before that, Mr. Carter was associated for 20 years with Sabine
Corporation, ultimately serving as President and Chief Operating Officer from
1986 to 1989. Mr. Carter consults for Endowment Advisors, Inc. with respect to
its EEP Partnerships and Associated Energy Managers, Inc. with respect to its
Energy Income Fund, L.P. and is a director of Abraxas Petroleum Corporation. Mr.
Carter has a B.B.A. in Petroleum Land Management from the University of Texas
and has completed the Program for Management Development at the Harvard
University Business School.
 
                                       50
<PAGE>   52
 
     Alexis M. Cranberg has served as a Director of the Company since 1992. Mr.
Cranberg is President of Aspect Management Corporation, an oil and gas
exploration and investment company. In addition, Mr. Cranberg is a Director for
Westport Oil and Gas Company, Inc. and a past Director of General Atlantic
Resources, Inc. and United Meridian Corporation. Mr. Cranberg is a nominee for
Director of Frontier Natural Gas Corp. He holds a B.S. in Petroleum Engineering
from the University of Texas and an M.B.A. from Stanford University.
 
     Gary J. Milavec has served as a Director of the Company since 1995. Mr.
Milavec is a Managing Director of RIMCO, an investment management firm
specializing in the energy industry. Prior to joining RIMCO in 1990, Mr. Milavec
spent two years in the corporate finance department of Rauscher Pierce Refsnes,
Inc. and three years as a geological engineer with Shell Western E&P, Inc. He
also serves as a director of Universal Seismic Associates, Inc. and Texoil, Inc.
Mr. Milavec holds a B.A. in Geology from the University of Rochester, an M.S. in
Geology from the University of Oklahoma and an M.B.A. from the University of
Houston.
 
     Stephen P. Reynolds has served as a Director of the Company since 1996. Mr.
Reynolds is a managing member of General Atlantic Partners, LLC ("GAP LLC") and
has been with GAP LLC or its predecessor entities since April 1980. Mr. Reynolds
is also President of GAP III Investors, Inc., the general partner of General
Atlantic Partners III, L.P., and is a general partner and limited partner of
GAP-Brigham Partners, L.P. Mr. Reynolds is on the board of directors of Solo
Serve Corporation, a publicly traded off-price soft goods retail company, and
Computer Learning Centers, Inc., a publicly traded company providing technology
related training. Mr. Reynolds is a nominee for Director of SS&C Technologies,
Inc. Mr. Reynolds holds a B.A. in Economics from Amherst College and a Masters
degree in Accounting from New York University.
 
     All directors are elected to serve until the next annual meeting of
stockholders and until their successors are elected and qualified. Executive
officers are generally elected annually by the Board of Directors to serve,
subject to the discretion of the Board of Directors, until their successors are
elected or appointed.
 
     There is no family relationship between any of the directors or between any
director and any executive officer of the Company except that Ben M. Brigham and
Anne L. Brigham are married and David T. Brigham is the brother of Ben M.
Brigham. For information regarding certain business relationships between the
Company and certain of its directors, see "Certain Transactions."
 
COMMITTEES OF THE BOARD
 
     The Company's Board of Directors formed standing audit and compensation
committees on February 26, 1997, which are composed of Harold D. Carter, Alexis
M. Cranberg and Gary J. Milavec. The Audit Committee's primary responsibilities
are to (i) recommend the Company's independent auditors to the Board of
Directors, (ii) review with the Company's auditors the plan and scope of the
auditor's annual audit, the results thereof and the auditors' fees, (iii) review
the Company's financial statements and (iv) take such other action as it deems
appropriate as to the accuracy and completeness of financial records of the
Company and financial information gathering,reporting policies and procedures of
the Company. The Compensation Committee exercises the power of the Board of
Directors in connection with all matters relating to compensation of executive
officers, employee benefit plans and the administration of the Company's stock
option programs.
 
DIRECTOR COMPENSATION
 
     Fees and Expenses; Other Arrangements. Directors who are also employees of
the Company are not separately compensated for serving on the Board of
Directors. Directors who are not employees of the Company receive $5,000 per
year and $500 per meeting for their services as directors. In addition, the
Company reimburses Directors for the expenses incurred in connection with
attending meetings of the Board of Directors and its committees.
 
     Pursuant to a consulting agreement with Harold D. Carter that expired May
1, 1997, the Company paid Mr. Carter $6,000 per month through June 1996 and then
$7,200 per month for the remainder of the term of
 
                                       51
<PAGE>   53
 
the agreement to spend approximately 50% of his working time performing such
consulting and advisory services regarding the operations of the Company as the
Company requested, including service on the management committee of the
Company's predecessor partnership. Pursuant to a subsequent consulting agreement
that expires December 31, 1998, Mr. Carter continues to serve as a consultant to
the Company and is currently being compensated $7,200 per month for such
services and is reimbursed by the Company for his out-of-pocket expenses. In
addition, pursuant to the terms of Mr. Carter's consulting agreement, the
Company pays Associated Energy Managers, Inc. $1,000 per month to offset a
portion of Mr. Carter's office overhead expenses and to provide the Company with
limited use of part of Mr. Carter's office space for purposes of conducting
business while employees of the Company are in Dallas, Texas.
 
     Alexis M. Cranberg and Stephen P. Reynolds served on the management
committee of the Company's predecessor partnership pursuant to the terms of an
agreement with General Atlantic, and Gary J. Milavec served on the committee
pursuant to the terms of an agreement with RIMCO. The Company is not obligated
to nominate any of the three to serve as a Director of the Company in the
future.
 
     Director Stock Options. The Company's stockholders have approved the 1997
Director Stock Option Plan, pursuant to which each newly elected nonemployee
director shall be granted an option to purchase 1,000 shares of Common Stock and
each nonemployee director will receive an option to purchase 500 shares of
Common Stock on December 31 of each year. The options under the plan are granted
at fair market value on the grant date and become exercisable, subject to
certain conditions, in five equal annual installments on the first five
anniversaries of the grant date. The options terminate ten years from the grant
date, unless terminated sooner. Twenty-five thousand shares of Common Stock have
been authorized and reserved for issuance pursuant to the plan. Options to
purchase 2,000 shares of Common Stock were granted on December 31, 1997 to the
Company's four nonemployee directors pursuant to the 1997 Director Stock Option
Plan.
 
LIMITATION OF LIABILITY AND INDEMNIFICATION MATTERS
 
     In accordance with Section 102(b)(7) of the Delaware General Corporation
Law ("DGCL"), the Company's Certificate of Incorporation includes a provision
that, to the fullest extent permitted by law, eliminates the personal liability
of members of its Board of Directors to the Company or its stockholders for
monetary damages for breach of fiduciary duty as a director. Such provision does
not eliminate or limit the liability of a director (1) for any breach of a
director's duty of loyalty to the Company or its stockholders, (2) for acts or
omissions not in good faith or which involve intentional misconduct or a knowing
violation of a law, (3) for paying an unlawful dividend or approving an illegal
stock repurchase (as provided in Section 174 of the DGCL) or (4) for any
transaction from which the director derived an improper personal benefit.
 
     The Company has entered into indemnity agreements with each of its
executive officers and directors that provide for indemnification in certain
instances against liability and expenses incurred in connection with proceedings
brought by or in the right of the Company or by third parties by reason of a
person serving as an officer or director of the Company.
 
     The Company believes that these provisions and agreements will assist the
Company in attracting and retaining qualified individuals to serve as directors
and officers.
 
COMPENSATION COMMITTEE INTERLOCKS AND INSIDER PARTICIPATION
 
     The Company's compensation committee during the last ten months of the past
fiscal year consisted of Messrs. Carter, Cranberg and Milavec and all
determinations concerning executive compensation for such period for the
Company's executive officers were made by the compensation committee. The
compensation committee members abstained from participation in compensation
determinations concerning their own compensation. None of the executive officers
of the Company has served on the board of directors or on the compensation
committee of any other entity, any of whose officers served on the Board of
Directors of the Company.
 
                                       52
<PAGE>   54
 
EXECUTIVE COMPENSATION
 
     Summary of Cash and Certain Compensation. The following table sets forth
certain summary information concerning the compensation paid or awarded to the
Chief Executive Officer of the Company and the only other executive officers of
the Company who earned in excess of $100,000 in 1997 (the "named executive
officers") for the years indicated.
 
                           SUMMARY COMPENSATION TABLE
 
<TABLE>
<CAPTION>
                                                                                  LONG-TERM
                                                                                COMPENSATION
                                                                          -------------------------
                                              ANNUAL COMPENSATION                          SHARES
               NAME AND                  ------------------------------    RESTRICTED    UNDERLYING       ALL OTHER
          PRINCIPAL POSITION             YEAR   SALARY($)   BONUS($)(1)   STOCK AWARDS    OPTIONS     COMPENSATION($)(2)
          ------------------             ----   ---------   -----------   ------------   ----------   ------------------
<S>                                      <C>    <C>         <C>           <C>            <C>          <C>
Ben M. Brigham.........................  1997    228,125      30,600             --            --           5,690
  Chief Executive Officer, President
    and                                  1996    144,000      15,000             --            --           4,817
  Chairman of the Board
Jon L. Glass...........................  1997    127,301      43,268         66,964       208,333             354
  Vice President -- Exploration          1996    109,782       3,223             --            --              --
Craig M. Fleming.......................  1997    122,272      44,971         44,643        69,444             477
  Chief Financial Officer                1996    102,919       8,063             --            --              --
David T. Brigham.......................  1997    108,895      32,712         44,643        69,444             428
  Vice President -- Land and             1996     94,874      10,505             --            --              --
  Administration, Corporate Secretary
A. Lance Langford......................  1997    107,469      43,111             --        52,085             410
  Vice President -- Operations           1996     94,090       7,261             --            --              --
</TABLE>
 
---------------
 
(1) Includes the following moving allowances granted in 1997 to employees in
    connection with the Company's relocation of its corporate headquarters from
    Dallas, Texas, to Austin, Texas: Ben M. Brigham -- $30,600; Jon L.
    Glass -- $12,076; Craig M. Fleming -- $23,654; David T. Brigham -- $17,529;
    and A. Lance Langford -- $23,524.
 
(2) Amounts for Ben M. Brigham represent premiums paid by the Company under life
    and disability insurance plans of $1,442 and $4,248, respectively, in 1997,
    and $1,404 and $3,413, respectively, in 1996. Amounts for Jon L. Glass,
    Craig M. Fleming, David T. Brigham and A. Lance Langford represent premiums
    paid by the Company under a disability insurance plan in 1997.
 
     Option Grants. The following table contains information about stock option
grants to the named executive officers in 1997:
 
                       OPTION GRANTS IN LAST FISCAL YEAR
 
<TABLE>
<CAPTION>
                                                                                POTENTIAL REALIZED VALUE AT
                                                                                  ASSUMED ANNUAL RATES OF
                                                                                 STOCK PRICE APPRECIATION
                                         INDIVIDUAL GRANTS                          FOR OPTION TERM(1)
                         -------------------------------------------------   ---------------------------------
                         NUMBER OF     % OF TOTAL
                         SECURITIES     OPTIONS      EXERCISE
                         UNDERLYING    GRANTED TO    OR BASE
                          OPTIONS     EMPLOYEES IN    PRICE     EXPIRATION
         NAME            GRANTED(#)   FISCAL YEAR     ($/SH)       DATE        0%($)       5%($)      10%($)
         ----            ----------   ------------   --------   ----------   ---------   ---------   ---------
<S>                      <C>          <C>            <C>        <C>          <C>         <C>         <C>
Ben M. Brigham.........        --           --           --           --            --          --          --
Jon L. Glass...........   208,334         32.3         5.00       7/1/04     2,005,215   3,142,280   4,619,530
Craig M. Fleming.......    69,445         10.8         5.00       7/1/04       668,408   1,047,433   1,539,851
David T. Brigham.......    69,445         10.8         5.00       7/1/04       668,408   1,047,433   1,539,851
A. Lance Langford......    52,085          8.1         5.00       7/1/04       501,318     785,593   1,154,916
</TABLE>
 
---------------
 
(1) Amounts represent hypothetical gains that could be achieved for the options
    if they are exercised at the end of the option term. Those gains are based
    on assumed rates of stock price appreciation of 0%, 5% and 10% compounded
    annually from February 27, 1997, the date such options had been granted,
    through the expiration date. For the option term ending July 1, 2004, based
    on the closing price on The Nasdaq Stock
 
                                       53
<PAGE>   55
 
Market(SM) of the Common Stock of $14.63 on December 31, 1997, a share of the
Common Stock would have a value on July 1, 2004 of approximately $20.08 at an
assumed appreciation rate of 5% and approximately $27.17 at an assumed
     appreciation rate of 10%.
 
     Option Exercises and Year-End Option Values. The following table provides
information about the number of shares issued upon option exercises by the named
executive officers during 1997, and the corresponding value realized by the
named executive officers. The table also provides information about the number
and value of options that were held by the named executive officers at December
31, 1997.
 
                AGGREGATED OPTION EXERCISES IN LAST FISCAL YEAR
                            AND FY-END OPTION VALUES
 
<TABLE>
<CAPTION>
                                                           NUMBER OF SECURITIES          VALUE OF UNEXERCISED
                                                          UNDERLYING UNEXERCISED             IN-THE-MONEY
                              SHARES                       OPTIONS AT FY-END(#)          OPTIONS AT FY-END($)
                            ACQUIRED ON      VALUE      ---------------------------   ---------------------------
           NAME             EXERCISE(#)   REALIZED($)   EXERCISABLE   UNEXERCISABLE   EXERCISABLE   UNEXERCISABLE
           ----             -----------   -----------   -----------   -------------   -----------   -------------
<S>                         <C>           <C>           <C>           <C>             <C>           <C>
Ben M. Brigham............      --            --            --                --          --                 --
Jon L. Glass..............      --            --            --           208,334          --          2,005,215
Craig M. Fleming..........      --            --            --            69,445          --            668,408
David T. Brigham..........      --            --            --            69,445          --            668,408
A. Lance Langford.........      --            --            --            52,085          --            501,318
</TABLE>
 
  Employment Agreements
 
     The Company employs Ben M. Brigham under an employment agreement (the
"Employment Agreement") as Chief Executive Officer and President of the Company
for a five year term that began in February 1997. The Employment Agreement
contains rollover provisions so that at all times the term of the Employment
Agreement shall be not less than three years. The agreement provides for an
annual salary of $275,000, which the Board of Directors may further increase
from time to time. Mr. Brigham is also entitled to an annual cash bonus, not to
exceed 75% of his then current salary, determined based on criteria established
by the Board of Directors. Under the Employment Agreement, Mr. Brigham is
entitled to participate in any employee benefit programs that the Company
provides to its executive officers. The only employee benefit programs that the
Company offers to its officers and employees are group insurance coverage and
participation in the Company's 401(k) Retirement Plan, the 1997 Incentive Plan
and the Incentive Bonus Plan. If Mr. Brigham terminates his employment for good
reason, which includes a material reduction of Mr. Brigham's position without
cause or his written consent, breach of a material provision of the Employment
Agreement or improper notice of termination, or if the Company terminates Mr.
Brigham without cause, the Company must pay Mr. Brigham a sum equal to the
amount of his annual base salary that he would have received during the
remainder of his employment term plus the average of his annual bonuses received
in the preceding two years times the number of years in the remainder of his
employment term. Mr. Brigham's agreement also contains a three-year non-compete
and confidentiality clause with standard terms.
 
     Each of the other named executive officers of the Company is a party to a
confidentiality and noncompete agreement.
 
EMPLOYEE BENEFIT PLANS
 
     Employees' Restricted Stock. In February 1997, the Company, in connection
with the Exchange, issued 66,964 shares, 44,643 shares and 44,643 shares of
restricted stock to Jon L. Glass, Craig M. Fleming and David T. Brigham,
respectively, in exchange for restricted limited partnership interests issued to
them in 1994. Each agreement relating to the restricted stock contains
confidentiality, noncompete and vesting provisions. The shares awarded Messrs.
Brigham and Fleming vest over a three-year period -- 30% in each of July 1997
and 1998 and 40% in July 1999. Of the shares awarded to Mr. Glass, 45% have
already vested, 28.33% vest in July 1998, and 26.67% vest in July 1999.
 
                                       54
<PAGE>   56
 
     1997 Incentive Plan. The Board of Directors and the stockholders of the
Company approved the adoption of the Company's 1997 Incentive Plan (the "1997
Incentive Plan") as of February 27, 1997. The Compensation Committee selects
participants in the 1997 Incentive Plan from among those key employees and
others who hold positions of responsibility with the Company and whose
performance may have a significant effect on the success of the Company. An
aggregate of 1,588,169 shares of Common Stock have been authorized and reserved
for issuance pursuant to the 1997 Incentive Plan. In March 1997, options were
granted to purchase a total of 644,097 shares of Common Stock at an exercise
price per share of $5.00. These options vest over six years. Jon L. Glass, Craig
M. Fleming and David T. Brigham were granted options to purchase 208,334 shares,
69,445 shares and 69,445 shares of Common Stock, respectively. With the
exception of options to purchase 138,889 shares of Common Stock granted to Jon
L. Glass, these options vest as follows: 30% on July 1, 1998; 20% on July 1,
1999; 16.66% on July 1, 2000; 16.67% on July 1, 2001; and the balance on July 1,
2002. The balance of Mr. Glass' options (138,889 shares) vest as follows: 30% on
February 1, 1999; 20% on July 1, 1999; 16.66% on July 1, 2000; 16.67% on July 1,
2001; and 16.67% on July 1, 2002. Of the options issued in 1997 pursuant to the
1997 Incentive Plan, options to purchase 17,360 have been forfeited by certain
employees.
 
     In January 1998, options were granted to purchase 307,250 shares of Common
Stock at an exercise price of $12.875 per share. These options vest over six
years in three equal bi-annual installments starting the second year following
the date of grant.
 
     Subject to the provisions of the 1997 Incentive Plan, the Compensation
Committee is authorized to determine the type or types of awards made to each
participant and the terms, conditions and limitations applicable to each award.
In addition, the Compensation Committee has the exclusive power to interpret the
1997 Incentive Plan and to adopt rules and regulations that it may deem
necessary or appropriate, in keeping with the objectives of the 1997 Incentive
Plan.
 
     Pursuant to the 1997 Incentive Plan, participants will be eligible to
receive awards consisting of stock options, stock appreciation rights, stock,
restricted stock, cash or any combination of the foregoing. Stock options may be
either incentive stock options within the meaning of Section 422 of the Internal
Revenue Code of 1986, as amended, or nonqualified stock options.
 
