<PAGE>   1
 
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                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                             ---------------------
                                   FORM 10-K
                             ---------------------
(MARK ONE)
     [X]         ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
 
                  FOR THE FISCAL YEAR ENDED DECEMBER 31, 1997
 
                                       OR
 
     [ ]       TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
 
             FOR THE TRANSITION PERIOD FROM           TO
 
                            COMMISSION FILE NUMBER:
 
                          BRIGHAM EXPLORATION COMPANY
             (Exact name of Registrant as Specified in its Charter)
 
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<S>                                              <C>
                    DELAWARE                                        75-2692967
        (State or other jurisdiction of                          (I.R.S. Employer
         incorporation or organization)                        Identification No.)
 
           6300 BRIDGE POINT PARKWAY
             BUILDING 2, SUITE 500
                 AUSTIN, TEXAS                                        78730
    (Address of principal executive offices)                        (Zip Code)
</TABLE>
 
              (Registrant's telephone number, including area code)
 
          Securities registered pursuant to Section 12(b) of the Act:
 
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<CAPTION>
                                           NAME OF EACH EXCHANGE ON
      TITLE OF EACH CLASS                      WHICH REGISTERED
      -------------------                  ------------------------
<S>                                     <C>
             None                                    None
</TABLE>
 
          Securities registered pursuant to Section 12(g) of the Act:
                          COMMON STOCK, $.01 PAR VALUE
                                (Title of Class)
 
     Indicate by check mark whether the Registrant: (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
Registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes [X]  No [ ]
 
     Indicate by check mark if disclosure of delinquent filers pursuant to Item
405 of Regulation S-K is not contained herein, and will not be contained, to the
best of Registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10-K or any amendment to this
Form 10-K. [ ]
 
     As of March 24, 1998, the Registrant had outstanding 12,253,574 shares of
Common Stock. The aggregate market value of the Common Stock held by
non-affiliates of the Registrant, based upon the closing sale price of the
Common Stock on March 24, 1998, as reported on The Nasdaq Stock Market(SM), was
approximately $45 million.
 
                      DOCUMENTS INCORPORATED BY REFERENCE
 
     Portions of the definitive proxy statement for the Registrant's 1998 Annual
Meeting of Stockholders to be held on May 29, 1998, are incorporated by
reference in Part III of this Form 10-K. Such definitive proxy statement will be
filed with the Securities and Exchange Commission not later than 120 days
subsequent to December 31, 1997.
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                               TABLE OF CONTENTS
 
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                                                                        PAGE
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<S>       <C>                                                           <C>
                                   PART I
ITEM 1.   BUSINESS....................................................    1
ITEM 2.   PROPERTIES..................................................    7
ITEM 3.   LEGAL PROCEEDINGS...........................................   15
ITEM 4.   EXECUTIVE OFFICERS OF THE REGISTRANT........................   15
 
                                  PART II
ITEM 5.   MARKET FOR REGISTRANT'S COMMON EQUITY AND RELATED
          STOCKHOLDER MATTERS.........................................   17
ITEM 6.   SELECTED FINANCIAL DATA.....................................   18
ITEM 7.   MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
          AND RESULTS OF OPERATIONS...................................   19
ITEM 8.   FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA.................   30
ITEM 9.   CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING
          AND FINANCIAL DISCLOSURE....................................   30
 
                                  PART III
ITEM 10.  DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT..........   31
ITEM 11.  EXECUTIVE COMPENSATION......................................   31
ITEM 12.  SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND
          MANAGEMENT..................................................   31
ITEM 13.  CERTAIN RELATIONSHIPS AND RELATED PARTY TRANSACTIONS........   31
 
                                  PART IV
ITEM 14.  EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM
          8-K.........................................................   31
GLOSSARY OF OIL AND GAS TERMS.........................................   37
SIGNATURES............................................................   39
INDEX TO FINANCIAL STATEMENTS.........................................  F-1
</TABLE>
 
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                          BRIGHAM EXPLORATION COMPANY
 
                        1997 ANNUAL REPORT ON FORM 10-K
 
                                     PART I
 
ITEM 1. BUSINESS
 
OVERVIEW
 
     Brigham Exploration Company ("Brigham" or 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 oil
and natural gas provinces. The Company focuses its 3-D seismic activity in
provinces where it believes 3-D technology may be effectively applied and that
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 south 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 the West Texas region 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 oil and natural gas reserves. As of December 31, 1997,
Brigham has acquired 4,005 square miles (2.6 million acres) of 3-D seismic data
and has identified 1,170 potential drilling locations, of which the Company has
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 has drilled 324 exploratory
and 46 development wells on its 3-D generated prospects with an aggregate 63%
success rate and an average working interest of 24%. As of December 31, 1997,
the Company has added approximately 82 Bcfe of net proved reserves to its
reserve base, approximately 61 net Bcfe of which were discovered by Brigham
through its systematic 3-D 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 are 74% natural gas and 65%
categorized as proved developed reserves.
 
EXPLORATION AND OPERATING APPROACH
 
     The Company has acquired 3-D seismic data in 119 projects covering 4,005
square miles (2.6 million acres) in 20 geologic trends in seven basins and seven
states. Through 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 data in and around existing
production where the Company can benefit from the imaging of producing analogs.
These 3-D 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 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 oil
and natural gas.
 
     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
 
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and fractured reservoirs and pinchout plays). The Company seeks to supplement
its knowledge base with the best local geologic expertise available 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 data.
 
     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 the previous reservoir maps used by the industry (which generally
were based on subsurface geological information and 2-D seismic surveys),
enabling the Company to more precisely evaluate recoverable reserves and the
economic feasibility of projects and drilling locations.
 
     Brigham acquires most of its raw 3-D seismic data 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 data. 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 "Item 1. Business -- Industry Alliances."
 
EXPLORATION STAFF
 
     Over the last seven years the Company has assembled an exploration staff
that includes nine geophysicists, ten geologists, three petroleum engineers,
four computer applications specialists, three geophysical/
geological/engineering technicians, five landmen and five 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 250 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 oil and natural gas 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 data provides clearer and more
accurate projected images of complex geologic formations, which can assist a
user in evaluating whether to drill for oil and natural gas reserves. If a
decision to drill is made, 3-D seismic data 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 data 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 techniques to project the likely geologic
composition of a potential drilling location and potential locations of
undiscovered oil and natural gas reserves. This process relies on a comparison
of data with respect
 
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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 data
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 data. 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 has acquired approximately 850 square miles of 3-D seismic data in the
Anadarko Basin through December 31, 1997, and has 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 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 data acquisition in a
compressed cycle time, providing the Company with operational efficiencies.
 
