<PAGE>   1
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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                           --------------------------

                                   FORM 10-Q



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

               FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1998

                                       OR

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

          FOR THE TRANSITION PERIOD FROM _____________TO_____________

                         COMMISSION FILE NO. 001-11899
                         -----------------------------

                        THE HOUSTON EXPLORATION COMPANY
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

          DELAWARE                                      22-2674487
(STATE OR OTHER JURISDICTION OF              (IRS EMPLOYER IDENTIFICATION NO.)
INCORPORATION OR ORGANIZATION)


                       1100 LOUISIANA STREET, SUITE 2000
                           HOUSTON, TEXAS 77002-5219
             (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES AND ZIP CODE)

                                 (713) 830-6800
              (REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE)
                           --------------------------



         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
                                              ----    ----

         As of November 11, 1998, 23,896,340 shares of Common Stock, par value
$.01 per share, were outstanding.

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<PAGE>   2
                        THE HOUSTON EXPLORATION COMPANY

                               TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                                       Page
                                                                                                       ----
<S>                                                                                                      <C>
FACTORS AFFECTING FORWARD LOOKING STATEMENTS  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

PART I.  FINANCIAL INFORMATION

Item 1.      Consolidated Financial Statements (unaudited)

             Consolidated Balance Sheets -- September 30, 1998 and December 31, 1997  . . . . . . . . . . 4

             Consolidated Statements of Operations -- Three Month and Nine Month Periods Ended
                 September 30, 1998 and 1997  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

             Consolidated Statements of Cash Flows -- Nine Month Periods Ended
                 September 30, 1998 and 1997  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

             Notes to Consolidated Financial Statements . . . . . . . . . . . . . . . . . . . . . . . . . 7

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

PART II.     OTHER INFORMATION

Item 6.      Exhibits and Reports on Form 8-K . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  20

SIGNATURES  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  21
</TABLE>
<PAGE>   3
                  FACTORS AFFECTING FORWARD LOOKING STATEMENTS

         This Quarterly Report on Form 10-Q contains certain "forward-looking
statements" within the meaning of Section 27A of the Securities Act of 1993, as
amended, and Section 21E of the Securities Exchange Act of 1934, as amended. The
words "anticipate," "believe," "expect," "estimate," "project" and similar
expressions are intended to identify forward-looking statements. Without
limiting the foregoing, all statements under the caption "Item 2--Management's
Discussion and Analysis of Financial Condition and Results of Operations"
relating to the Company's anticipated capital expenditures, future cash flows
and borrowings, pursuit of potential future acquisition opportunities and
sources of funding for exploration and development are forward-looking
statements. Such statements are subject to certain risks and uncertainties, such
as the volatility of natural gas and oil prices, uncertainty of reserve
information and future net revenue estimates, reserve replacement risks,
drilling risks, operating risks of natural gas and oil operations, acquisition
risks, substantial capital requirements, government regulation, environmental
matters and competition. Should one or more of these risks or uncertainties
materialize, or should underlying assumptions prove incorrect, actual results
may vary materially from those anticipated, believed, expected, estimated or
projected. For additional discussion of such risks, uncertainties and
assumptions, see "Items 1 and 2. Business and Properties" and "Item 7.
Management's Discussion and Analysis of Financial Condition and Results of
Operations" included in the Company's Annual Report on Form 10-K filed under the
Securities Act of 1934, as amended.

         Unless otherwise indicated, references to "Houston Exploration" or the
"Company" refer to The Houston Exploration Company and its subsidiaries on a
combined basis.





                                      -3-
<PAGE>   4
PART I.  FINANCIAL INFORMATION

ITEMS 1.  FINANCIAL STATEMENTS

                        THE HOUSTON EXPLORATION COMPANY
                          CONSOLIDATED BALANCE SHEETS
                                 (IN THOUSANDS)