     Incentive Bonus Plan. In connection with the Exchange, the Company adopted
the Incentive Bonus Plan (the "Incentive Bonus Plan") previously established by
the Company's predecessor partnership. The Incentive Bonus Plan is designed to
pay cash compensation and bonuses to eligible employees of the Company. Under
the Incentive Bonus Plan, the Company maintains an incentive account for each
calendar year (each an "Incentive Account") and a discretionary bonus account
(the "Discretionary Bonus Account"). Prior to the beginning of each calendar
year, the President of the Company designates the employees of the Company who
are eligible to participate in the Incentive Account being established for such
year, and each such employee's percentage of interest (an "Account Percentage")
in such Incentive Account. Subject to certain adjustments provided under the
Incentive Bonus Plan, each Incentive Account is credited with an amount equal to
one-half of the net revenue received by the Company which is equivalent to a one
percent interest in the Company's net revenue interest in the oil and gas
produced from each Company well drilled or reentered after April 30, 1992, and
the Discretionary Bonus Account is credited with an amount equal to the amount
credited to each Incentive Account. The President has discretion to allocate a
greater interest to the accounts. Within 30 days after each March 31 and
September 30, an employee who has been designated to have an Account Percentage
in the Incentive Account established for a particular year receives cash
compensation equal to his or her Account Percentage in such Incentive Account
multiplied by the amount credited to that Incentive Account for the six-month
period then ended. In addition, the President of the Company has the discretion
to award cash bonuses to any Company employee from the amounts credited to the
Discretionary Bonus Account. The participation of an employee under the
Incentive Bonus Plan terminates when he or she ceases to be an employee of the
Company for any reason. The President of the Company may amend or terminate the
Incentive Bonus Plan at any time.
 
                                       55
<PAGE>   57
 
                              CERTAIN TRANSACTIONS
 
     In connection with the land work necessary prior to and during 3-D seismic
acquisitions, the Company engages Brigham Land Management ("BLM"), an
independent company owned and managed by Vincent M. Brigham, a brother of Ben M.
Brigham, who is the Company's Chief Executive Officer, President and Chairman of
the Board, and David T. Brigham, who is a Vice President of the Company. BLM
specializes in conducting the field land work necessary prior to and during 3-D
seismic acquisitions. BLM has regional expertise in the Anadarko Basin and the
Texas Panhandle, and, to a lesser extent, West Texas. BLM performs these
services for the Company using BLM's employees and independent contractors. BLM
performs approximately one-third of the Company's work in the Anadarko Basin. In
1995, 1996 and 1997, the Company paid BLM approximately $382,000, $596,000 and
$837,000, respectively. Other participants in the Company's 3-D seismic projects
reimbursed the Company for a portion of these amounts. Based on its experience
with other firms in the area, the Company believes that BLM's charges are at or
below those of other firms.
 
     In 1994, the Company, through its subsidiary Quest Resources, L.L.C.,
formed Venture Acquisitions, L.P. ("Venture") with affiliates of RIMCO, a holder
of in excess of 5% of the Common Stock, to provide the Company with the capital
to acquire interests in certain potential drilling locations, producing
properties and 3-D seismic projects. The RIMCO affiliates have contributed $5.2
million to Venture, and the Company has contributed $286,138. Until the first
payout under the Venture limited partnership agreement, the Company's share of
all capital costs is 5%, and the Company's share of revenues and related
production expenses and costs is 10%. Between the first and second payout
levels, the Company's share of capital costs and revenues and related production
expenses and costs is 25% and thereafter increases to 50%. Venture acquired from
the Company an interest in (i) a 3-D project for approximately $75,000 in 1995,
and (ii) two 3-D delineated potential drilling locations and 3-D seismic for
approximately $83,000 in 1996. The Company billed Venture approximately $14,924
in 1995, $16,500 in 1996 and $56,658 in 1997 for its proportionate share of
exploration and overhead costs. Because RIMCO was not an affiliate of the
Company when the Venture partnership was formed, the Company believes that the
terms of the Venture partnership are no less favorable than could be obtained
from an unaffiliated third party. Gary J. Milavec, a director of the Company and
member of the Company's compensation committee, is employed by RIMCO.
 
     In November 1994, the Company, certain RIMCO affiliates and other unrelated
industry participants entered into a geophysical exploration agreement creating
an area of mutual interest in its Esperson Dome Project in Liberty and Harris
counties, Texas. The Company financed its participation in this project by
assigning its interest, and obligation to bear costs, to Vaquero Gas Company,
Inc. ("Vaquero"), a RIMCO affiliate, subject to a 5% net profits overriding
royalty interest and the right to receive up to 50% of Vaquero's interest on the
occurrence of certain payouts. The Company also retained responsibility for
managing the 3-D seismic acquisition and interpretation of the data after it had
been acquired. During 1995, 1996 and 1997, the Company received approximately
$25,000, $123,000 and $50,000, respectively, from the RIMCO affiliates,
including Vaquero, for workstation time and geoscientists' time in interpreting
the 3-D seismic that were acquired. Because RIMCO was not an affiliate of the
Company when the project was initiated and the interest to Vaquero was
transferred, the Company believes that the terms of the arrangement are no less
favorable than could be obtained from an unaffiliated third party.
 
     In January 1997, the Company, RIMCO and Tigre Energy Corporation ("Tigre")
entered into an agreement under which the Company had been initially assigned an
undivided 22% interest (subject to a proportionately reduced 3% overriding
royalty interest) in a project ("Tigre Point") located in Vermillion Parish,
Louisiana in return for paying certain costs of acquiring 3-D seismic and land
within the project area. The Company acquired an additional 12.5% working
interest from RIMCO and an additional 37.5% working interest from Tigre in parts
of the project under the same terms as the initial 25% interest. The Company
believes that the arrangements with RIMCO affiliates relating to Tigre Point are
on terms no less favorable than could be obtained from an unaffiliated third
party, because RIMCO and Tigre, an unaffiliated third party, are participants in
the project on substantially similar terms.
 
     The Company and an affiliate of Universal Seismic Associates, Inc. ("USA"),
a public company of which RIMCO affiliates beneficially own approximately 22% of
the outstanding common stock, have entered
 
                                       56
<PAGE>   58
 
into a geophysical exploration agreement covering an area of mutual interest on
the Gulf Coast. Under the terms of the agreement, USA conducted a 3-D seismic
program established by the Company and USA and processed the data acquired under
the program at cost, and the Company will interpret the resulting seismic for
the benefit of the Company and USA at no charge to USA. Subject to a party's
electing not to participate in an acquired interest, the Company and USA will
each own an undivided 50% interest in all land interests acquired within the
area of mutual interest. Through December 31, 1997, the Company had incurred
$209,314 of costs under those arrangements. Based on its experience in acquiring
3-D seismic, the Company believes that it has acquired 3-D seismic under this
agreement on terms, and that the arrangement is on terms, no less favorable than
could be obtained from an unaffiliated third party.
 
     In 1993 and 1994 the Company issued to RIMCO 10% Notes in principal amounts
of $3.0 million and $4.9 million, respectively. In 1995 the Company issued RIMCO
additional 10% Notes in a principal amount of $2.6 million, and in the same
year, issued RIMCO 5% Notes in a principal amount of $16.0 million, $10.5
million of which was used to repay all the outstanding 10% Notes. The 5% Notes
were exchanged for 1,754,464 shares of Common Stock in the Exchange. In 1995,
1996 and 1997, the Company paid RIMCO $631,989, $809,332 and $340,000,
respectively, in interest payments on the 5% Notes and the 10% Notes. In 1995,
1996 and 1997, the Company distributed to RIMCO $102,107, $82,097 and $48,150,
respectively for RIMCO's overriding royalty interest in certain natural gas and
oil properties.
 
     Pursuant to a consulting agreement with Harold D. Carter that expired May
1, 1997, the Company paid Mr. Carter $6,000 per month through June 1996 and
$7,200 per month for the remainder of the term of the agreement to spend
approximately 50% of his working time performing such consulting and advisory
services regarding the operations of the Company as the Company requested,
including service on the management committee of the Company's predecessor
partnership. Pursuant to this agreement, Mr. Carter received $72,000 in 1995,
$79,200 in 1996 and $86,580 in 1997. Additional disbursements totaling
approximately $13,000 were made by the Company to Mr. Carter during 1997 for the
reimbursement of certain expenses. Pursuant to the terms of a subsequent
consulting agreement, the Company will continue to utilize Mr. Carter's
consulting services through December 31, 1998 and pay Mr. Carter $7,200 per
month for those services and reimburse Mr. Carter for certain out-of-pocket
expenses during the term of the agreement. In addition, pursuant to the terms of
Mr. Carter's consulting agreement, the Company pays Associated Energy Managers,
Inc. $1,000 per month to offset a portion of Mr. Carter's office overhead
expenses and to provide the Company with limited use of part of Mr. Carter's
office space for purposes of conducting business while employees of the Company
are in Dallas, Texas.
 
     In 1995, 1996 and 1997, the Company paid $35,000, $110,000 and $18,000 to
Aspect and affiliates of Alexis M. Cranberg, a director of the Company, to
acquire interests in a project in Grady County, Oklahoma and a project in
Hardeman and Wilbarger counties, Texas and Jackson County, Oklahoma. Based on
its experience in the industry, the Company believes that these transactions are
on terms no less favorable than could be obtained from an unaffiliated third
party. The Company billed Aspect and other affiliates of Alexis M. Cranberg
$13,000 in 1995 and $68,000 in 1996 for its proportionate share of the costs
related to the projects.
 
     The Company has entered into a Registration Rights Agreement with General
Atlantic Partners III, L.P., GAP-Brigham Partners, L.P., RIMCO Partners, L.P.
II, RIMCO Partners, L.P. III and RIMCO Partners, L.P. IV, Ben M. Brigham, Anne
L. Brigham, Harold D. Carter, Craig M. Fleming, David T. Brigham and Jon L.
Glass. Pursuant to the Registration Rights Agreement, Anne and Ben Brigham,
acting together, the RIMCO entities, acting together, and the General Atlantic
entities, acting together, each may separately require the Company to register
securities, on one occasion, if the shares to be registered have an estimated
aggregate offering price to the public of at least $3.0 million. One additional
registration is allowed if any registrable securities requested to be included
in a previous registration statement have not been disposed of in accordance
with that previous registration. The Registration Rights Agreement also provides
"piggyback" registration rights for all registrations of registrable securities
for the Company or another security holder. In an underwritten offering,
however, the Company may exclude all or a portion of the securities being
 
                                       57
<PAGE>   59
 
registered pursuant to "piggyback" registration rights if the managing
underwriter determines that including those securities would raise a substantial
doubt about whether the proposed offering could be consummated. The Registration
Rights Agreement contains customary indemnity by the Company in favor of persons
selling securities in a registration governed by the Registration Rights
Agreement, and by those persons in favor of the Company, relating to the
information included in or omitted from the Registration Statement.
 
                       PRINCIPAL AND SELLING STOCKHOLDERS
 
     The table below sets forth information concerning (i) the only persons
known by the Company, based upon statements filed by such persons pursuant to
Section 13(d) or 13(g) of the Securities Exchange Act of 1934, as amended (the
"Exchange Act"), to own beneficially in excess of 5% of the Common Stock as of
May 27, 1998, and (ii) the shares of Common Stock beneficially owned, as of May
27, 1998, by each director of the Company, each executive officer listed in the
Summary Compensation Table included elsewhere in this Prospectus, and all
directors and executive officers of the Company as a group. Except as indicated,
each individual has sole voting power and sole investment power over all shares
listed opposite his name.
 
<TABLE>
<CAPTION>
                                                                SHARES             SHARES BENEFICIALLY
                                                          BENEFICIALLY OWNED         OWNED AFTER THE
                                                       PRIOR TO THE OFFERING(1)         OFFERING
                                                       -------------------------   -------------------
NAME AND ADDRESS OF BENEFICIAL OWNER                      NUMBER       PERCENT      NUMBER     PERCENT
------------------------------------                   ------------   ----------   ---------   -------
<S>                                                    <C>            <C>          <C>         <C>
Ben M. Brigham(2)....................................   3,719,342        30.16%    3,719,342   23.64%
  6300 Bridge Point Parkway, Bldg. 2, Suite 500
  Austin, Texas 78730
Anne L. Brigham(2)...................................   3,719,342        30.16%    3,719,342   23.64%
  6300 Bridge Point Parkway, Bldg. 2, Suite 500
  Austin, Texas 78730
General Atlantic Partners, L.L.C.(3).................   2,807,143        22.76%    2,807,143   17.84%
  Three Pickwick Plaza
  Greenwich, Connecticut 06830
Resource Investors Management Company(4).............   1,754,464        14.23%    1,754,464   11.15%
  600 Travis Street, Suite 6875
  Houston, Texas 77002
R. Chaney & Co., Inc.(5).............................     635,000         5.15%      635,000    4.04%
  909 Fannin, Suite 1275
  Two Houston Center
  Houston, Texas 77010
Craig M. Fleming(6)..................................      65,477         *           65,477    2.17%
Jon L. Glass(7)......................................      88,798         *           88,798     *
David T. Brigham(8)..................................      66,477         *           66,477     *
A. Lance Langford(9).................................      18,365         *           18,365     *
Harold D. Carter.....................................     341,893         2.77%      341,893     *
Gary J. Milavec(10)..................................          --            --
Alexis M. Cranberg...................................          --            --
Stephen P. Reynolds(11)..............................          --            --
All directors and executive officers as a group
  (11 persons)(6)(7)(8)..............................   4,220,485        34.22%                27.33%
</TABLE>
 
---------------
 
  *  Represents less than 1%.
 
 (1) Beneficial ownership is determined in accordance with the rules of the SEC
     and generally includes voting or disposition power with respect to
     securities.
 
                                       58
<PAGE>   60
 
 (2) Includes 1,831,414 shares owned by Ben M. Brigham and 1,831,410 shares
     owned by Anne L. Brigham, who are husband and wife; 28,272 shares owned by
     Ben M. Brigham and Anne L. Brigham as Trustees under Brigham Parental Trust
     I; 28,246 shares owned by Ben M. Brigham and Anne L. Brigham as Trustees
     under Brigham Parental Trust II; and 1,000 shares held by David T. Brigham,
     as custodian for Elizabeth R. Brigham under the Texas Uniform Transfers to
     Minors Act.
 
 (3) Includes 2,679,418 shares held by GAP III; and 127,725 shares held by
     GAP-Brigham Partners, L.P. ("GAP-Brigham"). Stephen P. Reynolds is the
     general partner and a limited partner in GAP-Brigham and is President of
     GAP III Investors, Inc., the general partner of GAP III.
 
 (4) Includes 612,308 shares held by RIMCO Partners, L.P. II, 307,031 shares
     held by RIMCO Partners, L.P. III and 835,125 shares held by RIMCO Partners,
     L.P. IV (collectively, the "RIMCO Partnerships"). RIMCO is the general
     partner of each of the RIMCO Partnerships. The general partner of RIMCO is
     RIMCO Associates, Inc.
 
 (5) Includes 610,000 shares held by R. Chaney & Partners III L.P. ("Fund III")
     and 25,000 shares held by R. Chaney & Partners IV L.P. ("Fund IV"). R.
     Chaney & Partners, Inc. ("Partners") is the sole general partner of Fund
     III, and R. Chaney Investments, Inc. ("Investments") is the sole general
     partner of Fund IV. Mr. Robert H. Chaney is the sole shareholder of
     Partners and Investments.
 
 (6) Includes 44,643 shares of restricted stock, which vest as follows: 30% in
     July 1997, 30% in July 1998 and 40% in July 1999; and 20,834 shares of
     Common Stock issuable upon exercise of certain stock options that vest July
     1, 1998.
 
 (7) Includes 66,964 shares of restricted stock, which vest as follows: 16.67%
     in February 1997, 28.33% in July 1997, 28.33% in July 1998 and 26.67% in
     July 1999; and 20,834 shares of Common Stock issuable upon exercise of
     certain stock options that vest July 1, 1998.
 
 (8) Includes 44,643 shares of restricted stock, which vest as follows: 30% in
     July 1997, 30% in July 1998 and 40% in July 1999; 1,000 shares gifted by
     Ben M. Brigham and Anne L. Brigham; and 20,834 shares of Common Stock
     issuable upon exercise of certain stock options that vest July 1, 1998.
 
 (9) Includes 17,365 shares of Common Stock issuable upon exercise of certain
     stock options that vest July 1, 1998.
 
(10) Gary J. Milavec is a Managing Director of RIMCO, the general partner of
     each of the RIMCO Partnerships, and is a Vice President of RIMCO
     Associates, Inc., the general partner of RIMCO. As such, Mr. Milavec may be
     deemed to share voting and investment power with respect to the 612,308
     shares held by RIMCO Partners, L.P. II, the 307,031 shares held by RIMCO
     Partners, L.P. III and the 835,125 shares held by RIMCO Partners, L.P. IV.
     Mr. Milavec disclaims beneficial ownership of shares beneficially owned by
     RIMCO and the RIMCO Partnerships.
 
(11) Stephen P. Reynolds is the general partner and a limited partner in
     GAP-Brigham and is President of GAP III Investors, Inc., the general
     partner of GAP III. As such, Mr. Reynolds may be deemed to share voting and
     investment power with respect to the 2,679,418 shares held by GAP III and
     the 127,725 shares held by GAP-Brigham. Mr. Reynolds disclaims beneficial
     ownership of shares owned by GAP III and GAP-Brigham except to the extent
     of his pecuniary interest therein.
 
                          DESCRIPTION OF CAPITAL STOCK
 
     The authorized capital stock of the Company consists of 30 million shares
of Common Stock, par value $.01 per share, and 10 million shares of preferred
stock, par value $.01 per share ("Preferred Stock"). As of May 27, 1998, the
Company had outstanding 12,253,574 shares of Common Stock held of record by 65
stockholders and stock options for an aggregate of 935,987 shares.
 
COMMON STOCK
 
     The holders of Common Stock are entitled to one vote for each share held of
record on all matters submitted to the stockholders. The Certificate of
Incorporation of the Company does not allow the stockholders to take action by
less than unanimous consent. Each share of Common Stock is entitled to
 
                                       59
<PAGE>   61
 
participate equally in dividends, if, as and when declared by the Company's
Board of Directors, and in the distribution of assets in the event of
liquidation, subject in all cases to any prior rights of outstanding shares of
Preferred Stock. The Company has never paid cash dividends on its Common Stock
and is currently restricted from doing so by the Credit Facility. The shares of
Common Stock have no preemptive or conversion rights, redemption rights, or
sinking fund provisions. The outstanding shares of Common Stock are, and the
shares of Common Stock offered hereby upon issuance and sale will be, duly
authorized, validly issued, fully paid, and nonassessable.
 
PREFERRED STOCK
 
     The Company has no outstanding Preferred Stock. The Company is authorized
to issue 10 million shares of Preferred Stock. The Company's Board of Directors
may establish, without stockholder approval, one or more classes or series of
Preferred Stock having the number of shares, designations, relative voting
rights, dividend rates, liquidation and other rights, preferences, and
limitations that the Board of Directors may designate. The Company believes that
this power to issue Preferred Stock will provide flexibility in connection with
possible corporate transactions. The issuance of Preferred Stock, however, could
adversely affect the voting power of holders of Common Stock and restrict their
rights to receive payments upon liquidation of the Company. It could also have
the effect of delaying, deferring or preventing a change in control of the
Company. The Company does not currently plan to issue Preferred Stock.
 
DELAWARE LAW PROVISIONS
 
     The Company is a Delaware corporation and is subject to Section 203 of the
Delaware General Corporation Law. Generally, Section 203 prohibits the Company
from engaging in a "business combination" (as defined in Section 203) with an
"interested stockholder" (defined generally as a person owning 15% or more of
the Company's outstanding voting stock) for three years following the date that
person becomes an interested stockholder, unless (a) before that person became
an interested stockholder, the Company's Board of Directors approved the
transaction in which the interested stockholder became an interested stockholder
or approved the business combination; (b) upon completion of the transaction
that resulted in the interested stockholder's becoming an interested
stockholder, the interested stockholder owns at least 85% of the voting stock
outstanding at the time the transaction commenced (excluding stock held by
directors who are also officers of the Company and by employee stock plans that
do not provide employees with the right to determine confidentially whether
shares held subject to the plan will be tendered in a tender or exchange offer);
or (c) following the transaction in which that person became an interested
stockholder, the business combination is approved by the Company's Board of
Directors and authorized at a meeting of stockholders by the affirmative vote of
the holders of at least two-thirds of the outstanding voting stock not owned by
the interested stockholder.
 