     In addition, Veritas Geoservices, Ltd. currently 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 data. 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 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
 
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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 data under a second alliance
with Veritas in the Anadarko Basin. From August through December 1997, the
Company has acquired approximately 225 square miles of 3-D seismic data 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 at
least a 75% 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 costs 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
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. The Company is currently in discussions with Gasco to renew its
agreement, although the percentages of costs borne and interest assigned may
vary under any renewal or extension of this agreement, and there is no guarantee
that any renewal will be agreed upon. The Company believes that these agreements
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.
 
NATURAL GAS AND OIL MARKETING AND MAJOR CUSTOMERS
 
     Most of the Company's natural gas and oil production is sold 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 may in the future materially affect the Company's ability
to sell its natural gas or oil production. See "Item 7. 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 oil
and natural gas leases on properties. The Company's competitors include major
integrated oil and natural gas companies and numerous independent oil and
natural gas companies, individuals and drilling
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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 oil and natural gas 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 "Item 7.
Management's Discussion and Analysis of Financial Conditional Results of
Operations -- 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 oil and
natural gas 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 future results of
operations and financial condition. See "Item 7. Management's Discussion and
Analysis of Financial Condition and Results of Operations -- 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.
 
     The Company's operations are subject to hazards and risks inherent in
drilling for and producing and transporting oil and natural gas, 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 oil and natural gas 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 financial condition and results of
operations.
 
EMPLOYEES
 
     On March 24, 1998, the Company had 57 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 broker service
companies to provide field landmen to the Company. 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.
 
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. The Company also
leases a 4,100 square foot office at 450 Gears Road, Suite 240, Houston, Texas
77067.
 
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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 oil and natural gas properties. See "Item 7. Management's Discussion
and Analysis of Financial Condition and Results of Operations."
 
GOVERNMENTAL REGULATION
 
     The Company's oil and natural gas 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.
 
ENVIRONMENTAL MATTERS
 
     The Company's operations and properties are 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 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 onshore and offshore facilities
that may affect waters of the United States, the OPA requires an operator to
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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 oil and natural gas. 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
"Item 7. Management's Discussion and Analysis of Financial Condition and Results
of Operations -- Other Matters" and "-- Risk Factors -- Compliance with
Environmental Regulations."
 
ITEM 2. PROPERTIES
 
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 south 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 that 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 data 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 data 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 data, (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 oil and natural gas 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
 
                                        7
<PAGE>   10
 
be no assurance that the budgeted wells will, if drilled, encounter reservoirs
of commercial quantities of natural gas or oil.
 
<TABLE>
<CAPTION>
                                                                                                1998 CAPITAL BUDGET
                                                                       UNDRILLED   ---------------------------------------------
                          3-D SEISMIC       3-D SEISMIC      GROSS     POTENTIAL                    CAPITAL EXPENDITURES ($MM)
                        DATA ACQUIRED/     DATA BUDGETED     WELLS     DRILLING       WELLS       ------------------------------
                       INTERPRETED AS OF   TO BE ACQUIRED   DRILLED    LOCATIONS     DRILLED        NET
                        12/31/97 (GROSS    IN 1998 (GROSS   THROUGH      AS OF     ------------   SEISMIC      NET
      PROVINCE            SQ. MILES)         SQ. MILES)     12/31/97   12/31/97    GROSS   NET    AND LAND   DRILLING   TOTAL(1)
---------------------  -----------------   --------------   --------   ---------   -----   ----   --------   --------   --------
<S>                    <C>                 <C>              <C>        <C>         <C>     <C>    <C>        <C>        <C>
Anadarko Basin.......    1,515 / 1,195          547            55         364        52    20.8    $12.6      $19.1      $31.7
Gulf Coast...........      566 /   325          393            11         110        17     8.2      2.4        8.8       11.2
West Texas...........    1,649 / 1,600           27           287         302        31    13.2      1.7        7.9        9.6
Others (2)...........      275 /   275           --            17          24         1     0.2       --        0.2        0.2
                         -------------          ---           ---         ---       ---    ----    -----      -----      -----
         Total.......    4,005 / 3,395          967           370         800       100    42.4    $16.7      $36.0      $52.7
                         =============          ===           ===         ===       ===    ====    =====      =====      =====
</TABLE>
 
---------------
 
(1) 3-D seismic and land acquisition costs and drilling expenditures.
 
(2) 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 data. 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.
 
     Following its initial 3-D seismic acquisition in the province in 1991 (12.5
square miles), the Company acquired 51 square miles of 3-D seismic in 1993. Over
the last several years the Company has accelerated its activity in the Anadarko
Basin, acquiring 151 square miles of 3-D seismic in 1994, 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 data 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 547 square miles (350,080 acres) of additional 3-D seismic
data 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 38.2 net Bcfe and had acquired 21.5 net Bcfe of
proved reserves. In 1997, the Company completed 19 wells in 23 attempts in its
Anadarko Basin province with an average working interest of 39%, adding 28.1 net
Bcfe of proved reserves. 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 52 gross (20.8 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 Project. The Company's largest
 
                                        8
<PAGE>   11
 
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. Brigham owns a 36.4% working interest in the well
and plans to drill two development wells in 1998 in which the Company will own
an average 63.7% 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 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 at a calculated open flow rate of 128 MMcfe per day
and tested an initial production rate of 6.1 MMcfe per day. A development well
will be drilled on this discovery early 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 shoot a 30 square mile 3-D
seismic program over the 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 Project, where Ward operates the majority
of the drilling operations.
 
     Gulf Coast. The onshore Gulf Coast region of south 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 knowledge base to
generate 3-D 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, Expanded Vicksburg and Yegua 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 data in seven projects in the
onshore Gulf Coast province. The Company anticipates acquiring 393 square miles
(251,520 acres) of additional 3-D seismic data 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 2.9 net
Bcfe. In 1997, the Company completed seven wells in 10 attempts with an average
working interest of 9% adding 2.9 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 17 gross (8.2 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 seismic data. The Esperson Dome
Project targets structurally trapped sands in the Miocene, Vicksburg and
Yegua/Cook Mountain series ranging in depth from 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
 
                                        9
<PAGE>   12
 
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 in Duval and Webb counties, Texas. Initially Brigham
participated in the acquisition of 48 square miles of 3-D seismic data 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. Brigham currently
plans to drill four additional wells in this project in 1998. The Caliente
Project is a non-proprietary seismic program that covers an additional 362
square miles on which seismic data is currently being acquired. 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 three
exploratory wells budgeted in this project for 1998.
 
     Another project in South Texas is Brigham's Diablo Project covering
approximately 4,000 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 a major oil company
that controls adjoining acreage to jointly explore on 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
several 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 retains a 46.1% 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 Bcfe 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. A 200 square mile 3-D seismic program over this acreage will be
initiated in early 1998, with initial drilling anticipated for early 1999.
Brigham plans to retain a 50% to 55% working interest in 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 Company will acquire approximately 90 square miles
of new proprietary 3-D seismic to merge with 65 square miles of speculative 3-D
data already in inventory. The region has potential in the shallow, nonpressured
Miocene and Frio sands as well as the deeper, pressured Frio sands.
Interpretation of the existing data is ongoing, with acquisition of new data
scheduled to begin in April 1998. Brigham plans to retain a 50% working interest
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 data covering a 7,200
acre lease block in Louisiana state waters, where Brigham currently controls a
75% working interest. The project will target 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 1998, targeting greater than
200 Bcf of unrisked potential.
 
     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.
 
                                       10
<PAGE>   13
 
     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 27 square miles (17,280 acres) of additional 3-D
seismic data 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 19.4 net Bcfe. In 1997, the
Company completed 19 wells in 34 attempts with an average working interest of
45% adding 1.7 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 31 gross (13.2 net) wells in 1998.
 
     One area in which the Company increased its activity is the Midland Basin,
where the Company 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 18.75% to 91%. In 1998 the Company has
acquired 27 square miles of 3-D seismic data in three additional 3-D 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 programs covering
approximately 137 square miles acquired in 1996 and 1997, the Company has
identified numerous potential 3-D delineated drilling locations and has leased
over 6,400 gross (1,600 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). The Company plans to spud a deep test in its Longhorn
Project during 1998.
 
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.
 
                                       11
<PAGE>   14
 
(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, and $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 as
of which the Company's reserves and present value data 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 March 24, 1998, the price of
natural gas on the NYMEX ranged from $2.00 per MMBtu to $2.38 per MMBtu and the
price of oil on the NYMEX ranged from $13.21 per Bbl to $17.82 per Bbl. There
are numerous uncertainties inherent in estimating oil and natural gas 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
oil and natural gas 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 oil and
natural gas prices, operating costs and other factors. The revisions may be
material. Accordingly, reserve estimates are often different from the quantities
of oil and natural gas 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 "Item 7. Management's Discussion and Analysis of Financial
Condition and Results of Operations -- 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 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.
 
                                       12
<PAGE>   15
 
DRILLING ACTIVITIES
 
     The Company drilled, or participated in the drilling of, the following
number of wells during the periods indicated.
 
<TABLE>
<CAPTION>
                                                              YEAR ENDED DECEMBER 31,
                                                  -----------------------------------------------
                                                      1995             1996             1997
                                                  -------------    -------------    -------------
                                                  GROSS    NET     GROSS    NET     GROSS    NET
                                                  -----    ----    -----    ----    -----    ----
<S>                                               <C>      <C>     <C>      <C>     <C>      <C>
Exploratory Wells:
  Natural gas...................................    5       1.2      5       1.2     15       6.3
  Oil...........................................   37       8.1     22       5.2     21       7.9
  Non-productive................................   32       8.7     24       7.0     26       9.8
                                                   --      ----     --      ----     --      ----
          Total.................................   74      18.0     51      13.4     62      24.0
                                                   ==      ====     ==      ====     ==      ====
Development Wells:
  Natural gas...................................   --        --     10       1.3      4       1.6
  Oil...........................................    4       0.5      5       1.0      6       1.8
  Non-productive................................   --        --      1       0.2      1       0.6
                                                   --      ----     --      ----     --      ----
          Total.................................    4       0.5     16       2.5     11       4.0
                                                   ==      ====     ==      ====     ==      ====
</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
                                        ---------------    -------------    -------------
                                        GROSS     NET      GROSS    NET     GROSS    NET
                                        -----    ------    -----    ----    -----    ----
<S>                                     <C>      <C>       <C>      <C>     <C>      <C>
Province:
  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.
 
  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 oil and natural gas, 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
 
                                       13
<PAGE>   16
 
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
                                --------------   -----------------   -----------------
                                GROSS     NET     GROSS      NET      GROSS      NET
                                ------   -----   -------   -------   -------   -------
<S>                             <C>      <C>     <C>       <C>       <C>       <C>
Province:
  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 oil
and natural gas for the periods indicated.
 
<TABLE>
<CAPTION>
                                                            YEAR ENDED DECEMBER 31,
                                                           --------------------------
                                                            1995      1996      1997
                                                           ------    ------    ------
<S>                                                        <C>       <C>       <C>
Production:
  Natural gas (MMcf).....................................     272       698     1,382
  Oil (MBbls)............................................     177       227       291
  Natural gas equivalent (MMcfe).........................   1,332     2,060     3,126
Average sales price(1):
  Natural gas (per Mcf)..................................  $ 1.62    $ 2.30    $ 2.56
  Oil (per Bbl)..........................................  $17.76    $19.98    $19.40
Average production expenses and taxes (per Mcfe).........  $  .69    $  .53    $  .55
</TABLE>
 
---------------
 
(1) Reflects the results of hedging activities in the periods presented.
 
                                       14
<PAGE>   17
 
COSTS INCURRED
 
     The costs incurred in oil and natural gas 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.
 
ITEM 3. LEGAL PROCEEDINGS
 
     The Company is not a party to any material pending legal proceedings other
than ordinary routine litigation incidental to the Company's business.
 
ITEM 4. EXECUTIVE OFFICERS OF THE REGISTRANT
 
     Pursuant to Instruction 3 to Item 401(b) of the Regulation S-K and General
Instruction G(3) to Form 10-K, the following information is included in Part I
of this report.
 
     The following table sets forth certain information concerning the executive
officers of the Company as of December 31, 1997:
 
<TABLE>
<CAPTION>
                 NAME                   AGE                   POSITION
                 ----                   ---                   --------
<S>                                     <C>    <C>
Ben M. Brigham........................  38     Chief Executive Officer and President
Anne L. Brigham.......................  36     Executive Vice President
Jon L. Glass..........................  42     Vice President -- Exploration
Craig M. Fleming......................  40     Chief Financial Officer
David T. Brigham......................  37     Vice President -- Land and
                                               Administration, Corporate Secretary
A. Lance Langford.....................  35     Vice President -- Operations
Karen E. Lynch........................  36     Vice President and General Counsel
</TABLE>
 
     Set forth below is a description of the backgrounds of the executive
officers 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. 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.
 
                                       15
<PAGE>   18
 
     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.
 