     Under Section 203, these restrictions also do not apply to certain business
combinations proposed by an interested stockholder following the announcement or
notification of one of certain extraordinary transactions involving the Company
and a person who was not an interested stockholder during the previous three
years or who became an interested stockholder with the approval of a majority of
the Company's directors, if that extraordinary transaction is approved or not
opposed by a majority of the directors who were directors before any person
became an interested stockholder in the previous three years or who were
recommended for election or elected to succeed such directors by a majority of
such directors then in office.
 
REGISTRATION RIGHTS
 
     The Company has entered into a Registration Rights Agreement with General
Atlantic Partners III, L.P., GAP-Brigham Partners, L.P., RIMCO Partners, L.P.
II, RIMCO Partners, L.P. III and RIMCO Partners, L.P. IV, Ben M. Brigham, Anne
L. Brigham, Harold D. Carter, Craig M. Fleming, David T. Brigham and Jon L.
Glass. Pursuant to the Registration Rights Agreement, Anne and Ben Brigham,
acting together, the General Atlantic entities, acting together, and the RIMCO
entities, acting together, each may separately require the Company to register
securities, on one occasion, if the shares to be registered have an estimated
aggregate offering price to the public of at least $3 million. One additional
registration is allowed if
                                       60
<PAGE>   62
 
any registrable securities requested to be included in a previous registration
statement were not disposed of in accordance with that previous registration.
The Registration Rights Agreement also provides "piggyback" registration rights
after the Offering for all registrations of registrable securities for the
Company or another security holder. In an underwritten offering, however, the
Company may exclude all or a portion of the securities being registered pursuant
to "piggyback" registration rights if the managing underwriter determines that
including those securities would raise a substantial doubt about whether the
proposed offering could be consummated. The Registration Rights Agreement
contains customary indemnity by the Company in favor of persons selling
securities in a registration governed by the Registration Rights Agreement, and
by those persons in favor of the Company, relating to the information included
in or omitted from the Registration Statement.
 
TRANSFER AGENT AND REGISTRAR
 
     The Transfer Agent and Registrar for the Common Stock is American Stock
Transfer & Trust Company.
 
                        SHARES ELIGIBLE FOR FUTURE SALE
 
     Upon completion of the Offering, the Company will have 15,653,574 shares of
Common Stock outstanding (15,653,574 shares if the Underwriters exercise their
over-allotment option in full). Of these 15,653,574 shares, the shares of Common
Stock offered hereby will be freely transferable without restriction under the
Securities Act unless they are held by the Company's affiliates, as that term is
used in Rule 144 under the Securities Act. 8,929,574 shares of Common Stock were
issued in reliance on exemptions from the registration requirements of the
Securities Act and are eligible for sale under Rule 144, based on current SEC
rules and subject to compliance with the volume and other requirements of Rule
144. Beginning February 27, 1999, all of those shares of Common Stock will
become eligible for sale under Rule 144(k) if they are not held by affiliates of
the Company. 6,850,000 shares of Common Stock that will be issued in the
Offering or that were sold in the Company's initial public offering are freely
tradeable, except to the extent that they are held by affiliates of the Company.
 
     In general, under Rule 144 a person (or persons whose sales are
aggregated), including an affiliate, who has beneficially owned shares for at
least one year is entitled to sell in broker transactions, within any three-
month period commencing 90 days after the Offering, a number of shares that does
not exceed the greater of (i) 1% of the then outstanding Common Stock
(approximately 156,536 shares immediately after the Offering) or (ii) the
average weekly trading volume in the Common Stock during the four calendar weeks
preceding the sale, subject to the filing of a Form 144 with respect to the sale
and other limitations. In addition, a person who was not an affiliate of the
Company during the three months preceding a sale and who has beneficially owned
the shares proposed to be sold for at least two years is entitled to sell the
shares under Rule 144(k) without regard to the manner-of-sale, volume and other
limitations of Rule 144. The SEC has proposed modifications to Rule 144 that
could change some of these requirements.
 
     The holders of 8,421,431 shares of Common Stock and their permitted
transferees are entitled to demand registration of those shares under the
Securities Act, and the holders of 8,928,574 shares of Common Stock are entitled
to "piggyback" registration rights. See "Description of Capital
Stock -- Registration Rights."
 
               shares of Common Stock are subject to "lock-up" agreements; these
shares will be released from such agreements 90 days after the date of this
Prospectus. See "Underwriting."
 
     Options covering 935,987 shares of Common Stock are outstanding, with an
average exercise price of $7.61 per share, subject to vesting.
 
                                       61
<PAGE>   63
 
                                  UNDERWRITING
 
     The Underwriters named below (the "Underwriters"), for whom Bear, Stearns &
Co. Inc., Dain Rauscher Wessels, a division of Dain Rauscher Incorporated ("Dain
Rauscher Wessels"), and Howard, Weil, Labouisse, Friedrichs Incorporated are
acting as Representatives (the "Representatives"), have severally agreed,
subject to the terms and conditions of the Underwriting Agreement, to purchase
from the Company the aggregate number of shares of Common Stock set forth
opposite their names below:
 
<TABLE>
<CAPTION>
                                                               NUMBER
                        UNDERWRITER                           OF SHARES
                        -----------                           ---------
<S>                                                           <C>
Bear, Stearns & Co. Inc.....................................
Dain Rauscher Wessels.......................................
Howard, Weil, Labouisse, Friedrichs Incorporated............
                                                               ------
          Total.............................................
                                                               ======
</TABLE>
 
     The Underwriting Agreement provides that the obligations of the
Underwriters thereunder are subject to the approval of certain legal matters by
their counsel and to various other conditions. The nature of the obligations of
the Underwriters is such that they are committed to purchase all of the shares
of Common Stock offered hereby if any are purchased.
 
     The Representatives have advised the Company that the Underwriters propose
initially to offer the shares of Common Stock offered hereby directly to the
public at the initial public offering price set forth on the cover page of this
Prospectus. The Underwriters may allow a selected dealer concession of not more
than $     per share, and the Underwriters may allow, and such dealers may
reallow, concessions not in excess of $     per share to certain other dealers.
After the initial public offering, the public offering price and concessions and
reallowances to dealers may be changed by the Representatives.
 
     The Selling Stockholders have granted an option to the Underwriters,
exercisable at any time during the 30-day period after the date of this
Prospectus, to purchase from the Company and the Selling Stockholders up to an
additional 510,000 shares of Common Stock at the initial public offering price
set forth on the cover page of this Prospectus, less the underwriting discount.
Of this amount, an option to purchase        shares has been granted by General
Atlantic and        shares by RIMCO. The Company has granted an option to the
Underwriters to purchase such additional shares in the event that a Selling
Stockholder fails to meet its obligations to sell such shares. The Underwriters
may exercise such option solely for the purpose of covering over-allotments, if
any, made in connection with the sale of the shares of Common Stock offered
hereby. To the extent that the Underwriters exercise this option, each
Underwriter will be committed, subject to certain conditions, to purchase a
number of the additional shares of Common Stock proportionate to such
Underwriter's purchase obligations set forth in the table set forth above.
 
     During and after the Offering, the Underwriters may purchase and sell the
Common Stock in the open market. These transactions may include over-allotment
and stabilizing transactions and purchases to cover syndicate short positions
created in connection with the Offering. The Underwriters may also impose a
penalty bid, whereby selling concessions allowed to syndicate members or other
broker-dealers in respect of the Common Stock sold in the Offering for their
account may be reclaimed by the syndicate if such Common Stock is repurchased by
the syndicate in stabilizing or covering transactions. These activities may
stabilize, maintain or otherwise affect the market price of the Common Stock,
which may be higher than the price that might otherwise prevail in the open
market, and, if commenced, may be discontinued at any time.
 
     The Underwriting Agreement provides that the Company and the Selling
Stockholders will indemnify the several Underwriters against certain
liabilities, including liabilities under the Securities Act, or will contribute
to payments the Underwriters may be required to make in respect thereof.
 
     Each of the Company, its officers, directors and the holders        shares
of its outstanding Common Stock, have entered into "lock-up" agreements with the
Underwriters with respect to the sale of shares of Common Stock. Under these
agreements, the Company, its officers, directors and certain stockholders have
 
                                       62
<PAGE>   64
 
agreed not to offer, sell, agree to sell, grant any option for the sale of or
otherwise dispose of, directly or indirectly, any shares of Common Stock (or any
security convertible into, exercisable for or exchangeable for Common Stock)
without the consent of Bear, Stearns & Co. Inc. for a period of 90 days after
the date of this Prospectus, except that the Company may issue shares of Common
Stock upon the exercise of options granted under its stock option plans. After
the expiration of the "lock-up" agreements, such persons will be entitled to
sell, distribute or otherwise dispose of the Common Stock that they hold subject
to the provisions of applicable securities laws.
 
     The Representatives have informed the Company that they do not expect sales
to discretionary accounts by the Underwriters to exceed five percent of the
total number of shares of Common Stock offered by them.
 
                                 LEGAL MATTERS
 
     Certain legal matters in connection with the Common Stock being offered
hereby will be passed upon for the Company by Thompson & Knight, P.C., Dallas,
Texas. Certain legal matters will be passed upon for the Underwriters by Vinson
& Elkins L.L.P., Dallas, Texas.
 
                                    EXPERTS
 
     The financial statements of Brigham Exploration Company as of December 31,
1997 and 1996 and for each of the three years in the period ended December 31,
1997 included in this Prospectus have been so included in reliance on the report
of Price Waterhouse LLP, independent accountants, given on authority of said
firm as experts in auditing and accounting.
 
     The letter of Cawley, Gillespie & Associates, Inc., independent oil and gas
consultants, set forth in this Prospectus as Appendix A has been included herein
in reliance upon the firm as expert with respect to the matters contained in
that letter. In addition, the information with respect to the reserve reports
prepared by Cawley Gillespie has been included herein in reliance upon by the
firm as experts with respect to such information.
 
                             AVAILABLE INFORMATION
 
     The Company has filed with the Commission a Registration Statement on Form
S-1 (as amended and together with all exhibits thereto, the "Registration
Statement") under the Securities Act, with respect to the shares of Common Stock
offered by this Prospectus. This Prospectus constitutes a part of the
Registration Statement and does not contain all of the information set forth in
the Registration Statement, certain parts of which are omitted from this
Prospectus as permitted by the rules and regulations of the SEC. Statements in
this Prospectus about the contents of any contract or other document are not
necessarily complete; reference is made in each instance to the copy of the
contract or other document filed as an exhibit to the Registration Statement.
Each such statement is qualified in all respects by such reference. The
Registration Statement and accompanying exhibits and schedules may by inspected
and copies may be obtained (at prescribed rates) at the public reference
facilities of the SEC at Judiciary Plaza, 450 Fifth Street, N.W., Room 1024,
Washington, D.C. 20549. Copies of the Registration Statement may also be
inspected at the SEC's regional offices at 7 World Trade Center, Suite 1300, New
York, New York 10048 and Citicorp Center, 500 West Madison Street, Suite 1400,
Chicago, Illinois 60661-2511. In addition, the Common Stock will be listed on
the Nasdaq National Market, 1735 K Street, N.W., Washington, D.C. 20006-1500,
where such material may also be inspected and copied.
 
     The Company is subject to the information and periodic reporting
requirements of the Securities Exchange Act of 1934, and, in accordance
therewith, files periodic reports, proxy statements and other information with
the SEC. Such periodic reports, proxy statements and other information will be
available for inspection and copying at the public reference facilities and
regional offices referred to above. In addition, these reports, proxy statements
and other information may also be obtained from the web site that the SEC
maintains at http://www.sec.gov.
 
                                       63
<PAGE>   65
 
                     GLOSSARY OF CERTAIN OIL AND GAS TERMS
 
     The following are abbreviations and definitions of certain terms commonly
used in the oil and gas industry and this Prospectus.
 
     Bbl. One stock tank barrel, or 42 U.S. gallons liquid volume, used herein
in reference to oil or other liquid hydrocarbons.
 
     Bcf. One billion cubic feet.
 
     Bcfe. One billion cubic feet of natural gas equivalent. In reference to
natural gas, natural gas equivalents are determined using the ratio of 6 Mcf of
natural gas to 1 Bbl of oil, condensate or natural gas liquids.
 
     Completion. The installation of permanent equipment for the production of
natural gas or oil.
 
     Developed Acreage. The number of acres which are allocated or assignable to
producing wells or wells capable of production.
 
     Development Well. A well drilled within the proved area of natural gas or
an oil reservoir to the depth of a stratigraphic horizon known to be productive.
 
     Drilling Costs. The costs associated with drilling and completing a well
(exclusive of seismic and land acquisition costs for that well and future
development costs associated with proved undeveloped reserves added by the well)
divided by total proved reserve additions.
 
     Dry Well. A well found to be incapable of producing either natural gas or
oil in sufficient quantities to justify completion of natural gas or an oil
well.
 
     Exploratory Well. A well drilled to find and produce natural gas or oil in
an unproved area, to find a new reservoir in a field previously found to be
productive of natural gas or oil in another reservoir, or to extend a known
reservoir.
 
     Finding and Development Costs. Capital costs incurred in the acquisition,
exploration and development of proved natural gas and oil reserves divided by
proved reserve additions.
 
     Gross Acres or Gross Wells. The total acres or wells, as the case may be,
in which the Company has a working interest.
 
     Mbbl. One thousand barrels of oil or other liquid hydrocarbons.
 
     Mcf. One thousand cubic feet of natural gas.
 
     Mcfe. One thousand cubic feet of natural gas equivalent.
 
     MMBbl. One million barrels of oil or other liquid hydrocarbons.
 
     MMBtu. One million Btu, or British Thermal Units. One British Thermal Unit
is the quantity of heat required to raise the temperature of one pound of water
by one degree Fahrenheit.
 
     MMcf. One million cubic feet of natural gas.
 
     MMcfe. One million cubic feet of natural gas equivalent.
 
     Net Acres or Net Wells. Gross acres or wells multiplied, in each case, by
the percentage working interest owned by the Company.
 
     Net Production. Production that is owned by the Company less royalties and
production due others.
 
     Oil. Crude oil or condensate.
 
     Operator. The individual or company responsible for the exploration,
development, and production of natural gas or an oil well or lease.
 
     Present Value of Future Net Revenues or PV-10. The pretax present value of
estimated future revenues to be generated from the production of proved reserves
calculated in accordance with SEC guidelines, net of
 
                                       64
<PAGE>   66
 
estimated production and future development costs, using prices and costs as of
the date of estimation without future escalation, without giving effect to
non-property related expenses such as general and administrative expenses, debt
service and depreciation, depletion and amortization, and discounted using an
annual discount rate of 10%.
 
     Proved Developed Reserves. Reserves that can be expected to be recovered
through existing wells with existing equipment and operating methods.
 
     Proved Reserves. The estimated quantities of crude oil, natural gas and
natural gas liquids which geological and engineering data demonstrate with
reasonable certainty to be recoverable in future years from known reservoirs
under existing economic and operating conditions.
 
     Proved Undeveloped Reserves. Reserves that are expected to be recovered
from new wells on undrilled acreage or from existing wells where a relatively
major expenditure is required for recompletion.
 
     Royalty. An interest in an oil and gas lease that gives the owner of the
interest the right to receive a portion of the production from the leased
acreage (or of the proceeds of the sale thereof), but generally does not require
the owner to pay any portion of the costs of drilling or operating the wells on
the leased acreage. Royalties may be either landowner's royalties, which are
reserved by the owner of the leased acreage at the time the lease is granted, or
overriding royalties, which are usually reserved by an owner of the leasehold in
connection with a transfer to a subsequent owner.
 
     Spud. Start drilling a new well (or restart).
 
     Success Rate. The number of wells on which production casing has been run
for a completion attempt as a percentage of the number of wells drilled.
 
     2-D Seismic. The method by which a cross-section of the earth's subsurface
is created through the interpretation of reflecting seismic data collected along
a single source profile.
 
     3-D Seismic. The method by which a three dimensional image of the earth's
subsurface is created through the interpretation of reflection seismic data
collected over surface grid. 3-D seismic surveys allow for a more detailed
understanding of the subsurface than do conventional surveys and contribute
significantly to field appraisal, development and production.
 
     Working Interest. An interest in an oil and gas lease that gives the owner
of the interest the right to drill for and produce natural gas and oil on the
leased acreage and requires the owner to pay a share of the costs of drilling
and production operations.
 
                                       65
<PAGE>   67
 
                          BRIGHAM EXPLORATION COMPANY
 
                         INDEX TO FINANCIAL STATEMENTS
 
<TABLE>
<CAPTION>
                                                              PAGE
                                                              ----
<S>                                                           <C>
Report of Independent Accountants...........................   F-2
Consolidated Balance Sheets as of December 31, 1997 and
  1996......................................................   F-3
Consolidated Statements of Operations for the Years Ended
  December 31, 1997, 1996, and 1995.........................   F-4
Consolidated Statements of Stockholders' Equity for the
  Years Ended December 31, 1997, 1996, and 1995.............   F-5
Consolidated Statements of Cash Flows for the Years Ended
  December 31, 1997, 1996, and 1995.........................   F-6
Notes to the December 31, 1997 Consolidated Financial
  Statements................................................   F-7
Condensed Consolidated Balance Sheets as of December 31,
  1997 and March 31, 1998...................................  F-20
Condensed Consolidated Statements of Operations for the
  Three Months Ended March 31, 1997 and 1998................  F-21
Condensed Consolidated Statements of Cash Flows for the
  Three Months Ended March 31, 1997 and 1998................  F-22
Notes to the March 31, 1998 Condensed Consolidated Financial
  Statements................................................  F-23
</TABLE>
 
                                       F-1
<PAGE>   68
 
                       REPORT OF INDEPENDENT ACCOUNTANTS
 
To the Board of Directors
and Stockholders of Brigham Exploration Company
 
     In our opinion, the accompanying balance sheets and the related statements
of operations, of stockholders' equity and of cash flows present fairly, in all
material respects, the financial position of Brigham Exploration Company at
December 31, 1997 and 1996, and the results of its operations and its cash flows
for each of the three years in the period ended December 31, 1997, in conformity
with generally accepted accounting principles. These financial statements are
the responsibility of the Company's management; our responsibility is to express
an opinion on these financial statements based on our audits. We conducted our
audits of these statements in accordance with generally accepted auditing
standards which require that we plan and perform the audit to obtain reasonable
assurance about whether the financial statements are free of material
misstatement. An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements, assessing the
accounting principles used and significant estimates made by management, and
evaluating the overall financial statement presentation. We believe that our
audits provide a reasonable basis for the opinion expressed above.
 
                                            PRICE WATERHOUSE LLP
 
Houston, Texas
March 6, 1998
 
                                       F-2
<PAGE>   69
 
                          BRIGHAM EXPLORATION COMPANY
 
                          CONSOLIDATED BALANCE SHEETS
                                 (IN THOUSANDS)
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                                DECEMBER 31,
                                                              -----------------
                                                               1997      1996
                                                              -------   -------
<S>                                                           <C>       <C>
Current assets:
  Cash and cash equivalents.................................  $ 1,701   $ 1,447
  Accounts receivable.......................................    4,909     2,696
  Prepaid expenses..........................................      280       152
                                                              -------   -------
          Total current assets..............................    6,890     4,295
                                                              -------   -------
Natural gas and oil properties, at cost, net................   84,176    28,005
Other property and equipment, at cost, net..................    1,239       532
Drilling advances paid......................................       78       419
Other noncurrent assets.....................................       18       363
                                                              -------   -------
                                                              $92,401   $33,614
                                                              =======   =======
 
                     LIABILITIES AND STOCKHOLDERS' EQUITY
 
Current liabilities:
  Accounts payable..........................................  $11,892   $ 2,937
  Accrued drilling costs....................................    2,406       915
  Participant advances received.............................      489     1,137
  Other current liabilities.................................      726       628
                                                              -------   -------
          Total current liabilities.........................   15,513     5,617
                                                              -------   -------
Notes payable...............................................   32,000     8,000
Subordinated notes payable -- related party.................       --    16,000
Other noncurrent liabilities................................      507       753
Deferred income tax liability...............................    1,228        --
Stockholders' equity:
  Predecessor capital.......................................       --     3,244
  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        --
  Additional paid-in capital................................   44,344        --
  Unearned stock compensation...............................   (1,340)       --
  Retained earnings.........................................       26        --
                                                              -------   -------
          Total stockholders' equity........................   43,153     3,244
                                                              -------   -------
                                                              $92,401   $33,614
                                                              =======   =======
</TABLE>
 
  The Company uses the full cost method to account for its natural gas and oil
                                  properties.
 
        See accompanying notes to the consolidated financial statements.
 
                                       F-3
<PAGE>   70
 
                          BRIGHAM EXPLORATION COMPANY
 
                     CONSOLIDATED STATEMENTS OF OPERATIONS
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)
 
<TABLE>
<CAPTION>
                                                                YEAR ENDED DECEMBER 31,
                                                              ---------------------------
                                                               1997      1996      1995
                                                              -------   -------   -------
<S>                                                           <C>       <C>       <C>
Revenues:
  Natural gas and oil sales.................................  $ 9,184   $ 6,141   $ 3,578
  Workstation revenue.......................................      637       627       635
                                                              -------   -------   -------
                                                                9,821     6,768     4,213
                                                              -------   -------   -------
Costs and expenses:
  Lease operating...........................................    1,151       726       761
  Production taxes..........................................      549       362       165
  General and administrative................................    3,570     2,199     1,897
  Depletion of natural gas and oil properties...............    2,732     2,323     1,626
  Depreciation and amortization.............................      306       487       533
  Amortization of stock compensation........................      276        --        --
                                                              -------   -------   -------
                                                                8,584     6,097     4,982
                                                              -------   -------   -------
     Operating income (loss)................................    1,237       671      (769)
                                                              -------   -------   -------
Other income (expense):
  Interest income...........................................      145        52       128
  Interest expense..........................................   (1,017)     (373)     (187)
  Interest expense -- related party.........................     (173)     (800)     (749)
                                                              -------   -------   -------
                                                               (1,045)   (1,121)     (808)
                                                              -------   -------   -------
Net income (loss) before income taxes.......................      192      (450)   (1,577)
Income tax expense..........................................   (1,228)       --        --
                                                              -------   -------   -------
  Net loss..................................................  $(1,036)  $  (450)  $(1,577)
                                                              =======   =======   =======
Net loss per share:
  Basic/Diluted.............................................  $ (0.09)  $ (0.05)  $ (0.18)
Common shares outstanding:
  Basic/Diluted.............................................   11,081     8,929     8,929
</TABLE>
 
        See accompanying notes to the consolidated financial statements.
 
                                       F-4
<PAGE>   71
 
                          BRIGHAM EXPLORATION COMPANY
 
                 CONSOLIDATED STATEMENT OF STOCKHOLDERS' EQUITY
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                              COMMON STOCK        ADDITIONAL     UNEARNED
                          ---------------------    PAID-IN        STOCK       RETAINED   PREDECESSOR
                            SHARES      AMOUNTS    CAPITAL     COMPENSATION   EARNINGS     CAPITAL       TOTAL
                          -----------   -------   ----------   ------------   --------   ------------   -------
<S>                       <C>           <C>       <C>          <C>            <C>        <C>            <C>
Balance,
  December 31, 1994.....           --    $ --      $    --       $    --        $--        $ 5,271      $ 5,271
  Net loss..............           --      --           --            --         --         (1,577)      (1,577)
                          -----------    ----      -------       -------        ---        -------      -------
Balance,
  December 31, 1995.....           --      --           --            --         --          3,694        3,694
  Net loss..............           --      --           --            --         --           (450)        (450)
                          -----------    ----      -------       -------        ---        -------      -------
Balance,
  December 31, 1996.....           --      --           --            --         --          3,244        3,244
Consummation of the
  Exchange..............    8,928,574      90       19,580            --         --         (3,244)      16,426
Issuance of stock
  options...............           --      --        1,932        (1,932)        --             --           --
Issuance of common
  stock.................    3,325,000      33       23,894            --         --             --       23,927
Net loss for period
  ended February 27,
  1997..................           --      --       (4,869)           --         --             --       (4,869)
Net income for period
  from February 27, 1997
  to Dec. 31, 1997......           --      --        3,807            --         26             --        3,833
  (Note 1) Amortization
     of unearned stock
     compensation.......           --      --           --           592         --             --          592
                          -----------    ----      -------       -------        ---        -------      -------
Balance,
  December 31, 1997.....   12,253,574    $123      $44,344       $(1,340)       $26        $    --      $43,153
                          ===========    ====      =======       =======        ===        =======      =======
</TABLE>
 
        See accompanying notes to the consolidated financial statements.
 
                                       F-5
<PAGE>   72
 
                          BRIGHAM EXPLORATION COMPANY
 
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                                 YEAR ENDED DECEMBER 31,
                                                              ------------------------------
                                                                1997       1996       1995
                                                              --------   --------   --------
<S>                                                           <C>        <C>        <C>
Cash flows from operating activities:
  Net loss..................................................  $ (1,036)  $   (450)  $ (1,577)
  Adjustments to reconcile net loss to cash provided by
     operating activities:
     Depletion of natural gas and oil properties............     2,732      2,323      1,626
     Depreciation and amortization..........................       306        487        533
     Amortization of stock compensation.....................       276         --         --
     Changes in working capital and other items:
       (Increase) decrease in accounts receivable...........    (2,213)    (1,440)       413
       (Increase) decrease in prepaid expenses..............      (128)        25       (107)
       Increase in accounts payable.........................     8,955      1,619        128
       Increase (decrease) in participant advances
          received..........................................      (648)       804         92
       Increase in other current liabilities................        50         60        151
       Increase in deferred interest payable -- related
          party.............................................        53        320        113
       Increase in deferred income tax liability............     1,228         --         --
       Other noncurrent assets..............................       281       (224)       (26)
       Other noncurrent liabilities.........................       (50)       186         37
                                                              --------   --------   --------
          Net cash provided by operating activities.........     9,806      3,710      1,383
                                                              --------   --------   --------
Cash flows from investing activities:
  Additions to natural gas and oil properties...............   (57,170)   (13,612)    (7,935)
  Proceeds from the sale of natural gas and oil
     properties.............................................        74      2,149         --
  Additions to other property and equipment.................      (545)       (41)       (51)
  (Increase) decrease in drilling advances paid.............       341       (292)       (19)
                                                              --------   --------   --------
          Net cash used by investing activities.............   (57,300)   (11,796)    (8,005)
                                                              --------   --------   --------
Cash flows from financing activities:
  Proceeds from issuance of common stock....................    23,927         --         --
  Proceeds from issuance of subordinated notes payable......        --         --     16,000
  Increase in notes payable.................................    37,250      8,000      2,560
  Repayment of notes payable................................   (13,250)        --    (10,510)
  Principal payments on capital lease obligations...........      (179)      (269)      (326)
                                                              --------   --------   --------
          Net cash provided by financing activities.........    47,748      7,731      7,724
                                                              --------   --------   --------
Net increase (decrease) in cash and cash equivalents........       254       (355)     1,102
Cash and cash equivalents, beginning of year................     1,447      1,802        700
                                                              --------   --------   --------
Cash and cash equivalents, end of year......................  $  1,701   $  1,447   $  1,802
                                                              ========   ========   ========
Supplemental disclosure of cash flow information:
  Cash paid during the year for interest....................  $  1,679   $    762   $    654
                                                              ========   ========   ========
Supplemental disclosure of noncash investing and financing
  activities:
  Capital lease asset additions.............................  $    403   $    101   $    208
                                                              ========   ========   ========
</TABLE>
 
        See accompanying notes to the consolidated financial statements.
 
                                       F-6
<PAGE>   73
 
                          BRIGHAM EXPLORATION COMPANY
 
                 NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS
 
1. ORGANIZATION AND NATURE OF OPERATIONS
 
     Brigham Exploration 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"). Hereinafter, Brigham Exploration Company and the Partnership are
collectively referred to as "the Company." Brigham, Inc. is a Nevada 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 primarily in the Permian and Hardeman Basins of
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
$13.3 million in outstanding borrowings under the existing revolving credit
facility.
 
2. SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES
 
  Basis of Accounting
 
     The preparation of financial statements in conformity with generally
accepted accounting principles requires management to make estimates and
assumptions that affect the reported amounts of assets and liabilities and
disclosure of contingent assets and liabilities at the date of the financial
statements and the reported amounts of revenues and expenses during the
reporting period. Actual results may differ from those estimates.
 
     The Exchange has been reflected in the consolidated financial statements of
the Company as a reorganization.
 
  Principles of Consolidation
 
     The accompanying financial statements include the accounts of the Company
and its wholly-owned subsidiaries, and its proportionate share of assets,
liabilities and income and expenses of the limited partnerships in which the
Company, or any of its subsidiaries has a participating interest. All
significant intercompany accounts and transactions have been eliminated.
 
  Cash and Cash Equivalents
 
     The Company considers all highly liquid financial instruments with an
original maturity of three months or less to be cash equivalents.
 
                                       F-7
<PAGE>   74
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
  Property and Equipment
 
     The Company uses the full cost method of accounting for its investment in
natural gas and oil properties. Under this method, all acquisition, exploration
and development costs, including certain payroll and other internal costs,
incurred for the purpose of finding natural gas and oil reserves are
capitalized. Costs associated with production and general corporate activities
are expensed in the period incurred.
 
     The capitalized costs of the Company's natural gas and oil properties plus
future development, dismantlement, restoration and abandonment costs (the
"Amortizable Base"), net of estimated of salvage values, are amortized using the
unit-of-production method based upon estimates of total proved reserve
quantities. The Company's capitalized costs of its natural gas and oil
properties, net of accumulated amortization, are limited to the total of
estimated future net cash flows from proved natural gas and oil reserves,
discounted at ten percent, plus the cost of unevaluated properties. There are
many factors, including global events, that may influence the production,
processing, marketing and valuation of natural gas and oil. A reduction in the
valuation of natural gas and oil properties resulting from declining prices or
production could adversely impact depletion rates and ceiling test limitations.
 
     All costs directly associated with the acquisition and evaluation of
unproved properties are initially excluded from the Amortizable Base. Upon the
interpretation by the Company of the 3-D seismic data associated with unproved
properties, the geological and geophysical costs related to acreage that is not
specifically identified as prospective are added to the Amortizable Base.
Geological and geophysical costs associated with prospective acreage, as well as
leasehold costs, are added to the Amortizable Base when the prospects are
drilled. Costs of prospective acreage are reviewed annually for impairment on a
property-by-property basis.
 
     Other property and equipment, which primarily consists of 3-D seismic
interpretation workstations, are depreciated on a straight-line basis over the
estimated useful lives of the assets after considering salvage value. Estimated
useful lives are as follows:
 
<TABLE>
<S>                                                           <C>
Furniture and fixtures......................................  10 years
Machinery and equipment.....................................   5 years
3-D seismic interpretation workstations and software........   3 years
</TABLE>
 
     Betterments and major improvements that extend the useful lives are
capitalized, while expenditures for repairs and maintenance of a minor nature
are expensed as incurred.
 
  Revenue Recognition
 
     The Company recognizes natural gas and oil sales from its interests in
producing wells under the sales method of accounting. Under the sales method,
the Company recognizes revenues based on the amount of natural gas or oil sold
to purchasers, which may differ from the amounts to which the Company is
entitled based on its interest in the properties. Gas balancing obligations as
of December 31, 1995, 1996 and 1997 were not significant. Net realized gains or
losses arising from the Company's crude oil price swaps (see Note 10) are
recognized in the period incurred as a component of natural gas and oil sales.
 
     Industry participants in the Company's seismic programs are charged on an
hourly basis for the work performed by the Company on its 3-D seismic
interpretation workstations. The Company recognizes workstation revenue as
service is provided.
 
                                       F-8
<PAGE>   75
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
  Federal and State Income Taxes
 
     Prior to the consummation of the Exchange, there was no income tax
provision included in the financial statements as the Partnership was not a
taxpaying entity. 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 became subject to federal
income taxes through its ownership by the Company.
 
     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.
Related to this election, the Company recorded a $3.8 million deferred income
tax benefit, resulting in a net $1.2 million deferred income tax charge for the
year ended December 31, 1997.
 
  Earnings Per Share
 
     The Company has adopted Statement of Financial Accounting Standards
("SFAS") No. 128 "Earnings per Share." This statement establishes new standards
for computing and presenting earnings per share ("EPS") and requires restatement
of all prior-period EPS information.
 
  Recent Pronouncements
 
     In June 1997, the Financial Accounting Standards Board issued SFAS No. 130,
"Reporting Comprehensive Income," which will become effective for the Company in
1998. SFAS No. 130 will require companies to present certain items as separate
components of stockholders' equity. Management does not believe that the effect
of implementing this standard will materially impact the Company's financial
statements.
 
3. ACQUISITION
 
     On November 12, 1997, the Company acquired a 50% interest in certain
producing properties in Grady County, Oklahoma (the "Acquisition"). These
properties were formerly owned by Mobil and were acquired by Ward Petroleum. The
acquisition has been accounted for as a purchase and the results of operations
of the properties acquired are included in the Company's results of operations
effective September 1, 1997. The purchase price of $13.4 million was financed
primarily through the Company's existing revolving credit facility and was based
on the Company's determination of the fair value of the assets acquired.
 
  Pro Forma Information
 
     The following unaudited pro forma statement of operations information has
been prepared to give effect to the Acquisition as if the transaction had
occurred at the beginning of 1996 and 1997. The historical results of operations
have been adjusted to reflect (i) the difference between the acquired
properties' historical depletion and such expense calculated based on the value
allocated to the acquired assets, (ii) the increase in interest expense
associated with the debt issued in the transaction, and (iii) the increase in
federal income taxes related to historical net income attributable to the
properties acquired. The pro forma amounts do not
 
                                       F-9
<PAGE>   76
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
purport to be indicative of the results of operations that would have been
reported had the Acquisition occurred as of the dates indicated, or that may be
reported in the future (in thousands).
 
<TABLE>
<CAPTION>
                                                                 PRO FORMA
                                                                 YEAR ENDED
                                                                DECEMBER 31,
                                                              ----------------
                                                               1997      1996
                                                              -------   ------
<S>                                                           <C>       <C>
Revenues....................................................  $11,194   $8,516
Costs and expenses:
  Lease operating and production taxes......................    1,864    1,300
  General and administrative................................    3,570    2,199
  Depletion of natural gas and oil properties...............    3,307    2,791
  Depreciation and amortization.............................      582      487
  Interest expense, net.....................................    2,235    2,355
                                                              -------   ------
  Total costs and expenses..................................   11,558    9,132
                                                              -------   ------
Net loss before income taxes................................     (364)    (616)
  Income tax expense........................................    1,039       --
                                                              -------   ------
Net loss....................................................  $(1,403)  $ (616)
                                                              =======   ======
Net loss per share:
  Basic/Diluted.............................................  $ (0.13)  $(0.07)
                                                              =======   ======
Common shares outstanding:
  Basic/Diluted.............................................   11,081    8,929
                                                              =======   ======
</TABLE>
 
4. PROPERTY AND EQUIPMENT
 
     Property and equipment, at cost, are summarized as follows (in thousands):
 
<TABLE>
<CAPTION>
                                                                DECEMBER 31,
                                                              -----------------
                                                               1997      1996
                                                              -------   -------
<S>                                                           <C>       <C>
Natural gas and oil properties..............................  $96,458   $37,555
Accumulated depletion.......................................  (12,282)   (9,550)
                                                              -------   -------
                                                               84,176    28,005
                                                              -------   -------
Other property and equipment:
  3-D seismic interpretation workstations and software......    1,693     1,456
  Office furniture and equipment............................    1,095       384
  Accumulated depreciation..................................   (1,549)   (1,308)
                                                              -------   -------
                                                                1,239       532
                                                              -------   -------
                                                              $85,415   $28,537
                                                              =======   =======
</TABLE>
 
     The Company sold its interest in certain producing properties for $2.1
million and $74,000 during 1996
and 1997, respectively. No gain or loss was recognized on these transaction
because the Company applies the full cost method of accounting for its
investment in natural gas and oil properties.
 
     The Company capitalizes certain payroll and other internal costs directly
attributable to acquisition, exploration and development activities as part of
its investment in natural gas and oil properties over the periods benefited by
these activities. During the years ended December 31, 1995, 1996 and 1997,
certain payroll and other internal costs incurred of $1,640,196, $1,826,013 and
$3,330,518, respectively, were capitalized.
 
                                      F-10
<PAGE>   77
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
5. NOTES PAYABLE AND SUBORDINATED NOTES PAYABLE
 
     In April 1996, the Company entered into a revolving credit facility with
Bank One, Texas, NA (the "Bank One Facility") which provided for borrowings up
to $25 million. On November 10, 1997, the Bank One Facility was amended and the
amount available under the agreement was increased to $75 million. The Company's
borrowings under the Bank One Facility were limited to a borrowing base
determined periodically by the lender. This determination was based upon the
Company's proved net gas and oil properties.
 
     The amounts outstanding under the revolving credit facility, excluding a
$5.4 million special advance made November 12, 1997, bore interest, at the
borrower's option, at the Base Rate or (i) LIBOR plus 1.75% if the principal
outstanding is less than or equal to 50% of the borrowing base, (ii) LIBOR plus
2.0% if the principal outstanding is less than or equal to 75% but more than 50%
of the borrowing base, and (iii) LIBOR plus 2.25% if the principal outstanding
is greater than 75% of the borrowing base. The Base Rate is the fluctuating rate
of interest per annum established from time to time by the lender. Interest
accrued on the $5.4 million special advance at 11.50% per annum. The Company
also paid a quarterly commitment fee of 0.5% per annum for the unused portion of
the borrowing base.
 