                                       16
<PAGE>   19
 
                                    PART II
 
ITEM 5. MARKET FOR REGISTRANT'S COMMON EQUITY AND RELATED STOCKHOLDER MATTERS
 
     The Company's Common Stock (the "Common Stock") has been publicly traded on
The Nasdaq Stock Market(SM) under the symbol "BEXP" since the Company's initial
public offering effective May 8, 1997. The following table summarizes the high
and low sales prices on The Nasdaq Stock Market(SM) for each quarterly period
since the Company's initial public offering:
 
<TABLE>
<CAPTION>
                                                                COMMON STOCK
                                                              ----------------
                                                               HIGH      LOW
                                                              ------    ------
<S>                                                           <C>       <C>
1997:
Second Quarter (from May 9, 1997)...........................  $ 8.75    $ 7.00
Third Quarter...............................................  $14.31    $ 8.25
Fourth Quarter..............................................  $17.13    $12.00
</TABLE>
 
     The closing market price of the Company's Common Stock on March 24, 1998
was $12.88 per share. As of March 24, 1998, the Company estimates that there
were more than 60 record and 900 beneficial owners of the Company's Common
Stock.
 
     No dividends have been declared or paid on the Company's Common Stock to
date. The Company intends to retain all future earnings for the development of
its business.
 
                                       17
<PAGE>   20
 
ITEM 6. SELECTED FINANCIAL DATA
 
     The following selected consolidated financial data should be read in
conjunction with "Item 7. Management's Discussion and Analysis of Financial
Condition and Results of Operations" and the Company's consolidated financial
statements and related notes included in "Item 8. Financial Statements and
Supplementary Data."
 
<TABLE>
<CAPTION>
                                                                            YEAR ENDED DECEMBER 31,
                                                              ---------------------------------------------------
                                                               1993        1994      1995       1996       1997
                                                              -------     -------   -------   --------   --------
<S>                                                           <C>         <C>       <C>       <C>        <C>
STATEMENT OF OPERATIONS DATA:
  Revenues:
    Natural gas and oil sales...............................  $   937     $ 2,565   $ 3,578   $  6,141   $  9,184
    Workstation revenue.....................................      467         815       635        627        637
                                                              -------     -------   -------   --------   --------
        Total revenues......................................    1,404       3,380     4,213      6,768      9,821
  Costs and expenses:
    Lease operating.........................................      111         491       761        726      1,151
    Production taxes........................................       47         126       165        362        549
    General and administrative..............................    1,433       1,785     1,897      2,199      3,570
    Depletion of natural gas and oil properties.............    4,371(1)    1,104     1,626      2,323      2,732
    Depreciation and amortization...........................      406         561       533        487        582
                                                              -------     -------   -------   --------   --------
        Total costs and expenses............................    6,368       4,067     4,982      6,097      8,584
                                                              -------     -------   -------   --------   --------
  Operating income (loss)...................................   (4,964)       (687)     (769)       671      1,237
  Other income (expense):
    Interest income.........................................        6          56       128         52        145
    Interest expense........................................     (105)       (668)     (936)    (1,173)    (1,190)
                                                              -------     -------   -------   --------   --------
        Total other income (expense)........................      (99)       (612)     (808)    (1,121)    (1,045)
  Net income (loss) before income taxes.....................   (5,063)     (1,299)   (1,577)      (450)       192
  Income tax expense, net...................................       --          --        --         --     (1,228)(2)
                                                              -------     -------   -------   --------   --------
        Net loss............................................  $(5,063)    $(1,299)  $(1,577)  $   (450)  $ (1,036)
                                                              =======     =======   =======   ========   ========
  Net loss per share -- basic/diluted.......................  $ (0.57)    $ (0.15)  $ (0.18)  $  (0.05)  $  (0.09)
                                                              =======     =======   =======   ========   ========
  Weighted average shares outstanding -- basic/diluted......    8,929       8,929     8,929      8,929     11,081
STATEMENT OF CASH FLOWS DATA:
  Net cash provided by (used in) operating activities.......  $  (730)    $   626   $ 1,383   $  3,710   $  9,806
  Net cash used in investing activities.....................   (6,983)     (5,463)   (8,005)   (11,796)   (57,300)
  Net cash provided by financing activities.................    7,839       4,634     7,724      7,731     47,748
OTHER FINANCIAL DATA:
  Capital expenditures......................................  $ 6,632     $ 5,445   $ 7,935     13,612   $ 57,170
  EBITDA(3).................................................     (187)        978     1,390      3,481      4,551
  Operating cash flow(4)....................................     (286)        366       582      2,360      3,506
</TABLE>
 
<TABLE>
<CAPTION>
                                                                             AS OF DECEMBER 31,
                                                              -------------------------------------------------
                                                               1993        1994      1995      1996      1997
                                                              -------     -------   -------   -------   -------
<S>                                                           <C>         <C>       <C>       <C>       <C>
BALANCE SHEET DATA:
  Cash and cash equivalents.................................  $   903     $   700   $ 1,802   $ 1,447   $ 1,701
  Natural gas and oil properties, net.......................    7,803      11,970    18,538    28,005    84,176
  Total assets..............................................   14,003      15,781    22,916    33,614    92,401
  Notes payable.............................................    3,000       7,950    16,000    24,000    32,000
  Total equity..............................................    6,570       5,271     3,694     3,244    43,153
</TABLE>
 
---------------
 
(1) Includes a capitalized ceiling impairment of $3.3 million in 1993.
 
(2) Includes a net $1.2 million ($0.10 per share) non-cash deferred income tax
    charge related to the Company's conversion from a partnership to a
    corporation in 1997.
 
(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.
 
                                       18
<PAGE>   21
 
ITEM 7. 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 oil and natural gas provinces. From
inception in 1990 through December 31, 1997, Brigham has 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 oil and natural
gas in onshore domestic oil and natural gas 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 60.9 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 oil and natural gas 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 data, 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 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 data and increasing its working
interests during the drilling phase.
 
     From inception through 1993, the Company acquired 1,373 square miles of 3-D
seismic in 63 projects. The majority of the Company's 3-D seismic acquisitions
were concentrated in the Horseshoe Atoll and Eastern Shelf of the Permian Basin
and the Hardeman Basin of West Texas. The Company drilled seventy-nine 3-D
delineated wells during this period, increasing its revenues from oil and
natural gas production to $936,634 in 1993. The Company's production volumes
consisted of 85% oil on an equivalent basis. The Company's average working
interest in these wells was 14%. In 1992, the Company increased its capacity to
finance its project generation and drilling activities through a $10 million
private placement of equity. This financing partially funded the Company's
acquisition of 908 square miles of 3-D seismic data in 32 projects in 1993,
which contributed to the Company's reserve growth in subsequent years. The
Company also issued $3 million of 10% senior secured general obligation notes
(the "10% Notes") in 1993.
 
     During 1994, the Company acquired 423 square miles of 3-D seismic in 16
projects, primarily in the Horseshoe Atoll and Eastern Shelf areas of the
Permian Basin, the Hardeman Basin and the Anadarko Basin. The Company drilled
seventy-three 3-D delineated wells, increasing its revenues from oil and natural
gas production to $2.6 million. The Company's production volumes consisted of
84% oil on an equivalent basis. The Company's average working interest in wells
drilled in 1994 was 23%. To finance its project generation and drilling
activities, the Company supplemented cash flow from operations with capital from
the issuance of $4.9 million of its 10% Notes and the placement of working
interests in projects to industry participants. The Company's acquisition of
seismic data declined in 1994 compared to previous years as the Company
allocated a greater portion of its capital expenditure budget to drilling 3-D
delineated locations.
 
     During 1995, the Company significantly expanded its efforts in the Anadarko
Basin of Texas and Oklahoma by acquiring 195 square miles of 3-D seismic in four
projects in this basin, and initiated its exploration program in the Gulf Coast
with the Esperson Dome Project (39 square miles of 3-D seismic). The
 
                                       19
<PAGE>   22
 
Company also continued its efforts in the Horseshoe Atoll and Eastern Shelf
areas of the Permian Basin and the Hardeman Basin by acquiring 77 square miles
of 3-D seismic. The Company drilled seventy-eight 3-D delineated wells,
increasing its revenues from oil and natural gas production to $3.6 million. The
Company's production volumes consisted of 80% oil on an equivalent basis. The
Company's average working interest in wells drilled in 1995 was 24%. To finance
its project generation and drilling activities the Company supplemented cash
flow from operations with capital from the issuance of $2.6 million of the 10%
Notes, the issuance of $16 million principal amount of its 5% convertible
unsecured subordinated notes (the "5% Notes") and the placement of working
interests in projects to industry participants. The Company used $10.5 million
of the proceeds from the issuance of the 5% Notes to retire the then outstanding
balance of the 10% Notes.
 
     During 1996, the Company acquired 655 square miles of 3-D seismic data and
continued to focus the majority of its 3-D exploration efforts in the Anadarko
Basin and the Gulf Coast. The Company acquired 457 square miles (70%) of the 3-D
seismic data in eight projects in the Anadarko Basin, making this basin the most
active 3-D acquisition province for the Company in 1996. Brigham also
significantly increased its Gulf Coast activity, adding eight 3-D projects, and
continued to expand its operations through staff additions and opening a Houston
office in January 1997. While an increasing portion of the Company's capital was
dedicated to 3-D seismic and land acquisition and subsequent drilling in the
Anadarko Basin and the Gulf Coast, the Company continued to allocate a
significant amount of capital to the drilling of its 3-D delineated locations in
the West Texas region. During 1996, the Company drilled sixty-seven 3-D
delineated wells, increasing its revenues from oil and natural gas production to
$6.1 million. The Company's production volumes consisted of 66% oil on an
equivalent basis. The Company's average working interest in wells drilled in
1996 was 24%. The Company's fourth quarter 1996 revenue from oil and natural gas
production increased to $1.9 million from $955,000 in the fourth quarter of
1995. The Company supplemented cash flow from operations with borrowings under
its revolving credit facility with Bank One, Texas NA (the "Bank One Facility"),
the sale of producing properties and the placement of working interests in
projects to industry participants to finance its project generation and drilling
activities.
 
     In 1997, the Company acquired 1,243 square miles of 3-D seismic data 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 the 3-D
seismic data in nine projects in the Anadarko Basin, making this basin the most
active 3-D 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 data in four projects. Reflecting a continued increase in
the Company's 3-D seismic and land acquisition and subsequent drilling in the
Anadarko Basin and the Gulf Coast, the Company's change in geographic focus has
resulted in a larger percentage of its reserves and production consisting of
natural gas. During 1997, the Company drilled seventy-three 3-D delineated
wells, increasing its revenues from oil and natural gas 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 oil and natural gas
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 its Bank
One Facility, $25 million of equity capital raised in its initial public
offering of common 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 oil and natural
gas 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 data 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
 
                                       20
<PAGE>   23
 
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 oil and natural gas reserves plus the
capitalized cost of unproved properties, such costs are charged to operations.
Once incurred, a write-down of oil and natural gas properties is not reversed at
a later date. See Note 2 of Notes to the Consolidated Financial Statements.
 
     In connection with the exchange prior to the Company's initial public
offering of interests in the Company's predecessor partnership of shares of the
Company's Common Stock (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 $272,000 in
1998, $159,000 in 1999 and an aggregate of $192,000 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 date of the Exchange, 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.
 
RESULTS OF OPERATIONS
 
     The following table sets forth certain operating data for the periods
presented.
 
<TABLE>
<CAPTION>
                                                               YEAR ENDED DECEMBER 31,
                                                              --------------------------
                                                               1995      1996      1997
                                                              ------    ------    ------
<S>                                                           <C>       <C>       <C>
Production:
  Natural gas (MMcf)........................................     272       698     1,382
  Oil (MBbls)...............................................     177       227       291
  Natural gas equivalent (MMcfe)............................   1,332     2,060     3,126
Average sales prices per unit (1):
  Natural gas (per Mcf).....................................  $ 1.62    $ 2.30    $ 2.56
  Oil (per Bbl).............................................   17.76     19.98     19.40
  Natural gas equivalent (per Mcfe).........................    2.69      2.98      2.94
Costs and expenses per Mcfe:
  Lease operating...........................................  $ 0.57    $ 0.35    $ 0.37
  General and administrative................................    1.42      1.07      1.14
  Depletion of oil and natural gas properties...............    1.22      1.13      0.87
</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 -- Hedging Activities."
 
  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. 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
 
                                       21
<PAGE>   24
 
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. Oil and natural gas 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's 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.
 
     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 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 oil and natural gas production volumes from 1996 to
1997 due to the aforementioned factors. The Company does not expect general and
administrative expenses to increase significantly in 1998 and expects the per
unit rate to decrease due to an anticipated continuation of increases in natural
gas and oil production volumes throughout the year.
 