     In January 1998, the Company entered into a reserve-based revolving credit
facility with the Bank of Montreal (the "Bank of Montreal Facility"). The Bank
of Montreal Facility provides for borrowings up to $75 million until January 31,
1999, at which time the borrowing available will be redetermined by the Bank of
Montreal 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 Bank of Montreal 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 Bank of Montreal Facility are secured by
substantially all of the natural gas and oil properties of the Company. A
portion of the funds available under the Bank of Montreal Facility were used to
repay in full the Bank One Facility.
 
     The subordinated notes payable bore interest at 5% per annum and were due
in 2002. The notes were convertible into a 20% interest in the Company at any
time prior to maturity and were unsecured. Interest payments of 3% were due
semi-annually and the remaining 2% was deferred until maturity. Pursuant to the
Exchange (see Note 1), the holders of these notes exchanged the notes and
related deferred interest for shares of the Company's common stock.
 
6. CAPITAL LEASE OBLIGATIONS
 
     Property under capital leases consists of the following (in thousands):
 
<TABLE>
<CAPTION>
                                                              DECEMBER 31,
                                                              -------------
                                                              1997    1996
                                                              -----   -----
<S>                                                           <C>     <C>
3-D seismic interpretation workstations and software........  $ 497   $ 525
Office furniture and equipment..............................    204      17
                                                              -----   -----
                                                                701     542
Accumulated depreciation and amortization...................   (241)   (305)
                                                              -----   -----
                                                              $ 460   $ 237
                                                              =====   =====
</TABLE>
 
                                      F-11
<PAGE>   78
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
     The obligations under capital leases are at fixed interest rates ranging
from 9% to 17% and are collateralized by property, plant and equipment. The
future minimum lease payments under the capital leases and the present value of
the net minimum lease payments at December 31, 1997 are as follows (in
thousands):
 
<TABLE>
<S>                                                            <C>
1998........................................................   $ 261
1999........................................................     185
2000........................................................      99
2001........................................................      40
2002........................................................      24
                                                               -----
Total minimum lease payments................................     609
  Estimated executory costs included in capital leases......     (73)
                                                               -----
Net minimum lease payments..................................     536
  Amounts representing interest.............................     (81)
                                                               -----
Present value of net minimum lease payments.................     455
Less: current portion.......................................    (181)
                                                               -----
Noncurrent portion..........................................   $ 274
                                                               =====
</TABLE>
 
7. INCOME TAXES
 
     The provision for income taxes consists of the following (in thousands):
 
<TABLE>
<CAPTION>
                                                               YEAR ENDED
                                                              DECEMBER 31,
                                                                  1997
                                                              ------------
<S>                                                           <C>
Current income taxes:
  Federal...................................................     $   --
  State.....................................................         --
Deferred income taxes:
  Federal...................................................      1,228
  State.....................................................         --
                                                                 ------
                                                                 $1,228
                                                                 ======
</TABLE>
 
     The difference in income taxes provided and the amounts determined by
applying the federal statutory tax rate to income before income taxes result
from the following (in thousands):
 
<TABLE>
<CAPTION>
                                                               YEAR ENDED
                                                              DECEMBER 31,
                                                                  1997
                                                              ------------
<S>                                                           <C>
Tax at statutory rate.......................................     $   65
Add (deduct) the effect of:
  January and February income, not taxable..................        (44)
  Nondeductible expenses....................................         14
  Tax effect of Exchange....................................      1,193
                                                                 ------
                                                                 $1,228
                                                                 ======
</TABLE>
 
                                      F-12
<PAGE>   79
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
     The components of deferred income tax assets and liabilities are as follows
(in thousands):
 
<TABLE>
<CAPTION>
                                                               DECEMBER 31,
                                                                   1997
                                                               ------------
<S>                                                            <C>
Deferred tax assets:
  Net operating loss carryforwards..........................     $ 5,563
  Amortization of stock compensation........................          94
  Other.....................................................           3
                                                                 -------
                                                                   5,660
Deferred tax liability:
  Depreciable and depletable property.......................      (6,888)
                                                                 -------
                                                                 $(1,228)
                                                                 =======
</TABLE>
 
     The Company has regular and alternative minimum tax net operating loss
carryforwards of approximately $16,361 million and $8,441 million, respectively,
each including separate return limitation year carryovers of approximately
$1,352 million, which expire by December 31, 2012.
 
8. EARNINGS PER SHARE
 
     Earnings per share have been calculated in accordance with the provisions
of SFAS No. 128. The implementation of the 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 common share for 1996 and 1995 is based on shares
issued upon consummation of the Exchange, assuming such shares has been
outstanding for all periods presented. Earnings per share for 1997 is presented
giving effect to the shares issued pursuant to the Exchange as well as shares
issued in the initial public offering.
 
     At December 31, 1997, options to purchase 644,097 shares of common stock
were outstanding but were not included in the computation of diluted earnings
per share due to the anti-dilutive effect they would have on EPS if converted.
 
     In January 1998, the Company granted 309,247 stock options under the 1997
incentive plan (the "1997 Incentive Plan") with an exercise price of $12.88.
 
9. COMMITMENTS AND CONTINGENCIES
 
     The Company is, from time to time, party to certain lawsuits and claims
arising in the ordinary course of business. While the outcome of lawsuits and
claims cannot be predicted with certainty, management does not expect these
matters to have a materially adverse effect on the financial condition, results
of operations or cash flows of the Company.
 
                                      F-13
<PAGE>   80
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
     The Company leases office equipment and space under operating leases
expiring at various dates through 2007. The future minimum annual rental
payments under the noncancelable terms of these leases at December 31, 1997, are
as follows (in thousands):
 
<TABLE>
<S>                                                   <C>
1998................................................  $  765
1999................................................     763
2000................................................     684
2001................................................     684
2002................................................     342
                                                      ------
                                                      $3,238
                                                      ======
</TABLE>
 
     Rental expense for the years ended December 31, 1995, 1996 and 1997 was
$239,715, $253,112 and $606,173, respectively.
 
     Since the Company's major products are commodities, significant changes in
the prices of natural gas and oil could have a significant impact on the
Company's results of operations for any particular year.
 
     As of December 31, 1997, there were no known environmental or other
regulatory matters related to the Company's operations which are reasonably
expected to result in a material liability to the Company. Compliance with
environmental laws and regulations has not had, and is not expected to have, a
material adverse effect on the Company's capital expenditures, earnings or
competitive position.
 
     During 1997, approximately 14% and 12% of the Company's natural gas and oil
production was sold to two separate customers. During 1996, approximately 16%,
12% and 10% of the Company's natural gas and oil production was sold to three
separate customers. During 1995, approximately 14%, 11%, 10% and 10% of the
Company's natural gas and oil production was sold to four separate customers.
However, due to the availability of other markets, the Company does not believe
that the loss of any one of these individual customers would adversely affect
the Company's result of operations.
 
10. FINANCIAL INSTRUMENTS
 
     The Company periodically enters into commodity price swap agreements which
require payments to (or receipts from) counterparties based on the differential
between a fixed price and a variable price for a fixed quantity of natural gas
or crude oil without the exchange of the underlying volumes. The notional
amounts of these derivative financial instruments are based on planned
production from existing wells. The Company uses these derivative financial
instruments to manage market risks resulting from fluctuations in commodity
prices. Commodity price swaps are effective in minimizing these risks by
creating essentially equal and offsetting market exposures. The derivative
financial instruments held by the Company are not leveraged and are held for
purposes other than trading.
 
     At December 31, 1996, the Company was a party to crude oil swap based on an
average notional volume of 7,550 barrels of crude oil per month and a fixed
price of $22.70 per barrel. The contract expired in May 1997. The fair market
value of the crude oil price swap at December 31, 1996, based on the market
price of crude oil in December 1996, was $41,902. The Company was not a party to
any swap agreements at December 31, 1997.
 
     In February 1998, the Company entered into a hedging contract whereby
natural gas is purchased and sold subject to a fixed price swap agreement for
monthly periods from April 1998 through October 1999. Total natural gas subject
to this hedging contract is 2,750,000 MMBtu in 1998 and 3,040,000 MMBtu in 1999.
 
     The Company's non-derivative financial instruments include cash and cash
equivalents, accounts receivable, accounts payable and long-term debt. The
carrying amount of cash and cash equivalents, accounts
 
                                      F-14
<PAGE>   81
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
receivable and accounts payable approximate fair value because of their
immediate or short maturities. The carrying value of the Company's revolving
credit facility (see Note 5) approximates its fair market value since it bears
interest at floating market interest rates. At December 31, 1996, the carrying
amount of the Company's subordinated notes payable exceeded the fair market
value by $1.9 million, based on current rates offered to the Company for debt of
the same remaining maturity.
 
     The Company's accounts receivable relate to natural gas and oil sales to
various industry companies, amounts due from industry participants for
expenditures made by the Company on their behalf and workstation revenues.
Credit terms, typical of industry standards, are of a short-term nature and the
Company does not require collateral. The Company's accounts receivable at
December 31, 1997 do not represent significant credit risks as they are
dispersed across many counterparties. Counterparties to the crude oil price
swaps are investment grade financial institutions.
 
11. EMPLOYEE BENEFIT PLANS
 
  Retirement Savings Plan
 
     During 1996 the Company adopted a defined contribution 401(k) plan for
substantially all of its employees. Eligible employees may contribute up to 15%
of their compensation to this plan. The 401(k) plan provides that the Company
may, at its discretion, match employee contributions. The Company did not match
employee contributions in 1997 or 1996.
 
  Stock Compensation
 
     In 1994 three employees were granted restricted interests in the Company
which vest in increments through July 1999. At the date of grant, the value of
these interests was immaterial. On February 26, 1997, in connection with the
Exchange (see Note 1), the three employees transferred these company interests
to the Company in exchange for 156,250 shares of restricted common stock of the
Company. The terms of the restricted stock and the restricted company interests
are substantially the same. The shares vest over a three-year period ending in
1999. No compensation expense will result from this exchange.
 
     The Company adopted an incentive plan, effective upon completion of the
Exchange (see Note 1), which provides for the issuance of stock options, stock
appreciation rights, stock, restricted stock, cash or any combination of the
foregoing. The objective of this plan is to reward key employees whose
performance may have a significant effect on the success of the Company. An
aggregate of 1,588,170 shares of the Company's common stock was reserved for
issuance pursuant to this plan. The Compensation Committee of the Board of
Directors will determine the type of awards made to each participant and the
terms, conditions and limitations applicable to each award.
 
     The Company granted 644,097 stock options as of March 4, 1997. These
options were granted under the 1997 Incentive Plan established as part of the
Exchange (Note 1). These options have contractual lives of 7.3 years and have an
exercise price of $5.00 compared to the public offering price of $8.00. This
grant resulted in noncash compensation expense which is recognized over the
appropriate vesting period. None of these options were exercisable at December
31, 1997.
 
     As provided under SFAS 123, the Company estimates that the fair value of
these options on their grant date, using the Black-Scholes Option Pricing Model,
was $3.4 million ($5.32 per option). This valuation was determined using the
following assumptions: risk free interest rate of 6.24%; volatility factor of
the expected market prices of the Company's common stock of 38%; no expected
dividends; and weighted average option lives of 7.3 years. If this valuation
method were elected for accounting purposes, the estimated fair value of $3.4
million would be amortized over the appropriate vesting periods of the options
through 2003, resulting in a pro forma net loss for the year ended December 31,
1997 of $1.3 million, or $0.11 per common share.
 
                                      F-15
<PAGE>   82
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
12. RELATED PARTY TRANSACTIONS
 
     During the years ended December 31, 1995, 1996 and 1997, the Company paid
approximately $382,000, $596,000 and $837,000 respectively, in fees for land
acquisition services performed by a company owned by a brother of the Company's
President and Chief Executive Officer. Other participants in the Company's 3-D
seismic projects reimbursed the Company for a portion of these amounts.
 
     The Company also participated in various industry projects with affiliates
of the holder of the subordinated notes payable (see Note 5). During 1996 and
1997, the Company received approximately $123,000 and $50,000, respectively, for
workstation and geoscientists' time spent interpreting 3-D seismic data and
workstation use. In 1997, the Company paid approximately $214,000 for an
interest in an exploration project sold by the affiliates. The Company billed
the affiliates $197,000 in 1997 for their proportionate share of the costs
related to this and other projects in which the affiliates participate. The
Company also sold to an affiliate of the holders of the subordinated notes
payable an interest in (i) a 3-D project for approximately $75,000 in 1995 and
(ii) two 3-D delineated potential drilling locations and 3-D seismic data for
approximately $83,000 in 1996.
 
     In 1996 and 1997, the Company paid $110,000 and $18,000 for working
interests in natural gas and oil properties owned by affiliates of a member of
the Company's board of directors/management committee. The Company billed the
affiliates $13,000 and $68,000 in 1995 and 1996, respectively, for their
proportionate share of the costs related to this project.
 
     A limited partner and member of the Company's management committee served
as a consultant to the Company on various aspects of the Company's business and
strategic issues. Fees paid for these services by the Company were $72,000,
$79,200 and $86,580 for the twelve month periods ended December 31, 1995, 1996
and 1997, respectively. Additional disbursements totaling approximately $13,000
were made during 1997 for the reimbursement of certain expenses.
 
13. NATURAL GAS AND OIL EXPLORATION AND PRODUCTION ACTIVITIES
 
     The tables presented below provide supplemental information about natural
gas and oil exploration and production activities as defined by SFAS No. 69,
"Disclosures about Oil and Gas Producing Activities."
 
  Results of Operations for Natural Gas and Oil Producing Activities (in
thousands)
 
<TABLE>
<CAPTION>
                                                             YEAR ENDED DECEMBER 31,
                                                             ------------------------
                                                              1997     1996     1995
                                                             ------   ------   ------
<S>                                                          <C>      <C>      <C>
Natural gas and oil sales..................................  $9,184   $6,141   $3,578
Costs and expenses:
  Lease operating..........................................   1,151      726      761
  Production taxes.........................................     549      362      165
  Depletion of natural gas and oil properties..............   2,732    2,323    1,626
  Income taxes.............................................   1,322       --       --
                                                             ------   ------   ------
Total costs and expenses...................................   5,754    3,411    2,552
                                                             ------   ------   ------
                                                             $3,430   $2,730   $1,026
                                                             ======   ======   ======
Depletion per physical unit of production (equivalent Mcf
  of gas)..................................................  $ 0.87   $ 1.13   $ 1.22
                                                             ======   ======   ======
</TABLE>
 
     Natural gas and oil sales reflect the market prices of net production sold
or transferred, with appropriate adjustments for royalties, net profits interest
and other contractual provisions. Lease operating expenses include lifting costs
incurred to operate and maintain productive wells and related equipment,
including such costs as operating labor, repairs and maintenance, materials,
supplies and fuel consumed. Production taxes
 
                                      F-16
<PAGE>   83
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
include production and severance taxes. No provision was made for income taxes
for 1995 and 1996 since these taxes are the responsibility of the partners (see
Note 2). Depletion of natural gas and oil properties relates to capitalized
costs incurred in acquisition, exploration and development activities. Results
of operations do not include interest expense and general corporate amounts.
 
  Costs Incurred and Capitalized Costs
 
     The costs incurred in natural gas and oil acquisition, exploration and
development activities follow (in thousands):
 
<TABLE>
<CAPTION>
                                                                 DECEMBER 31,
                                                          ---------------------------
                                                           1997      1996      1995
                                                          -------   -------   -------
<S>                                                       <C>       <C>       <C>
Costs incurred for the year:
  Exploration...........................................  $29,421   $10,527   $ 6,893
  Property acquisition..................................   26,922     6,195     1,885
  Development...........................................    2,953     1,328       713
  Proceeds from participants............................     (319)   (4,111)   (1,296)
                                                          -------   -------   -------
                                                          $58,977   $13,939   $ 8,195
                                                          =======   =======   =======
</TABLE>
 
     Costs incurred represent amounts incurred by the Company for exploration,
property acquisition and development activities. Periodically, the Company will
receive proceeds from participants subsequent to project initiation for an
assignment of an interest in the project. These payments are represented by
proceeds from participants.
 
     Capitalized costs related to natural gas and oil acquisition, exploration
and development activities follow (in thousands):
 
<TABLE>
<CAPTION>
                                                                 DECEMBER 31,
                                                              ------------------
                                                                1997      1996
                                                              --------   -------
<S>                                                           <C>        <C>
Cost of natural gas and oil properties at year-end:
  Proved....................................................  $ 67,615   $30,487
  Unproved..................................................    28,843     7,068
                                                              --------   -------
  Total capitalized costs...................................    96,458    37,555
  Accumulated depletion.....................................   (12,282)   (9,550)
                                                              --------   -------
                                                              $ 84,176   $28,005
                                                              ========   =======
</TABLE>
 
     Following is a summary of costs (in thousands) excluded from depletion at
December 31, 1997, by year incurred. At this time, the Company is unable to
predict either the timing of the inclusion of these costs and the related
natural gas and oil reserves in its depletion computation or their potential
future impact on depletion rates.
 
<TABLE>
<CAPTION>
                                                 DECEMBER 31,
                                            -----------------------   PRIOR
                                             1997      1996    1995   YEARS     TOTAL
                                            -------   ------   ----   ------   -------
<S>                                         <C>       <C>      <C>    <C>      <C>
Property acquisition......................  $17,382   $2,515   $694   $1,852   $22,443
Exploration...............................    4,393    1,242    234      531     6,400
                                            -------   ------   ----   ------   -------
Total.....................................  $21,775   $3,757   $928   $2,383   $28,843
                                            =======   ======   ====   ======   =======
</TABLE>
 
                                      F-17
<PAGE>   84
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
14. NATURAL GAS AND OIL RESERVES AND RELATED FINANCIAL DATA (UNAUDITED)
 
     Information with respect to the Company's natural gas and oil producing
activities is presented in the following tables. Reserve quantities as well as
certain information regarding future production and discounted cash flows were
determined by the Company's independent petroleum consultants and internal
petroleum reservoir engineer.
 
  Natural Gas and Oil Reserve Data
 
     The following tables present the Company's estimates of its proved natural
gas and oil reserves. The Company emphasizes that reserve estimates are
approximates and are expected to change as additional information becomes
available. Reservoir engineering is a subjective process of estimating
underground accumulations of natural gas and oil that cannot be measured in an
exact way, and the accuracy of any reserve estimate is a function of the quality
of available data and of engineering and geological interpretation and judgment.
Accordingly, there can be no assurance that the reserves set forth herein will
ultimately be produced nor can there be assurance that the proved undeveloped
reserves will be developed within the periods anticipated. A substantial portion
of the reserve balances were estimated utilizing the volumetric method, as
opposed to the production performance method.
 
<TABLE>
<CAPTION>
                                                              NATURAL
                                                                GAS       OIL
                                                              (MMCF)    (MBBLS)
                                                              -------   -------
<S>                                                           <C>       <C>
Proved reserves at December 31, 1994........................   3,579     1,022
  Revisions to previous estimates...........................  (1,600)     (214)
  Extensions, discoveries and other additions...............   2,555     1,055
  Sales of minerals-in-place................................      (6)      (14)
  Production................................................    (271)     (177)
                                                              ------     -----
Proved reserves at December 31, 1995........................   4,257     1,672
  Revisions to previous estimates...........................  (1,005)     (232)
  Extensions, discoveries and other additions...............   7,742       996
  Purchase of minerals-in-place.............................     260         3
  Sales of minerals-in-place................................    (299)     (272)
  Production................................................    (698)     (227)
                                                              ------     -----
Proved reserves at December 31, 1996........................  10,257     1,940
  Revisions of previous estimates...........................  (3,044)     (447)
  Extensions, discoveries and other additions...............  33,721       735
  Purchase of minerals-in-place.............................  13,718     1,244
  Sales of minerals-in-place................................     (40)       --
  Production................................................  (1,382)     (291)
                                                              ------     -----
Proved reserves at December 31, 1997........................  53,230     3,181
                                                              ======     =====
Proved developed reserves at December 31:
  1995......................................................   3,819     1,274
  1996......................................................   6,034     1,453
  1997......................................................  30,677     2,665
</TABLE>
 
     Proved reserves are estimated quantities of crude natural gas and oil which
geological and engineering data indicate with reasonable certainty to be
recoverable in future years from known reservoirs under existing economic and
operating conditions. Proved developed reserves are proved reserves which can be
expected to be recovered through existing wells with existing equipment and
operating methods.
 