     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 18% from $2.3 million ($1.13 Mcfe) in 1996 to $2.7
million ($0.87 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 average 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 of
the 5% Notes in February 1997, the retirement of $13.3 million of borrowings
under the Bank One Facility in connection with the Company's May 1997 initial
public offering and $32 million of borrowings incurred under the Bank One
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 Bank
One 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 Mcf in 1995 to $2.30 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 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
 
                                       22
<PAGE>   25
 
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 data were acquired in 1995 and interpreted in 1996. 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.
 
     Lease operating expenses. Lease operating expenses decreased 5% from
$760,784 ($.57 Mcfe) in 1995 to $725,785 ($.35 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.
 
     General and administrative expenses. General and administrative expenses
increased 16% from $1.9 million ($1.42 Mcfe) in 1995 to $2.2 million ($1.07
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 oil and natural gas production from 1995 to
1996.
 
     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 43% from $1.6 million ($1.22 Mcfe) in 1995 to $2.3
million ($1.13 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 the 10% Notes and the issuance of $16
million in principal amount of the 5% Notes in August 1995. The Company entered
into the Bank One Facility in April 1996, which had an effective interest rate
of 7.9% at December 31, 1996.
 
LIQUIDITY AND CAPITAL RESOURCES
 
     The Company's primary sources of capital have been 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 with Bank One, Texas, NA. This facility had a
three-year term and was subject to certain borrowing base limitations. The
Company had borrowings outstanding under the Bank One Facility of $32 million as
of December 31, 1997. The Company retired the Bank One Facility in January 1998
with borrowings under its Bank of Montreal Facility.
 
     In January 1998, Brigham entered into a new reserve-based credit agreement
(the "Bank of Montreal Facility") with Bank of Montreal, 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 Bank of Montreal 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
Bank of Montreal Facility is due at maturity on January 26, 2001 with interest
due monthly. The interest rate for borrowings under the Bank of Montreal
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 is subject to typical covenants and
restrictions under the terms of the Bank of Montreal
 
                                       23
<PAGE>   26
 
Facility. The Company's obligations under the Bank of Montreal Facility are
secured by substantially all of the oil and natural gas properties of the
Company. See Note 5 of Notes to the Consolidated Financial Statements.
 
     The Company used a portion of the funds available under Bank of Montreal
Facility to repay the $32 million in borrowings outstanding at December 31, 1997
under its Bank One Facility, and it expects to utilize the remaining borrowing
capacity under the Bank of Montreal Facility together with cash flows from
operations to fund its budgeted capital expenditures in 1998.
 
     5% Notes. In August 1995, the Company entered into a note purchase
agreement with RIMCO under which RIMCO purchased $16 million in convertible
subordinated notes due September 1, 2002. These notes were unsecured and bore
interest at 5% per annum, of which 3% was currently payable and 2% was deferred
and payable at the maturity date. The balance outstanding under the 10% Notes
was retired with a portion of the proceeds from the issuance of the $16 million
in principal amount of the 5% Notes. RIMCO converted these notes and the
deferred interest thereon into a 19.65% equity interest in the Company in
February 1997. See Note 5 of Notes to the Consolidated Financial Statements.
 
  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 oil and natural gas 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 oil and natural gas revenues, net of lease operating
expenses, production taxes and general and administrative expenses.
 
     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 square
miles of 3-D seismic data in 1997, 655 square miles in 1996, and 311 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 Flows from Financing Activities. Cash flows from financing activities
for 1997 were $47.7 million, primarily as a result of borrowings under the Bank
One 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 Bank One Facility. Cash
flows from financing activities for 1995 were $7.7 million, primarily 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.
 
  Capital Expenditures
 
     The Company estimates capital expenditures in 1998 will be approximately
$57.5 million. The Company expects to incur these capital expenditures primarily
to drill 100 gross (42.4 net) planned wells, acquire approximately 970 square
miles of 3-D seismic data and continue to add to and upgrade its 3-D seismic
interpretation hardware and software. The actual number of wells drilled and
square miles acquired may differ significantly from these estimates. See "Item
2. Properties -- Primary Exploration Provinces" and "-- Forward Looking
Information".
 
     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 cash flow from
operations and borrowings under the Bank of Montreal Facility should allow the
Company to finance its operations at least through 1998 based on current
conditions, additional
 
                                       24
<PAGE>   27
 
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 oil and natural gas sales price fluctuations
and to thereby 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 oil and natural gas
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 1995 and a decrease 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
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
oil and natural gas prices. If the price of oil and natural gas 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, oil and natural gas, 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," and "Item 1.
Business -- Governmental Regulation" and "-- Environmental Matters."
 
                                       25
<PAGE>   28
 
FORWARD LOOKING INFORMATION
 
     Brigham or its representatives may make forward looking statements, oral or
written, including statements in this report's Management's Discussion and
Analysis of Financial Condition and Results of Operations, press releases and
filings with the SEC, regarding estimated future net revenues from oil and
natural gas reserves and the present value thereof, planned capital expenditures
(including the amount and nature thereof), increases in oil and gas 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 oil and gas prices, the ability
of the Company to successfully integrate the business and operations of acquired
companies, government regulations and other factors set forth among the risk
factors noted below or in the description of the Company's business in Item 1 of
this report. 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
 
     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. 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 data 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 data 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 data 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.
 
     Volatility of Oil and Natural Gas Prices. The Company's revenues, operating
results and future rate of growth are highly dependent upon the prices received
for the Company's oil and natural gas. Historically, the markets for oil and
natural gas have been volatile and are likely to continue to be volatile in the
future. Various factors beyond the control of the Company will affect prices of
its oil and natural gas, including worldwide and domestic supplies of oil and
natural gas, 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,
weather conditions, domestic and
 
                                       26
<PAGE>   29
 
foreign governmental regulations and taxes, and the overall economic
environment. During 1997, the high and low prices for oil on the NYMEX were
$26.62 per Bbl and $17.60 per Bbl, and the high and low prices for natural gas
on the NYMEX were $3.79 per MMBtu and $1.78 per MMBtu. From January 1, 1998
through March 24, 1998, the price of oil on the NYMEX ranged from $13.21 per Bbl
to $17.82 per Bbl and the price of natural gas on the NYMEX ranged from $2.00
per MMBtu to $2.38 per MMBtu. It is impossible to predict future oil and natural
gas price movements with certainty. Declines in natural gas and oil prices may
materially adversely affect the Company's financial condition, liquidity,
ability to finance planned capital expenditures 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 natural gas or oil 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 "Item 1. Business -- Competition."
 
     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 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. 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 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.
 
     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 and $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. 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 December 31, 1997, the
Company's retained earnings were $26,000 and its total stockholders' equity was
$43.2 million. In addition, the Company's future operating results may fluctuate
significantly depending upon a number of factors, including industry conditions,
prices of oil and natural gas, 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 "Item 6. Selected Financial Data."
 
     Reserve Replacement Risk. In general, production from oil and natural gas
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 oil and natural gas
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 oil and natural gas reserves would be
impaired. The Company participates in a substantial percentage of its wells as
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,
 
                                       27
<PAGE>   30
 
although the Company's revenues could increase if prevailing prices for oil and
natural gas increase significantly, the Company's finding and development costs
could also increase.
 
     Operating Hazards and Uninsured Risks. The Company's operations are subject
to hazards and risks inherent in drilling for and producing and transporting oil
and natural gas, 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 oil and natural gas 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 financial condition and results of operations. In addition, pollution
and environmental risks generally are not fully insurable. See "Item 2.
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 herein 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 oil and natural gas 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 oil and natural gas 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 oil and natural gas 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 oil and natural gas 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 oil and natural
gas 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 "Item 2. Properties -- Oil and Natural Gas
Reserves."
 
     The Present Value of Future Net Revenues referred to herein should not be
construed as the current market value of the estimated oil and natural gas
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. From January 1, 1998 through
March 24, 1998, the price of natural gas on the NYMEX ranged from $2.00 per
MMBtu to $2.38 per MMBtu and the price of oil on the NYMEX ranged from $13.21
per Bbl to $17.82 per Bbl. Actual future net cash flows also will be affected by
factors such as the amount and timing of actual production, supply and demand
for oil and natural gas, 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 oil and natural gas
properties. In addition, the 10% discount factor, which must be used to
calculate discounted future net cash flows for reporting purposes, is not
necessarily the most appropriate discount factor
 
                                       28
<PAGE>   31
 
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 oil
and natural gas 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 oil and natural gas 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 oil and natural gas 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 environment could have a
material adverse effect on the Company. See "Item 1. Business -- 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 marketing of, oil and natural gas, 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 "Item 1. Business -- 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 "Item 1.
Business -- Environmental Matters."
 
     Risk of Hedging Activities. In an attempt to reduce its sensitivity to
energy price volatility, the Company uses swap arrangements that generally
result in a fixed price over a period of six to eighteen months. 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 oil and natural
gas 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. See "-- Other Matters -- Hedging
Activities."
 
     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 generally
delivers natural gas through gas gathering systems and gas pipelines that it
does not own. Federal and state regulation of oil and natural gas 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 oil and natural gas. Any dramatic change in market
factors could have a material adverse effect on the Company.
 
                                       29
<PAGE>   32
 
     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 oil and natural gas
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 Chief Executive Officer,
President 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, results of operations, development efforts and ability to
grow. There can be no assurance that the Company will be successful in
attracting and retaining such executives, geophysicists, geologists and
engineers. See "Item 1. Management -- Directors and Executive Officers" and
"Business -- Exploration Staff."
 
     Control by Existing Stockholders. As of March 24, 1998, directors,
executive officers and principal stockholders of the Company, and certain of
their affiliates, beneficially owned approximately 72% 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 make 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.
 
     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, 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.
 
ITEM 8. FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA
 
     The Company's Consolidated Financial Statements required by this item are
included on the pages immediately following the Index to Financial Statements
appearing on page F-1.
 
ITEM 9. CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND
        FINANCIAL DISCLOSURE
 
     None.
 
                                       30
<PAGE>   33
 
                                    PART III
 
ITEM 10. DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT
 
     The information required by this item is incorporated by reference to
information under the caption "Proposal 1 -- Election of Directors" and to the
information under the caption "Compliance with Section 16(a) of the Securities
Exchange Act of 1934" in the Company's definitive Proxy Statement (the "1998
Proxy Statement") for its annual meeting of stockholders to be held on May 29,
1998. The 1998 Proxy Statement will be filed with the Securities and Exchange
Commission (the "Commission") not later than 120 days subsequent to December 31,
1997.
 
     Pursuant to Item 401(b) of Regulation S-K, the information required by this
item with respect to executive officers of the Company is set forth in Part I of
this report.
 
ITEM 11. EXECUTIVE COMPENSATION
 
     The information required by this item is incorporated herein by reference
to the 1998 Proxy Statement, which will be filed with the Commission not later
than 120 days subsequent to December 31, 1997.
 
ITEM 12. SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT
 
     The information required by this item is incorporated herein by reference
to the 1998 Proxy Statement, which will be filed with the Commission not later
than 120 days subsequent to December 31, 1997.
 
ITEM 13. CERTAIN RELATIONSHIPS AND RELATED PARTY TRANSACTIONS
 
     The information required by this item is incorporated herein by reference
to the 1998 Proxy Statement, which will be filed with the Commission not later
than 120 days subsequent to December 31, 1997.
 
                                    PART IV
 
ITEM 14. EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K
 
     (a) 1. Consolidated Financial Statements:
 
             See Index to Consolidated Financial Statements on page F-1.
 
         2. Financial Statement Schedules:
 
             See Index to Consolidated Financial Statements on page F-1.
 
         3. Exhibits: The following documents are filed as exhibits to this
report:
 
<TABLE>
<CAPTION>
         NUMBER                                  DESCRIPTION
         ------                                  -----------
<C>                      <S>
         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).
</TABLE>
 
                                       31
<PAGE>   34
 
<TABLE>
<CAPTION>
         NUMBER                                  DESCRIPTION
         ------                                  -----------
<C>                      <S>
        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).
        10.2             -- 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).
        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 2, 1995, by and between
                            Brigham Oil & Gas, L.P. and Harold D. Carter (filed as
                            Exhibit 10.6 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        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).
</TABLE>
 
                                       32
<PAGE>   35
 
<TABLE>
<CAPTION>
         NUMBER                                  DESCRIPTION
         ------                                  -----------
<C>                      <S>
        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 Bridgepoint 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).
        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).
</TABLE>
 
                                       33
<PAGE>   36
 
<TABLE>
<CAPTION>
         NUMBER                                  DESCRIPTION
         ------                                  -----------
<C>                      <S>
        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).
        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).
</TABLE>
 
                                       34
<PAGE>   37
 
<TABLE>
<CAPTION>
         NUMBER                                  DESCRIPTION
         ------                                  -----------
<C>                      <S>
        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).
        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 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 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).
</TABLE>
 
                                       35
<PAGE>   38
 
<TABLE>
<CAPTION>
         NUMBER                                  DESCRIPTION
         ------                                  -----------
<C>                      <S>
        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).
        10.36            -- Credit Agreement dated as of January 26, 1998 among
                            Brigham Oil & Gas, L.P., Bank of Montreal, as Agent, and
                            the lenders signatory thereto.
        21               -- Subsidiaries of the Registrant.
        27               -- Financial Data Schedule.
</TABLE>
 
---------------
 
* Management contract or compensatory plan.
 