                                      F-18
<PAGE>   85
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
  Standardized Measure of Discounted Future Net Cash Inflows and Changes Therein
 
     The following table presents a standardized measure of discounted future
net cash inflows (in thousands) relating to proved natural gas and oil reserves.
Future cash flows were computed by applying year end prices of natural gas and
oil relating to the Company's proved reserves to the estimated year-end
quantities of those reserves. Future price changes were considered only to the
extent provided by contractual agreements in existence at year-end. Future
production and development costs were computed by estimating those expenditures
expected to occur in developing and producing the proved natural gas and oil
reserves at the end of the year, based on year-end costs. Actual future cash
inflows may vary considerably and the standardized measure does not necessarily
represent the fair value of the Company's natural gas and oil reserves.
 
<TABLE>
<CAPTION>
                                                                DECEMBER 31,
                                                       ------------------------------
                                                         1997       1996       1995
                                                       --------   --------   --------
<S>                                                    <C>        <C>        <C>
Future cash inflows..................................  $165,156   $ 84,987   $ 38,333
Future development and production costs..............   (40,923)   (20,998)   (12,543)
Future income taxes..................................   (22,919)        --         --
                                                       --------   --------   --------
Future net cash inflows..............................  $101,314   $ 63,989   $ 25,790
                                                       ========   ========   ========
Future net cash inflow before income taxes,
  discounted at 10% per annum........................  $ 69,249   $ 44,506   $ 18,222
                                                       ========   ========   ========
Standardized measure of future net cash inflows
  discounted at 10% per annum........................  $ 64,274   $ 44,506   $ 18,222
                                                       ========   ========   ========
</TABLE>
 
     The average natural gas and oil prices used to calculate the future net
cash inflows at December 31, 1997 were $16.64 per barrel and $2.11 per Mcf,
respectively. At December 31, 1997, the NYMEX price for natural gas was $2.26
per MMBtu and the NYMEX price for oil was $17.64 per barrel. From January 1,
1998 to March 24, 1997, the NYMEX price for natural gas ranged from $2.00 per
MMBtu to $2.38 per MMBtu and the NYMEX price for oil ranged from $13.21 per
barrel to $17.82 per barrel.
 
     Changes in the future net cash inflows discounted at 10% per annum follow:
 
<TABLE>
<CAPTION>
                                                                 DECEMBER 31,
                                                         ----------------------------
                                                           1997      1996      1995
                                                         --------   -------   -------
<S>                                                      <C>        <C>       <C>
Beginning of period....................................  $ 44,506   $18,222   $10,240
  Sales of natural gas and oil produced, net of
     production costs..................................    (7,484)   (5,053)   (2,652)
  Development costs incurred...........................     1,955       246       169
  Extensions and discoveries...........................    38,016    29,457    11,669
  Purchases of minerals-in-place.......................    16,965       384        --
  Sales of minerals-in-place...........................       (94)   (2,380)     (198)
  Net change of prices and production costs............   (20,466)    7,023     1,394
  Change in future development costs...................       319       303       419
  Changes in production rates and other................    (1,954)     (342)     (364)
  Revisions of quantity estimates......................    (6,964)   (5,176)   (3,479)
  Accretion of discount................................     4,450     1,822     1,024
  Change in income taxes...............................    (4,975)       --        --
                                                         --------   -------   -------
End of period..........................................  $ 64,274   $44,506   $18,222
                                                         ========   =======   =======
</TABLE>
 
                                      F-19
<PAGE>   86
 
                          BRIGHAM EXPLORATION COMPANY
 
                             CONDENSED CONSOLIDATED
                                 BALANCE SHEETS
                                 (IN THOUSANDS)
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                              DECEMBER 31,    MARCH 31,
                                                                  1997          1998
                                                              ------------   -----------
                                                                             (UNAUDITED)
<S>                                                           <C>            <C>
Current assets:
  Cash and cash equivalents.................................    $ 1,701       $  1,800
  Accounts receivable.......................................      4,909          5,510
  Prepaid expenses..........................................        280            267
                                                                -------       --------
          Total current assets..............................      6,890          7,577
                                                                -------       --------
Natural gas and oil properties, at cost, net................     84,176         96,676
Other property and equipment, at cost, net..................      1,239          1,374
Drilling advances paid......................................         78             62
Deferred loan fees..........................................         --          1,805
Other noncurrent assets.....................................         18             14
                                                                -------       --------
                                                                $92,401       $107,508
                                                                =======       ========
 
                          LIABILITIES AND STOCKHOLDERS' EQUITY
 
Current liabilities:
  Accounts payable..........................................    $11,892       $  5,819
  Accrued drilling costs....................................      2,406          3,071
  Participant advances received.............................        489          3,110
  Other current liabilities.................................        726          1,374
                                                                -------       --------
          Total current liabilities.........................     15,513         13,374
                                                                -------       --------
Notes payable...............................................     32,000         50,000
Other noncurrent liabilities................................        507            478
Deferred income tax liability...............................      1,228            914
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         44,344
  Unearned stock compensation...............................     (1,340)        (1,136)
  Retained earnings (accumulated deficit)...................         26           (589)
                                                                -------       --------
          Total stockholders' equity........................     43,153         42,742
                                                                -------       --------
                                                                $92,401       $107,508
                                                                =======       ========
</TABLE>
 
   See accompanying notes to the condensed consolidated financial statements.
 
                                      F-20
<PAGE>   87
 
                          BRIGHAM EXPLORATION COMPANY
 
                             CONDENSED CONSOLIDATED
                            STATEMENTS OF OPERATIONS
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                THREE MONTHS
                                                              ENDED MARCH 31,
                                                              ----------------
                                                               1997      1998
                                                              -------   ------
<S>                                                           <C>       <C>
Revenues:
  Natural gas and oil sales.................................  $ 2,136   $3,143
  Workstation revenue.......................................      164      114
                                                              -------   ------
                                                                2,300    3,257
                                                              -------   ------
Costs and expenses:
  Lease operating...........................................      206      414
  Production taxes..........................................      127      188
  General and administrative................................      702    1,154
  Depletion of natural gas and oil properties...............      687    1,267
  Depreciation and amortization.............................      108       83
  Amortization of stock compensation                               29       95
                                                              -------   ------
                                                                1,859    3,201
                                                              -------   ------
     Operating income.......................................      441       56
                                                              -------   ------
Other income (expense):
  Interest income...........................................       18       37
  Interest expense..........................................     (216)  (1,022)
  Interest expense -- related party.........................     (174)      --
                                                              -------   ------
                                                                 (372)    (985)
                                                              -------   ------
Net income (loss) before income taxes.......................       69     (929)
Income tax (expense) benefit................................   (4,964)     314
                                                              -------   ------
  Net loss..................................................  $(4,895)  $ (615)
                                                              =======   ======
Net loss per share:
  Basic/Diluted.............................................  $ (0.55)  $(0.05)
Weighted average common shares outstanding:
  Basic/Diluted.............................................    8,929   12,254
</TABLE>
 
   See accompanying notes to the condensed consolidated financial statements.
 
                                      F-21
<PAGE>   88
 
                          BRIGHAM EXPLORATION COMPANY
 
                             CONDENSED CONSOLIDATED
                            STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                 THREE          THREE
                                                              MONTHS ENDED   MONTHS ENDED
                                                               MARCH 31,      MARCH 31,
                                                                  1997           1998
                                                              ------------   ------------
<S>                                                           <C>            <C>
Cash flows from operating activities:
  Net loss..................................................    $(4,895)       $   (615)
  Adjustments to reconcile net loss to cash provided by
     operating activities:
     Depletion of natural gas and oil properties............        687           1,267
     Depreciation and amortization..........................        108              83
     Amortization of stock compensation.....................         29              95
     Amortization of deferred loan fees.....................         --             106
     Changes in deferred income tax liability...............      4,964            (314)
     Changes in working capital and other items.............      3,331          (3,418)
                                                                -------        --------
          Net cash provided (used) by operating
            activities......................................      4,224          (2,796)
                                                                -------        --------
Cash flows from investing activities:
  Additions to natural gas and oil properties...............     (6,830)        (12,993)
  Additions to other property and equipment.................        (33)           (159)
  (Increase) decrease in drilling advances paid.............       (321)             16
  Increase in exploration advances paid.....................       (117)             --
                                                                -------        --------
       Net cash used by investing activities................     (7,301)        (13,136)
                                                                -------        --------
Cash flows from financing activities:
  Increase in notes payable.................................      2,850          52,800
  Repayment of notes payable................................         --         (34,800)
  Principal payments on capital lease obligations...........        (56)            (58)
  Deferred loan fees........................................         --          (1,911)
                                                                -------        --------
       Net cash provided by financing activities............      2,794          16,031
                                                                -------        --------
Net (decrease) increase in cash and cash equivalents........       (283)             99
Cash and cash equivalents, beginning of period..............      1,447           1,701
                                                                -------        --------
Cash and cash equivalents, end of period....................    $ 1,164        $  1,800
                                                                =======        ========
</TABLE>
 
   See accompanying notes to the condensed consolidated financial statements.
 
                                      F-22
<PAGE>   89
 
                          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 March 31, 1998 reflect the consolidated accounts of the Company. The
unaudited condensed consolidated statements of operations and of cash flows for
the three months ended March 31, 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 March 31, 1997 and for the three months ended March
31, 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.
 
3. NOTES PAYABLE
 
     In January 1998, the Company entered into a new reserve based revolving
credit facility (the "Credit Facility"). The Credit Facility provides for
borrowings up to $75 million, all of which is immediately available for
borrowing to fund capital expenditures, until January 31, 1999, at which time
the borrowing availability
 
                                      F-23
<PAGE>   90
                          BRIGHAM EXPLORATION COMPANY
 
                      NOTES TO THE CONDENSED CONSOLIDATED
                      FINANCIAL STATEMENTS -- (CONTINUED)
 
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 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 three months ended March 31, 1997 is
based on shares of common stock issued upon consummation of the Exchange (Note
1). At March 31, 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.
 
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
 
                                      F-24
<PAGE>   91
                          BRIGHAM EXPLORATION COMPANY
 
                      NOTES TO THE CONDENSED CONSOLIDATED
                      FINANCIAL STATEMENTS -- (CONTINUED)
 
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.
 
                                      F-25
<PAGE>   92
 
                                  May 26, 1998
 
Brigham Exploration Company
6300 Bridge Point Parkway
Building Two, Suite 500
Austin, Texas 78730
 
Re:     Evaluation
       BRIGHAM EXPLORATION COMPANY
       Proved Reserves
       As of December 31, 1997
 
       Pursuant to the Guidelines of the Securities
       and Exchange Commission for Reporting
       Corporate Reserves and Future Net Revenue
 
Gentlemen:
 
     As requested, we are submitting our estimated proven reserves and future
net cash flows, as of December 31, 1997, attributable to the interest of Brigham
Exploration Company in certain natural gas and oil properties. The evaluated
properties are located in various counties in Kansas, New Mexico, Oklahoma and
Texas. This report was prepared using constant prices and costs and conforms to
the guidelines of the Securities and Exchange Commission (SEC).
 
     Composite forecasts for the total proved, proved developed producing,
proved developed non-producing and proved undeveloped estimates are presented by
category in Tables I-P, I-PDP, I-PDNP and I-PUD, respectively. The proved
reserves and economics for all three groups are summarized as follows:
 
<TABLE>
<CAPTION>
                                         NET RESERVES             FUTURE NET CASH FLOW
                                    -----------------------   ----------------------------
                                       OIL          GAS                      PRESENT WORTH
CATEGORY                            (BARRELS)      (MCF)         TOTAL          AT 10%
--------                            ---------   -----------   ------------   -------------
<S>                                 <C>         <C>           <C>            <C>
Proved Developed:
  Producing......................   2,146,422    26,002,050   $ 67,895,820    $44,240,260
  Non-Producing..................     518,606     4,674,717     14,544,070      3,980,896
Proved Undeveloped...............     516,290    22,552,930     41,783,310     21,028,250
                                    ---------   -----------   ------------    -----------
     Total Proved................   3,181,318    53,229,700   $124,233,200    $69,249,406
                                    =========   ===========   ============    ===========
</TABLE>
 
     Future revenue is prior to deducting state production taxes and ad valorem
taxes. Future net cash flow is after deducting these taxes, future capital costs
and operating expenses, but before consideration of federal income taxes. In
accordance with SEC guidelines, the future net cash flow has been discounted at
an annual rate of ten percent to determine its "present worth". The present
worth is shown to indicate the effect of time on the value of money and should
not be construed as being the fair market value of the properties.
 
     The oil reserves include oil and condensate. Oil volumes are expressed in
barrels (42 U.S. gallons). Gas volumes are expressed in thousands of standard
cubic feet (Mcf) at contract temperature and pressure base.
 
     Our estimates are for proved reserves only and do not include any probable
or possible reserves nor have any values been attributed to interest in acreage
beyond the location for which undeveloped reserves have been estimated.
 
     Oil and gas prices being received at December 31, 1997 were utilized as
furnished. Direct lease operating expenses are based on 1996 and 1997 historical
data and do not include general and administrative overhead. Investments are
capital costs for pumping unit installations, work-overs and drilling costs and
were utilized as furnished. All economic factors were held constant in
accordance with SEC guidelines.
 
     An on-site field inspection of the properties has not been performed nor
have the mechanical operation or condition of the wells and their related
facilities been examined nor have the wells been tested by Cawley, Gillespie &
Associates, Inc. Possible environmental liability related to the properties has
not been investigated
 
                                       A-1
<PAGE>   93
 
nor considered. The cost of plugging and the salvage value of equipment at
abandonment have not been included.
 
     The reserve classifications and the economic considerations used herein
conform to the criteria of the Securities and Exchange Commission. The reserves
and economics are predicated on regulatory agency classifications, rules,
policies, laws, taxes and royalties currently in effect except as noted herein.
The possible effects of changes in legislation or other Federal or State
restrictive actions which could affect the reserves and economics have not been
considered.
 
     The proved reserve estimates and forecasts were based upon interpretations
of data furnished by your office and available from our files. All estimates
represent our best judgment based on the data available at the time of
preparation. It should be realized that the reserve estimates, the reserves
actually recovered, the revenue derived therefrom and the actual cost incurred
could be more or less than the estimated amounts. Additionally, the prices and
costs may vary from those utilized which may increase or decrease both the
volume and future net revenue.
 
     Ownership was accepted as furnished and has not been independently
confirmed. We are independent registered professional engineers and geologists.
We do not own an interest in the properties or Brigham Exploration Company and
are not employed on a contingent basis. Our work-papers and related data
utilized in the preparation of these estimates are available in our office.
 
                                            Yours very truly,
 
                                            Cawley, Gillespie & Associates, Inc.
 
                                                    /s/ AARON CAWLEY
 
                                            ------------------------------------
                                                     Aaron Cawley, P.E.
                                                  Executive Vice President
AC:rkf
 
                                       A-2
<PAGE>   94
 
======================================================
 
    NO DEALER, SALESPERSON OR OTHER PERSON HAS BEEN AUTHORIZED TO GIVE ANY
INFORMATION OR TO MAKE ANY REPRESENTATIONS OTHER THAN THOSE CONTAINED IN THIS
PROSPECTUS IN CONNECTION WITH THE OFFER MADE BY THIS PROSPECTUS AND, IF GIVEN OR
MADE, SUCH INFORMATION OR REPRESENTATIONS MUST NOT BE RELIED UPON AS HAVING BEEN
AUTHORIZED BY THE COMPANY OR ANY OF THE UNDERWRITERS. THIS PROSPECTUS DOES NOT
CONSTITUTE AN OFFER TO SELL OR THE SOLICITATION OF ANY OFFER TO BUY ANY
SECURITIES OTHER THAN THE SHARES OF COMMON STOCK OFFERED BY THIS PROSPECTUS, NOR
DOES IT CONSTITUTE AN OFFER TO SELL OR A SOLICITATION OF ANY OFFER TO BUY THE
SHARES OF COMMON STOCK BY ANYONE IN ANY JURISDICTION IN WHICH SUCH OFFER OR
SOLICITATION IS NOT AUTHORIZED, OR IN WHICH THE PERSON MAKING SUCH OFFER OR
SOLICITATION IS NOT QUALIFIED TO DO SO, OR TO ANY PERSON TO WHOM IT IS UNLAWFUL
TO MAKE SUCH OFFER OR SOLICITATION. NEITHER THE DELIVERY OF THIS PROSPECTUS NOR
ANY SALE MADE HEREUNDER SHALL, UNDER ANY CIRCUMSTANCES, CREATE ANY IMPLICATION
THAT THE INFORMATION CONTAINED HEREIN IS CORRECT AS OF ANY TIME SUBSEQUENT TO
THE DATE HEREOF.
 
                             ---------------------
 
                               TABLE OF CONTENTS
 
<TABLE>
<CAPTION>
                                            PAGE
                                            ----
<S>                                         <C>
Prospectus Summary........................
Disclosure Regarding Forward-Looking
  Statements..............................
Risk Factors..............................
The Company...............................
Use of Proceeds...........................
Price Range of Common Stock and Dividend
  Policy..................................
Capitalization............................
Selected Financial Data...................
Management's Discussion and Analysis of
  Financial Condition and Results of
  Operations..............................
Business and Properties...................
Management................................
Certain Transactions......................
Principal and Selling Stockholders........
Description of Capital Stock..............
Shares Eligible for Future Sale...........
Underwriting..............................
Legal Matters.............................
Experts...................................
Additional Information....................
Glossary of Certain Oil and Gas Terms.....
Index to Financial Statements.............  F-1
Letter of Cawley, Gillespie & Associates,
  Inc.....................................  A-1
</TABLE>
 
                             ---------------------
    UNTIL , 1998 (25 DAYS AFTER THE DATE OF THIS PROSPECTUS), ALL DEALERS
EFFECTING TRANSACTIONS IN THE SHARES OF THE COMMON STOCK, WHETHER OR NOT
PARTICIPATING IN THIS DISTRIBUTION, MAY BE REQUIRED TO DELIVER A PROSPECTUS.
THIS IS IN ADDITION TO THE OBLIGATION OF DEALERS TO DELIVER A PROSPECTUS WHEN
ACTING AS UNDERWRITERS AND WITH RESPECT TO THEIR UNSOLD ALLOTMENTS OR
SUBSCRIPTIONS.
======================================================
======================================================
 
                                           SHARES
 
                                     [LOGO]
 
                                  COMMON STOCK
                                ----------------
 
                                   PROSPECTUS
                                ----------------
 
                            BEAR, STEARNS & CO. INC.
 