     (b) The following reports on Form 8-K were filed by the Company during the
last quarter of the period covered by this Annual Report on Form 10-K:
 
          Current Report on Form 8-K filed January 23, 1998.
 
                                       36
<PAGE>   39
 
                         GLOSSARY OF 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 of natural gas liquids.
 
     CAEX. Computer-aided exploration.
 
     Completion. The installation of permanent equipment for the production of
oil or natural gas.
 
     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 an oil or
natural gas 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 oil or natural
gas in sufficient quantities to justify completion of an oil or gas well.
 
     Exploratory Well. A well drilled to find and produce oil or natural gas in
an unproved area, to find a new reservoir in a field previously found to be
productive of oil or gas in another reservoir, or to extend a known reservoir.
 
     Finding and Development Costs. Capital costs incurred in the acquisition,
exploration and development of proved oil and natural gas 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 an oil or gas well or lease.
 
                                       37
<PAGE>   40
 
     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 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).
 
     Standardized Measure of Discounted Future Net Cash Flows. The aftertax
present value of estimated future revenues to be generated from the production
of proved reserves calculated in accordance with SEC guidelines, net of
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%.
 
     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 oil and natural gas on the
leased acreage and requires the owner to pay a share of the costs of drilling
and production operations.
 
                                       38
<PAGE>   41
 
                                   SIGNATURES
 
     Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the Registrant has duly caused this report to be signed on
its behalf by the undersigned, hereunder duly authorized, as of March 25, 1998.
 
                                            BRIGHAM EXPLORATION COMPANY
 
                                            By:     /s/ BEN M. BRIGHAM
                                              ----------------------------------
                                                        Ben M. Brigham
                                                 Chief Executive Officer and
                                                           President
 
     Pursuant to the requirements of the Securities Exchange Act of 1934, this
report has been signed below as of March 25, 1998, by the following persons on
behalf of the Registrant and in the capacity indicated.
 
<TABLE>
<CAPTION>
                  SIGNATURE                                          TITLE
                  ---------                                          -----
<C>                                              <S>
 
             /s/ BEN M. BRIGHAM                  Chief Executive Officer, President and
---------------------------------------------      Chairman of the Board
               Ben M. Brigham
 
             /s/ ANNE L. BRIGHAM                 Executive Vice President and Director
---------------------------------------------
               Anne L. Brigham
 
              /s/ JON L. GLASS                   Vice President -- Exploration and Director
---------------------------------------------
                Jon L. Glass
 
            /s/ CRAIG M. FLEMING                 Chief Financial Officer (principal financial
---------------------------------------------      and accounting officer)
              Craig M. Fleming
 
            /s/ HAROLD D. CARTER                 Director
---------------------------------------------
              Harold D. Carter
 
           /s/ ALEXIS M. CRANBERG                Director
---------------------------------------------
             Alexis M. Cranberg
 
             /s/ GARY J. MILAVEC                 Director
---------------------------------------------
               Gary J. Milavec
 
           /s/ STEPHEN P. REYNOLDS               Director
---------------------------------------------
             Stephen P. Reynolds
</TABLE>
 
                                       39
<PAGE>   42
 
                          BRIGHAM EXPLORATION COMPANY
 
                         INDEX TO FINANCIAL STATEMENTS
 
<TABLE>
<CAPTION>
                                                              PAGE
                                                              ----
<S>                                                           <C>
 
Financial Statements of Brigham Exploration Company
  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 as of
     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 Consolidated Financial Statements............  F-7
</TABLE>
 
                                       F-1
<PAGE>   43
 
                       REPORT OF INDEPENDENT ACCOUNTANTS
 
To the Board of Directors
and Stockholders of Brigham Exploration Company
 
     In our opinion, the accompanying consolidated balance sheets and the
related consolidated 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>   44
 
                          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         --
Commitments and contingencies
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>   45
 
                          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>   46
 
                          BRIGHAM EXPLORATION COMPANY
 
           CONSOLIDATED STATEMENT OF CHANGES IN 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 (Note 1)........          --      --        3,807            --         26             --       3,833
  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>   47
 
                          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>   48
 
                          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>   49
                          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.
 
  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
 
                                       F-8
<PAGE>   50
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
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>   51
                          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>   52
                          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, all of which was
immediately available for borrowing, 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>   53
                          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>   54
                          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 (Note 1), assuming such shares had 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>   55
                          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>   56
                          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 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-Sholes 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>   57
                          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 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
 
                                      F-16
<PAGE>   58
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
costs as operating labor, repairs and maintenance, materials, supplies and fuel
consumed. Production taxes include production and severance taxes. No provision
was made for income taxes for 1995 and 1996 since these taxes were 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>   59
                          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>   60
                          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, 1998, 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>   61
 
<TABLE>
<CAPTION>
         NUMBER                                  DESCRIPTION
         ------                                  -----------
<C>                      <S>
         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).
        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).
        10.2             -- 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).
        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 2, 1995, by and between
                            Brigham Oil & Gas, L.P. and Harold D. Carter (filed as
                            Exhibit 10.6 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        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).
</TABLE>
 
<PAGE>   62
 
<TABLE>
<CAPTION>
         NUMBER                                  DESCRIPTION
         ------                                  -----------
<C>                      <S>
        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 Bridgepoint 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).
        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).
</TABLE>
 
<PAGE>   63
 
<TABLE>
<CAPTION>
         NUMBER                                  DESCRIPTION
         ------                                  -----------
<C>                      <S>
        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).
        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).
</TABLE>
 
<PAGE>   64
 
<TABLE>
<CAPTION>
         NUMBER                                  DESCRIPTION
         ------                                  -----------
<C>                      <S>
        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).
        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 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 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).
</TABLE>
 
<PAGE>   65
 
<TABLE>
<CAPTION>
         NUMBER                                  DESCRIPTION
         ------                                  -----------
<C>                      <S>
        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).
        10.36            -- Credit Agreement dated as of January 26, 1998 among
                            Brigham Oil & Gas, L.P., Bank of Montreal, as Agent, and
                            the lenders signatory thereto.
        21               -- Subsidiaries of the Registrant.
        27               -- Financial Data Schedule.
</TABLE>
 
---------------
 
* Management contract or compensatory plan.
 
     (b) The following reports on Form 8-K were filed by the Company during the
last quarter of the period covered by this Annual Report on Form 10-K:
 
          Current Report on Form 8-K filed January 23, 1998.