                             DAIN RAUSCHER WESSELS
                    A DIVISION OF DAIN RAUSCHER INCORPORATED
 
                      HOWARD, WEIL, LABOUISSE, FRIEDRICHS
                                  INCORPORATED
                                            , 1998
 
======================================================
<PAGE>   95
 
                                    PART II
 
                     INFORMATION NOT REQUIRED IN PROSPECTUS
 
ITEM 13. OTHER EXPENSES OF ISSUANCE AND DISTRIBUTION
 
     The estimated expenses payable by Brigham Exploration Company (the
"Registrant" or the "Company") in connection with the registration of the
securities offered hereby, other than underwriting discounts and commissions,
are as follows:
 
<TABLE>
<S>                                                           <C>
SEC Registration Fee........................................  $13,940
NASD Filing Fee.............................................  $ 5,100
Nasdaq National Market Listing Fee..........................        *
Blue Sky Qualification Fees and Expenses....................        *
Accounting Fees and Expenses................................        *
Legal Fees and Expenses.....................................        *
Engineering Fees and Expenses...............................        *
Transfer Agent and Registrar Fees...........................        *
Printing and Engraving Expenses.............................        *
Miscellaneous...............................................        *
                                                              -------
          Total.............................................  $     *
                                                              =======
</TABLE>
 
---------------
 
* To be provided by amendment.
 
ITEM 14. INDEMNIFICATION OF DIRECTORS AND OFFICERS
 
     In accordance with Section 102(b)(7) of the Delaware General Corporation
Law ("DGCL"), the Company's Certificate of Incorporation includes a provision
that, to the fullest extent permitted by law, eliminates the personal liability
of members of its Board of Directors to the Company or its stockholders for
monetary damages for breach of fiduciary duty as a director. Such provision does
not eliminate or limit the liability of a director (1) for any breach of a
director's duty of loyalty to the Company or its stockholders, (2) for acts or
omissions not in good faith or which involve intentional misconduct or a knowing
violation of a law, (3) for paying an unlawful dividend or approving an illegal
stock repurchase (as provided in Section 174 of the DGCL) or (4) for any
transaction from which the director derived an improper personal benefit.
 
     Under Section 145 of the DGCL, the Registrant has the power to indemnify
any person who was or is a party or is threatened to be made a party to any
threatened, pending or completed action, suit or proceeding (other than an
action by or in the right of the corporation) by reason of the fact that the
person is or was a director, officer, employee or agent of any corporation,
partnership, joint venture, trust or other enterprise, reasonably incurred in
connection with such action, suit or proceeding. The power to indemnify applies
only if the person acted in good faith and in a manner the person reasonably
believed to be in or not opposed to the best interests of the corporation, and
with respect to any criminal action or proceeding, had no reasonable cause to
believe the person's conduct was unlawful.
 
     In the case of an action by or in the right of the Registrant, no
indemnification may be made with respect to any claim, issue or matter as to
which such person shall have been adjudged to be liable to the Registrant unless
and only to the extent that the court of chancery or the court in which such
action or suit was brought shall determine that despite the adjudication of
liability such person is fairly and reasonably entitled to indemnity for such
expenses which the court shall deem proper. Section 145 of the DGCL further
provides that to the extent a director or officer of the Registrant has been
successful in the defense of any action, suit or proceeding referred to above or
in the defense of any claim, issue or matter therein, that person shall be
indemnified against expenses (including attorney's fees) actually and reasonably
incurred in connection therewith.
 
                                      II-1
<PAGE>   96
 
     The Registrant also has the power to purchase and maintain insurance on
behalf of any person covering any liability incurred in that person's capacity
as a director, officer, employee or agent of the corporation, or arising out of
that person's status as such, whether or not the corporation would have the
power to indemnify against the liability.
 
     The Certificate of Incorporation and Bylaws provide that the Registrant
will indemnify its officers and directors and former officers and directors
against any expenses, judgments or settlement payments sustained or paid by such
persons as a result of having acted as an officer or director of the Registrant,
or, at the request of the Registrant, as an officer, director, agent or employee
of another business entity. The Certificate of Incorporation and Bylaws further
provide that the Registrant may, by action of its Board of Directors, provide
indemnification to employees and agents of the Registrant, individually or as a
group, with the same scope and effect as the indemnification of directors and
officers.
 
     The form of Indemnity Agreement contained in Exhibit 10.24 provides for the
indemnification in certain instances against liability and expenses incurred in
connection with proceedings brought by or in the right of the Company or by
third parties by reason of a person serving as an officer or director of the
Company.
 
     The form of Underwriting Agreement contained in Exhibit 1 provides for
indemnification of the directors and officers signing the Registration Statement
and certain controlling persons of the Company against certain liabilities
(including certain liabilities under the Securities Act of 1933 (the "Securities
Act")) in certain instances by the Underwriters.
 
ITEM 15. RECENT SALES OF UNREGISTERED SECURITIES
 
     The following information relates to all securities issued or sold by the
Registrant since inception and not registered under the Securities Act.
 
     Unless otherwise specifically provided, each of the transactions described
below was conducted in reliance upon the exemption from registration provided in
Section 4(2) of the Securities Act and the rules and regulations promulgated
thereunder. Furthermore, each of the certificates representing the Registrant's
securities issued in connection with such transactions contains a restrictive
legend, as appropriate, requiring each person acquiring such securities from the
Registrant to furnish investment representations to the Registrant and stating
that no underwriters participated in such transactions.
 
     The Registrant was formed on February 25, 1997. On February 26, 1997, the
Company sold three shares of the Registrant's Common Stock to Ben M. Brigham,
President of the Company. Pursuant to the terms of an Agreement and Plan of
Reorganization dated February 26, 1997 (the "Exchange Agreement") the Company
became the holding company for Brigham Oil & Gas, L.P., which conducts the
Registrant's operations and was formed in May 1992 (the "Partnership"). Pursuant
to the terms of the Exchange Agreement, the limited partners of the Partnership
received 634,868 shares of the Registrant's common stock. In addition, the
general partners or their stockholders received 6,539,239 shares of the
Registrant's common stock for each share of common stock of the general partner
owned by such stockholder. Each certificate issued in connection with such
exchange contained an appropriate restrictive legend.
 
     In August 1995, the Registrant issued $16 million principal amount of its
5% convertible subordinated notes (the "Notes") to Resource Investment
Management Company. Immediately after the consummation of the exchange described
above, RIMCO converted the Notes into 1,759,464 shares of the Registrant's
common stock. Each certificate issued in connection with that conversion
contained an appropriate restrictive legend.
 
     The Registrant and its predecessor have granted options that remain
outstanding to purchase an aggregate of 935,987 shares of Common Stock, subject
to vesting, and issued 156,250 shares of restricted stock to officers and key
employees.
 
                                      II-2
<PAGE>   97
 
ITEM 16. EXHIBITS AND FINANCIAL STATEMENT SCHEDULES
 
     (a) Exhibits:
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
          1++            -- Form of Underwriting Agreement
          2.1            -- Exchange Agreement (filed as Exhibit 2.1 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
          3.1            -- Certificate of Incorporation (filed as Exhibit 3.1 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
          3.2            -- Bylaws (filed as Exhibit 3.2 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
          4.1            -- Form of Common Stock Certificate (filed as Exhibit 4.1 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
          5++            -- Opinion of Thompson & Knight, A Professional Corporation
         10.1            -- Agreement of Limited Partnership, dated May 1, 1992,
                            between Brigham Exploration Company and General Atlantic
                            Partners III, L.P. as general partners, and Harold D.
                            Carter and GAP-Brigham Partners, L.P. as limited partners
                            (filed as Exhibit 10.1 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.1.1          -- Amendment No. 1 to Agreement of Limited Partnership of
                            Brigham Oil & Gas, L.P., dated May 1, 1992, by and among
                            Brigham Exploration Company, General Atlantic Partners
                            III, L.P., GAP-Brigham Partners, L.P. and Harold D.
                            Carter (filed as Exhibit 10.1.1 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.1.2          -- Amendment No. 2 to Agreement of Limited Partnership of
                            Brigham Oil & Gas, L.P., dated September 30, 1994, by and
                            among Brigham Exploration Company, General Atlantic
                            Partners III, L.P., GAP-Brigham Partners, L.P., Harold D.
                            Carter and the additional signatories thereto (filed as
                            Exhibit 10.1.2 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
         10.1.3          -- Amendment No. 3 to Agreement of Limited Partnership of
                            Brigham Oil & Gas, L.P., dated August 24, 1995, by and
                            among Brigham Exploration Company, General Atlantic
                            Partners III, L.P., GAP-Brigham Partners, L.P., Harold D.
                            Carter, Craig M. Fleming, David T. Brigham and Jon L.
                            Glass (filed as Exhibit 10.1.3 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.1.4++        -- Amended and Restated Agreement of Limited Partnership of
                            Brigham Oil & Gas, L.P., dated December 30, 1997 by and
                            among Brigham, Inc., Brigham Holdings I, L.L.C. and
                            Brigham Holdings II, L.L.C.
         10.2            -- Agreement of Limited Partnership of Venture Acquisitions,
                            L.P., dated September 23, 1994, by and between Quest
                            Resources, L.L.C. and RIMCO Energy, Inc. as general
                            partners, and RIMCO Production Company, Inc., RIMCO
                            Exploration Partners, L.P. I and RIMCO Exploration
                            Partners, L.P. II, as limited partners (filed as Exhibit
                            10.2 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
</TABLE>
 
                                      II-3
<PAGE>   98
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         10.3            -- Regulations of Quest Resources, L.L.C. (filed as Exhibit
                            10.3 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.4            -- Management and Ownership Agreement, dated September 23,
                            1994, by and among Brigham Oil & Gas, L.P., Brigham
                            Exploration Company, General Atlantic Partners III, L.P.,
                            Harold D. Carter, Ben M. Brigham and GAP-Brigham
                            Partners, L.P. (filed as Exhibit 10.4 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.5*++         -- Consulting Agreement, dated May 1, 1997, by and between
                            Brigham Oil & Gas, L.P. and Harold D. Carter.
         10.6*           -- Employment Agreement, by and between Brigham Exploration
                            Company and Ben M. Brigham (filed as Exhibit 10.7 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.7*           -- Form of Confidentiality and Noncompete Agreement between
                            the Registrant and each of its executive officers (filed
                            as Exhibit 10.8 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.8*           -- 1997 Incentive Plan of Brigham Exploration Company (filed
                            as Exhibit 10.9 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.8.1*         -- Form of Option Agreement for certain executive officers
                            (filed as Exhibit 10.9.1 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.8.2*         -- Option Agreement dated as of March 4, 1997, by and
                            between Brigham Exploration Company and Jon L. Glass
                            (filed as Exhibit 10.9.2 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.9*           -- Incentive Bonus Plan dated as of February 28, 1997 of
                            Brigham, Inc. and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.10 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
         10.10.1++       -- First Amendment to Two Bridge Point Lease Agreement dated
                            April 11, 1997 between Investors Life Insurance Company
                            of North America and Brigham Oil & Gas, L.P.
         10.10.2++       -- Second Amendment to Two Bridge Point Lease Agreement
                            dated October 13, 1997 between Investors Life Insurance
                            Company of North America and Brigham Oil & Gas, L.P.
         10.10.3++       -- Letter dated April 17, 1998 exercising Right of First
                            Refusal to Lease "3rd Option Space."
         10.10           -- Two Bridge Point Lease Agreement, dated September 30,
                            1996, by and between Investors Life Insurance Company of
                            North America and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.14 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
         10.11           -- Anadarko Basin Seismic Operations Agreement, dated
                            February 15, 1996, by and between Brigham Oil & Gas, L.P.
                            and Veritas Geophysical, Ltd. (filed as Exhibit 10.15 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
</TABLE>
 
                                      II-4
<PAGE>   99
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         10.11.1         -- Letter Amendment to Anadarko Basin Seismic Operations
                            Agreement, dated June 10, 1996, between Brigham Oil &
                            Gas, L.P. and Veritas Geophysical, Ltd. (filed as Exhibit
                            10.15.1 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
         10.12           -- Expense Allocation and Participation Agreement, dated
                            April 1, 1996, between Brigham Oil & Gas, L.P. and Gasco
                            Limited Partnership. (filed as Exhibit 10.16 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.12.1         -- Amendment to Expense Allocation and Participation
                            Agreement, dated October 21, 1996, between Brigham Oil &
                            Gas, L.P. and Gasco Limited Partnership (filed as Exhibit
                            10.16.1 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
         10.13           -- Expense Allocation and Participation Agreement, dated
                            April 1, 1996, between Brigham Oil & Gas, L.P. and Middle
                            Bay Oil Company, Inc. (filed as Exhibit 10.17 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.13.1         -- Amendment to Expense Allocation and Participation
                            Agreement, dated September 26, 1996, between Brigham Oil
                            & Gas, L.P. and Middle Bay Oil Company, Inc. (filed as
                            Exhibit 10.17.1 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.13.2         -- Letter Amendment to Expense Allocation and Participation
                            Agreement, dated May 20, 1996, between Brigham Oil & Gas,
                            L.P. and Middle Bay Oil Company, Inc. (filed as Exhibit
                            10.17.2 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
         10.14           -- Anadarko Basin Joint Participation Agreement, dated May
                            1, 1996, by and among Stephens Production Company and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.18 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.15           -- Anadarko Basin Joint Participation Agreement, dated May
                            1, 1996, by and between Vintage Petroleum, Inc. and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.19 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.16           -- Processing Alliance Agreement, dated July 20, 1993,
                            between Veritas Seismic Ltd. and Brigham Oil & Gas, L.P.
                            (filed as Exhibit 10.20 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333- 22491), and
                            incorporated herein by reference).
         10.16.1         -- Letter Amendment to Processing Alliance Agreement, dated
                            November 3, 1994, between Veritas Seismic Ltd. and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.20.1 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.17           -- Agreement and Assignment of Interest, West Bradley
                            Project, dated September 1, 1995, by and between Aspect
                            Resources Limited Liability Company and Brigham Oil &
                            Gas, L.P. (filed as Exhibit 10.21 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
</TABLE>
 
                                      II-5
<PAGE>   100
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         10.18           -- Agreement and Assignment of Interests in lands located in
                            Grady County, Oklahoma, West Bradley Project, dated
                            December 1, 1995, by and between Aspect Resources Limited
                            Liability Company, Brigham Oil & Gas, L.P. and Venture
                            Acquisitions, L.P. (filed as Exhibit 10.22 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.19           -- Agreement and Assignment of Interests, West Bradley
                            Project, dated December 1, 1995, by and between Aspect
                            Resources Limited Liability Company and Brigham Oil &
                            Gas, L.P. (filed as Exhibit 10.23 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.20           -- Geophysical Exploration Agreement, Hardeman Project,
                            Hardeman and Wilbarger Counties, Texas and Jackson
                            County, Oklahoma, dated March 15, 1993 by and among
                            General Atlantic Resources, Inc., Maynard Oil Company,
                            Ruja Muta Corporation, Tucker Scully Interests Ltd., JHJ
                            Exploration, Ltd., Cheyenne Petroleum Company, Antrim
                            Resources, Inc., and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.24 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
         10.21           -- Agreement and Partial Assignment of Interests in OK13-P
                            Prospect Area, Jackson County, Oklahoma (Hardeman
                            Project), dated August 1, 1995, by and between Brigham
                            Oil & Gas, L.P. and Aspect Resources Limited Liability
                            Company (filed as Exhibit 10.25 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.22           -- Agreement and Partial Assignment of Interests in Q140-E
                            Prospect Area, Hardeman County, Texas (Hardeman Project),
                            dated August 1, 1995, by and between Brigham Oil & Gas,
                            L.P. and Aspect Resources Limited Liability Company
                            (filed as Exhibit 10.26 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.23           -- Agreement and Partial Assignment of Interests in Hankins
                            #1 Chappel Prospect Agreement, Jackson County, Oklahoma
                            (Hardeman Project), dated March 21, 1996, by and between
                            Brigham Oil & Gas, L.P., NGR, Ltd. and Aspect Resources
                            Limited Liability Company (filed as Exhibit 10.27 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.24           -- Form of Indemnity Agreement between the Registrant and
                            each of its executive officers (filed as Exhibit 10.28 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.25           -- Registration Rights Agreement dated February 26, 1997 by
                            and among Brigham Exploration Company, General Atlantic
                            Partners III L.P., GAP-Brigham Partners, L.P., RIMCO
                            Partners, L.P. II, RIMCO Partners L.P. III, and RIMCO
                            Partners, L.P. IV, Ben M. Brigham, Anne L. Brigham,
                            Harold D. Carter, Craig M. Fleming, David T. Brigham and
                            Jon L. Glass (filed as Exhibit 10.29 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.26           -- 1997 Director Stock Option Plan (filed as Exhibit 10.30
                            to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.27           -- Form of Employee Stock Ownership Agreement (filed as
                            Exhibit 10.31 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
</TABLE>
 
                                      II-6
<PAGE>   101
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         10.28           -- Agreement and Assignment of Interest in Geophysical
                            Exploration Agreement, Esperson Dome Project, dated
                            November 1, 1994, by and between Brigham Oil & Gas, L.P.
                            and Vaquero Gas Company (filed as Exhibit 10.33 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.29           -- Geophysical Exploration Agreement, Southwest Danbury
                            Project, Brazoria County, Texas, dated as of July 1,
                            1996, by and among UNEXCO, Inc. and Brigham Oil & Gas,
                            L.P. (filed as Exhibit 10.34 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.30           -- Geophysical Exploration Agreement, Welder Project, Duval
                            County, Texas, dated as of October 1, 1996, by and among
                            UNEXCO, Inc. and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.35 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
         10.31           -- Proposed Trade Structure, RIMCO/Tigre Project, Vermillion
                            Parish, Louisiana, among Brigham Oil & Gas, L.P., Tigre
                            Energy Corporation and Resource Investors Management
                            Company (filed as Exhibit 10.36.1 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.31.1         -- Letter relating to Proposed Trade Structure, RIMCO/Tigre
                            Project, dated January 31, 1997, from Resource Investors
                            Management Company to Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.36.1 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.32           -- Anadarko Basin Seismic Operations Agreement II, dated as
                            of April 1, 1997, by and between Brigham Oil & Gas, L.P.
                            (filed as Exhibit 10.37 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.32.1         -- Letter Amendment to Anadarko Basin Seismic Operations
                            Agreement II, dated March 20, 1997, between Brigham Oil &
                            Gas, L.P. and Veritas DGC Land, Inc. (filed as Exhibit
                            10.37 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.33           -- Expense Allocation and Participation Agreement II, dated
                            April 1, 1997, between Brigham Oil & Gas, L.P., and Gasco
                            Limited Partnership (filed as Exhibit 10.31 to the
                            Company's Quarterly Report on Form 10-Q for the quarter
                            ended June 30, 1997, and incorporated herein by
                            reference).
         10.34           -- Credit Agreement dated as of January 26, 1998 among
                            Brigham Oil & Gas, L.P., Bank of Montreal, as Agent, and
                            the lenders signatory thereto (filed as Exhibit 10.36 to
                            the Company's Annual Report on Form 10-K for the year
                            ended December 31, 1997, and incorporated herein by
                            reference).
         10.34.1+        -- Guaranty Agreement dated January 26, 1998 by Brigham
                            Exploration Company in favor of Bank of Montreal, as
                            Agent, and each of the Lenders party to the Credit
                            Agreement.
         10.34.2++       -- First Amendment to Guaranty Agreement dated as of March
                            30, 1998 between Brigham Exploration Company and Bank of
                            Montreal, as agent for the Lenders party to the Credit
                            Agreement.
</TABLE>
 
                                      II-7
<PAGE>   102
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         21++            -- Subsidiaries of the Registrant.
         23.1++          -- Consent of Thompson & Knight, A Professional Corporation
                            (included in Exhibit 5 above).
         23.2+           -- Consent of Price Waterhouse LLP, independent public
                            accountants.
         23.3+           -- Consent of Cawley, Gillespie & Associates, Inc.,
                            independent petroleum engineers.
         24.1+           -- Powers of Attorney (included on the first signature page
                            to this Registration Statement).
</TABLE>
 
---------------
 
*    Management contract or compensatory plan.
 
++   To be filed by amendment.
 
+    Filed herewith.
 
     (b) Financial Statement Schedules: None.
 
ITEM 17. UNDERTAKINGS
 
     The undersigned Registrant hereby undertakes to provide to the Underwriters
at the closing specified in the Underwriting Agreements, certificates in such
denominations and registered in such names as required by the particular
Underwriter, to permit prompt delivery to each purchaser.
 
     The undersigned Registrant also hereby undertakes that:
 
          (1) For purposes of determining any liability under the Securities
     Act, the information omitted from the form of prospectus filed as part of
     this Registration Statement in reliance upon Rule 430A and contained in a
     form of prospectus filed by the registrant pursuant to Rule 424(b)(1) or
     (4) or 497(h) under the Securities Act shall be deemed to be part of this
     Registration Statement as of the time it was declared effective.
 
          (2) For the purpose of determining any liability under the Securities
     Act, each post-effective amendment that contains a form of prospectus shall
     be deemed to be a new registration statement relating to the securities
     offered therein, and the offering of such securities at that time shall be
     deemed to be the initial bona fide offering thereof.
 
     Insofar as indemnification for liabilities arising under the Securities Act
may be permitted to directors, officers and controlling persons of the
Registrant pursuant to the foregoing provisions, or otherwise, the registrant
has been advised that in the opinion of the Securities and Exchange Commission
such indemnification is against public policy as expressed in the Securities Act
and is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by the registrant of expenses
incurred or paid by a director, officer or controlling person of the registrant
in the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of such issue.
 
                                      II-8
<PAGE>   103
 
                                   SIGNATURES
 
     Pursuant to the requirements of the Securities Act of 1933, Brigham
Exploration Company has duly caused this Registration Statement to be signed on
its behalf by the undersigned, thereunto duly authorized, in Austin, Texas, on
May 28, 1998.
 
                                            BRIGHAM EXPLORATION COMPANY
 
                                            By:     /s/ BEN M. BRIGHAM
                                               ---------------------------------
                                                        Ben M. Brigham
                                              President, Chief Executive Officer
                                                              and
                                                    Chairman of the Board
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned directors and officers
of Brigham Exploration Company, a Delaware corporation, which is filing a
Registration Statement on Form S-1 with the Securities and Exchange Commission,
Washington, D.C. 20549 under the provisions of the Securities Act of 1933, as
amended (the "Securities Act"), hereby constitute and appoint Ben M. Brigham and
Craig M. Fleming, and each of them, the individual's true and lawful
attorneys-in-fact and agents, with full power of substitution and
resubstitution, for the person and in his or her name, place and stead, in any
and all capacities, to sign such Registration Statement and any or all
amendments, including post-effective amendments, to the Registration Statement,
including a Prospectus or an amended Prospectus therein and any registration
statement for the same offering that is to be effective upon filing pursuant to
Rule 462(b) under the Securities Act, and all other documents in connection
therewith to be filed with the Securities and Exchange Commission, granting unto
said attorneys-in-fact and agents, and each of them, full power and authority to
do and perform each and every act and thing requisite and necessary to be done
in and about the premises, as fully to all intents and purposes as he might or
could do in person, hereby ratifying and confirming all that said
attorneys-in-fact as agents or any of them, or their substitute or substitutes,
may lawfully do or cause to be done by virtue hereof.
 
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.
 
<TABLE>
<CAPTION>
                      SIGNATURE                                      TITLE                    DATE
                      ---------                                      -----                    ----
<C>                                                    <S>                                <C>
 
                 /s/ BEN M. BRIGHAM                    President, Chief Executive         May 28, 1998
-----------------------------------------------------  Officer and Chairman of the Board
                   Ben M. Brigham                      (principal executive officer)
 
                 /s/ ANNE L. BRIGHAM                   Executive Vice President and       May 28, 1998
-----------------------------------------------------  Director
                   Anne L. Brigham
 
                /s/ CRAIG M. FLEMING                   Chief Financial Officer            May 28, 1998
-----------------------------------------------------  (principal financial and
                  Craig M. Fleming                     accounting officer)
 
                  /s/ JON L. GLASS                     Vice President -- Exploration and  May 28, 1998
-----------------------------------------------------  Director
                    Jon L. Glass
</TABLE>
 
                                      II-9
<PAGE>   104
 
<TABLE>
<CAPTION>
                      SIGNATURE                                      TITLE                    DATE
                      ---------                                      -----                    ----
<C>                                                    <S>                                <C>
 
                /s/ HAROLD D. CARTER                   Director                           May 28, 1998
-----------------------------------------------------
                  Harold D. Carter
 
                 /s/ GARY J. MILAVEC                   Director                           May 28, 1998
-----------------------------------------------------
                   Gary J. Milavec
 
               /s/ ALEXIS M. CRANBERG                  Director                           May 28, 1998
-----------------------------------------------------
                 Alexis M. Cranberg
 
               /s/ STEPHEN P. REYNOLDS                 Director                           May 28, 1998
-----------------------------------------------------
                 Stephen P. Reynolds
</TABLE>
 
                                      II-10
<PAGE>   105
 
                               INDEX TO EXHIBITS
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
          1++            -- Form of Underwriting Agreement
          2.1            -- Exchange Agreement (filed as Exhibit 2.1 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
          3.1            -- Certificate of Incorporation (filed as Exhibit 3.1 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
          3.2            -- Bylaws (filed as Exhibit 3.2 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
          4.1            -- Form of Common Stock Certificate (filed as Exhibit 4.1 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
          5++            -- Opinion of Thompson & Knight, A Professional Corporation
         10.1            -- Agreement of Limited Partnership, dated May 1, 1992,
                            between Brigham Exploration Company and General Atlantic
                            Partners III, L.P. as general partners, and Harold D.
                            Carter and GAP-Brigham Partners, L.P. as limited partners
                            (filed as Exhibit 10.1 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.1.1          -- Amendment No. 1 to Agreement of Limited Partnership of
                            Brigham Oil & Gas, L.P., dated May 1, 1992, by and among
                            Brigham Exploration Company, General Atlantic Partners
                            III, L.P., GAP-Brigham Partners, L.P. and Harold D.
                            Carter (filed as Exhibit 10.1.1 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.1.2          -- Amendment No. 2 to Agreement of Limited Partnership of
                            Brigham Oil & Gas, L.P., dated September 30, 1994, by and
                            among Brigham Exploration Company, General Atlantic
                            Partners III, L.P., GAP-Brigham Partners, L.P., Harold D.
                            Carter and the additional signatories thereto (filed as
                            Exhibit 10.1.2 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
         10.1.3          -- Amendment No. 3 to Agreement of Limited Partnership of
                            Brigham Oil & Gas, L.P., dated August 24, 1995, by and
                            among Brigham Exploration Company, General Atlantic
                            Partners III, L.P., GAP-Brigham Partners, L.P., Harold D.
                            Carter, Craig M. Fleming, David T. Brigham and Jon L.
                            Glass (filed as Exhibit 10.1.3 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.1.4++        -- Amended and Restated Agreement of Limited Partnership of
                            Brigham Oil & Gas, L.P., dated December 30, 1997 by and
                            among Brigham, Inc., Brigham Holdings I, L.L.C. and
                            Brigham Holdings II, L.L.C.
         10.2            -- Agreement of Limited Partnership of Venture Acquisitions,
                            L.P., dated September 23, 1994, by and between Quest
                            Resources, L.L.C. and RIMCO Energy, Inc. as general
                            partners, and RIMCO Production Company, Inc., RIMCO
                            Exploration Partners, L.P. I and RIMCO Exploration
                            Partners, L.P. II, as limited partners (filed as Exhibit
                            10.2 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
</TABLE>
<PAGE>   106
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         10.3            -- Regulations of Quest Resources, L.L.C. (filed as Exhibit
                            10.3 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.4            -- Management and Ownership Agreement, dated September 23,
                            1994, by and among Brigham Oil & Gas, L.P., Brigham
                            Exploration Company, General Atlantic Partners III, L.P.,
                            Harold D. Carter, Ben M. Brigham and GAP-Brigham
                            Partners, L.P. (filed as Exhibit 10.4 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.5*++         -- Consulting Agreement, dated May 1, 1997, by and between
                            Brigham Oil & Gas, L.P. and Harold D. Carter.
         10.6*           -- Employment Agreement, by and between Brigham Exploration
                            Company and Ben M. Brigham (filed as Exhibit 10.7 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.7*           -- Form of Confidentiality and Noncompete Agreement between
                            the Registrant and each of its executive officers (filed
                            as Exhibit 10.8 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.8*           -- 1997 Incentive Plan of Brigham Exploration Company (filed
                            as Exhibit 10.9 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.8.1*         -- Form of Option Agreement for certain executive officers
                            (filed as Exhibit 10.9.1 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.8.2*         -- Option Agreement dated as of March 4, 1997, by and
                            between Brigham Exploration Company and Jon L. Glass
                            (filed as Exhibit 10.9.2 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.9*           -- Incentive Bonus Plan dated as of February 28, 1997 of
                            Brigham, Inc. and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.10 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
         10.10           -- Two Bridge Point Lease Agreement, dated September 30,
                            1996, by and between Investors Life Insurance Company of
                            North America and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.14 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
         10.10.1++       -- First Amendment to Two Bridge Point Lease Agreement dated
                            April 11, 1997 between Investors Life Insurance Company
                            of North America and Brigham Oil & Gas, L.P.
         10.10.2++       -- Second Amendment to Two Bridge Point Lease Agreement
                            dated October 13, 1997 between Investors Life Insurance
                            Company of North America and Brigham Oil & Gas, L.P.
         10.10.3++       -- Letter dated April 17, 1998 exercising Right of First
                            Refusal to Lease "3rd Option Space."
         10.11           -- Anadarko Basin Seismic Operations Agreement, dated
                            February 15, 1996, by and between Brigham Oil & Gas, L.P.
                            and Veritas Geophysical, Ltd. (filed as Exhibit 10.15 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
</TABLE>
<PAGE>   107
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         10.11.1         -- Letter Amendment to Anadarko Basin Seismic Operations
                            Agreement, dated June 10, 1996, between Brigham Oil &
                            Gas, L.P. and Veritas Geophysical, Ltd. (filed as Exhibit
                            10.15.1 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
         10.12           -- Expense Allocation and Participation Agreement, dated
                            April 1, 1996, between Brigham Oil & Gas, L.P. and Gasco
                            Limited Partnership. (filed as Exhibit 10.16 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.12.1         -- Amendment to Expense Allocation and Participation
                            Agreement, dated October 21, 1996, between Brigham Oil &
                            Gas, L.P. and Gasco Limited Partnership (filed as Exhibit
                            10.16.1 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
         10.13           -- Expense Allocation and Participation Agreement, dated
                            April 1, 1996, between Brigham Oil & Gas, L.P. and Middle
                            Bay Oil Company, Inc. (filed as Exhibit 10.17 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.13.1         -- Amendment to Expense Allocation and Participation
                            Agreement, dated September 26, 1996, between Brigham Oil
                            & Gas, L.P. and Middle Bay Oil Company, Inc. (filed as
                            Exhibit 10.17.1 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.13.2         -- Letter Amendment to Expense Allocation and Participation
                            Agreement, dated May 20, 1996, between Brigham Oil & Gas,
                            L.P. and Middle Bay Oil Company, Inc. (filed as Exhibit
                            10.17.2 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
         10.14           -- Anadarko Basin Joint Participation Agreement, dated May
                            1, 1996, by and among Stephens Production Company and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.18 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.15           -- Anadarko Basin Joint Participation Agreement, dated May
                            1, 1996, by and between Vintage Petroleum, Inc. and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.19 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.16           -- Processing Alliance Agreement, dated July 20, 1993,
                            between Veritas Seismic Ltd. and Brigham Oil & Gas, L.P.
                            (filed as Exhibit 10.20 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333- 22491), and
                            incorporated herein by reference).
         10.16.1         -- Letter Amendment to Processing Alliance Agreement, dated
                            November 3, 1994, between Veritas Seismic Ltd. and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.20.1 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.17           -- Agreement and Assignment of Interest, West Bradley
                            Project, dated September 1, 1995, by and between Aspect
                            Resources Limited Liability Company and Brigham Oil &
                            Gas, L.P. (filed as Exhibit 10.21 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
</TABLE>
<PAGE>   108
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         10.18           -- Agreement and Assignment of Interests in lands located in
                            Grady County, Oklahoma, West Bradley Project, dated
                            December 1, 1995, by and between Aspect Resources Limited
                            Liability Company, Brigham Oil & Gas, L.P. and Venture
                            Acquisitions, L.P. (filed as Exhibit 10.22 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.19           -- Agreement and Assignment of Interests, West Bradley
                            Project, dated December 1, 1995, by and between Aspect
                            Resources Limited Liability Company and Brigham Oil &
                            Gas, L.P. (filed as Exhibit 10.23 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.20           -- Geophysical Exploration Agreement, Hardeman Project,
                            Hardeman and Wilbarger Counties, Texas and Jackson
                            County, Oklahoma, dated March 15, 1993 by and among
                            General Atlantic Resources, Inc., Maynard Oil Company,
                            Ruja Muta Corporation, Tucker Scully Interests Ltd., JHJ
                            Exploration, Ltd., Cheyenne Petroleum Company, Antrim
                            Resources, Inc., and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.24 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
         10.21           -- Agreement and Partial Assignment of Interests in OK13-P
                            Prospect Area, Jackson County, Oklahoma (Hardeman
                            Project), dated August 1, 1995, by and between Brigham
                            Oil & Gas, L.P. and Aspect Resources Limited Liability
                            Company (filed as Exhibit 10.25 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.22           -- Agreement and Partial Assignment of Interests in Q140-E
                            Prospect Area, Hardeman County, Texas (Hardeman Project),
                            dated August 1, 1995, by and between Brigham Oil & Gas,
                            L.P. and Aspect Resources Limited Liability Company
                            (filed as Exhibit 10.26 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.23           -- Agreement and Partial Assignment of Interests in Hankins
                            #1 Chappel Prospect Agreement, Jackson County, Oklahoma
                            (Hardeman Project), dated March 21, 1996, by and between
                            Brigham Oil & Gas, L.P., NGR, Ltd. and Aspect Resources
                            Limited Liability Company (filed as Exhibit 10.27 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.24           -- Form of Indemnity Agreement between the Registrant and
                            each of its executive officers (filed as Exhibit 10.28 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.25           -- Registration Rights Agreement dated February 26, 1997 by
                            and among Brigham Exploration Company, General Atlantic
                            Partners III L.P., GAP-Brigham Partners, L.P., RIMCO
                            Partners, L.P. II, RIMCO Partners L.P. III, and RIMCO
                            Partners, L.P. IV, Ben M. Brigham, Anne L. Brigham,
                            Harold D. Carter, Craig M. Fleming, David T. Brigham and
                            Jon L. Glass (filed as Exhibit 10.29 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.26           -- 1997 Director Stock Option Plan (filed as Exhibit 10.30
                            to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.27           -- Form of Employee Stock Ownership Agreement (filed as
                            Exhibit 10.31 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
</TABLE>
<PAGE>   109
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         10.28           -- Agreement and Assignment of Interest in Geophysical
                            Exploration Agreement, Esperson Dome Project, dated
                            November 1, 1994, by and between Brigham Oil & Gas, L.P.
                            and Vaquero Gas Company (filed as Exhibit 10.33 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.29           -- Geophysical Exploration Agreement, Southwest Danbury
                            Project, Brazoria County, Texas, dated as of July 1,
                            1996, by and among UNEXCO, Inc. and Brigham Oil & Gas,
                            L.P. (filed as Exhibit 10.34 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.30           -- Geophysical Exploration Agreement, Welder Project, Duval
                            County, Texas, dated as of October 1, 1996, by and among
                            UNEXCO, Inc. and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.35 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
         10.31           -- Proposed Trade Structure, RIMCO/Tigre Project, Vermillion
                            Parish, Louisiana, among Brigham Oil & Gas, L.P., Tigre
                            Energy Corporation and Resource Investors Management
                            Company (filed as Exhibit 10.36.1 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         10.31.1         -- Letter relating to Proposed Trade Structure, RIMCO/Tigre
                            Project, dated January 31, 1997, from Resource Investors
                            Management Company to Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.36.1 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.32           -- Anadarko Basin Seismic Operations Agreement II, dated as
                            of April 1, 1997, by and between Brigham Oil & Gas, L.P.
                            (filed as Exhibit 10.37 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
         10.32.1         -- Letter Amendment to Anadarko Basin Seismic Operations
                            Agreement II, dated March 20, 1997, between Brigham Oil &
                            Gas, L.P. and Veritas DGC Land, Inc. (filed as Exhibit
                            10.37 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         10.33           -- Expense Allocation and Participation Agreement II, dated
                            April 1, 1997, between Brigham Oil & Gas, L.P., and Gasco
                            Limited Partnership (filed as Exhibit 10.31 to the
                            Company's Quarterly Report on Form 10-Q for the quarter
                            ended June 30, 1997, and incorporated herein by
                            reference).
         10.34           -- Credit Agreement dated as of January 26, 1998 among
                            Brigham Oil & Gas, L.P., Bank of Montreal, as Agent, and
                            the lenders signatory thereto (filed as Exhibit 10.36 to
                            the Company's Annual Report on Form 10-K for the year
                            ended December 31, 1997, and incorporated herein by
                            reference).
         10.34.1+        -- Guaranty Agreement dated January 26, 1998 by Brigham
                            Exploration Company in favor of Bank of Montreal, as
                            agent, and each of the Lenders party to the Credit
                            Agreement.
         10.34.2++       -- First Amendment to Guaranty Agreement dated as of March
                            30, 1998 between Brigham Exploration Company and Bank of
                            Montreal, as agent for the Lenders party to the Credit
                            Agreement.
</TABLE>
<PAGE>   110
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         21++            -- Subsidiaries of the Registrant.
         23.1++          -- Consent of Thompson & Knight, A Professional Corporation
                            (included in Exhibit 5 above).
         23.2+           -- Consent of Price Waterhouse LLP, independent public
                            accountants.
         23.3+           -- Consent of Cawley, Gillespie & Associates, Inc.,
                            independent petroleum engineers.
         24.1+           -- Powers of Attorney (included on the first signature page
                            to this Registration Statement).
</TABLE>
 
---------------
 
 * Management contract or compensatory plan.
 
++ To be filed by amendment.
 
 + Filed herewith.