<TABLE>
<CAPTION>
                                                                                      SEPTEMBER 30,   DECEMBER  31, 
                                                                                      --------------  --------------
                                                                                           1998            1997     
                                                                                      --------------  --------------
                                                                                       (UNAUDITED)
     <S>                                                                              <C>             <C>
     ASSETS:
     Cash and cash equivalents . . . . . . . . . . . . . . . . . . . . . . . . . .    $       810     $    4,745
     Accounts receivable . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         22,190         37,898
     Accounts receivable -- Brooklyn Union . . . . . . . . . . . . . . . . . . . .            637          1,303
     Inventories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          1,253          1,265
     Prepayments and other . . . . . . . . . . . . . . . . . . . . . . . . . . . .          1,168            645
                                                                                      -----------     ----------
               Total current assets  . . . . . . . . . . . . . . . . . . . . . . .         26,058         45,856
     Natural gas and oil properties, full cost method
       Unevaluated properties  . . . . . . . . . . . . . . . . . . . . . . . . . .        140,800        104,075
       Properties subject to amortization  . . . . . . . . . . . . . . . . . . . .        696,538        566,868
     Other property and equipment  . . . . . . . . . . . . . . . . . . . . . . . .          9,387          9,341
                                                                                      -----------     ----------
                                                                                          846,725        680,284
     Less: Accumulated depreciation, depletion and amortization  . . . . . . . . .       (295,771)      (236,546)
                                                                                      ------------    -----------
                                                                                          550,954        443,738
     Other assets  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          3,499          1,797
                                                                                      -----------     ----------
               TOTAL ASSETS  . . . . . . . . . . . . . . . . . . . . . . . . . . .    $   580,511     $  491,391
                                                                                      ===========     ==========
     LIABILITIES:
     Accounts payable and accrued expenses . . . . . . . . . . . . . . . . . . . .    $    35,325     $   42,432
     Deferred stock obligation . . . . . . . . . . . . . . . . . . . . . . . . . .             --          8,825
                                                                                      -----------     ----------
               Total current liabilities . . . . . . . . . . . . . . . . . . . . .         35,325         51,257
     Long-term debt  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        191,000        113,000
     Deferred federal income taxes . . . . . . . . . . . . . . . . . . . . . . . .         76,791         70,741
     Other deferred liabilities  . . . . . . . . . . . . . . . . . . . . . . . . .            156            206
                                                                                      -----------     ----------
               TOTAL LIABILITIES . . . . . . . . . . . . . . . . . . . . . . . . .        303,272        235,204
     COMMITMENTS AND CONTINGENCIES (SEE NOTE 4)

     STOCKHOLDERS' EQUITY:
       Common Stock, $.01 par value, 50,000 shares authorized and 23,896 shares
        issued and outstanding at September 30, 1998 and 23,361 shares issued
        and outstanding at December 31, 1997 . . . . . . . . . . . . . . . . . . .            239            234
       Additional paid-in capital  . . . . . . . . . . . . . . . . . . . . . . . .        230,922        221,907
       Retained earnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         46,078         34,046
                                                                                      -----------     ----------
               TOTAL STOCKHOLDERS' EQUITY  . . . . . . . . . . . . . . . . . . . .        277,239        256,187
                                                                                      -----------     ----------
               TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY  . . . . . . . . . . . .    $   580,511     $  491,391
                                                                                      ===========     ==========
</TABLE>




              The accompanying notes are an integral part of these
                       consolidated financial statements.





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<PAGE>   5
                        THE HOUSTON EXPLORATION COMPANY
                     CONSOLIDATED STATEMENTS OF OPERATIONS
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)


<TABLE>
<CAPTION>
                                                          THREE MONTHS ENDED,            NINE MONTHS ENDED,
                                                             SEPTEMBER 30,                 SEPTEMBER 30,      
                                                      --------------------------      ------------------------
                                                           1998         1997             1998         1997    
                                                      -------------  -----------      -----------  -----------
                                                                            (UNAUDITED)
<S>                                                   <C>            <C>              <C>          <C>        
 REVENUES:
   Natural gas and oil revenues  . . . . . . . . . .  $      30,545  $    29,065      $    98,570  $    76,129
   Other . . . . . . . . . . . . . . . . . . . . . .            308          247              878          731
                                                      -------------  -----------      -----------  -----------
           Total revenues  . . . . . . . . . . . . .         30,853       29,312           99,448       76,860
 OPERATING COSTS AND EXPENSES:
   Lease operating . . . . . . . . . . . . . . . . .          4,455        3,437           11,887        9,714
   Severance tax . . . . . . . . . . . . . . . . . .          1,249          908            3,717        2,644
   Depreciation, depletion and amortization  . . . .         19,759       15,517           59,264       39,472
   General and administrative, net . . . . . . . . .          1,463        1,385            4,745        4,341
                                                      -------------  -----------      -----------  -----------
           Total operating expenses  . . . . . . . .         26,926       21,247           79,613       56,171
 Income from operations  . . . . . . . . . . . . . .          3,927        8,065           19,835       20,689
 Interest expense, net . . . . . . . . . . . . . . .          1,279           65            2,529          494
                                                      -------------  -----------      -----------  -----------
 Net income before income taxes  . . . . . . . . . .          2,648        8,000           17,306       20,195
 Provision for federal income taxes  . . . . . . . .            645        2,475            5,274        5,535
                                                      -------------  -----------      -----------  -----------
 NET INCOME  . . . . . . . . . . . . . . . . . . . .  $       2,003  $     5,525      $    12,032  $    14,660
                                                      =============  ===========      ===========  ===========
 Net income per share  . . . . . . . . . . . . . . .  $        0.08  $      0.24      $      0.50  $      0.63
                                                      =============  ===========      ===========  ===========
 Net income per share -- assuming dilution . . . . .  $        0.08  $      0.23      $      0.50  $      0.61
                                                      =============  ===========      ===========  ===========
 
 Weighted average shares outstanding . . . . . . . .         23,896       23,333           23,725       23,333
 Weighted average shares outstanding -- assuming
     dilution  . . . . . . . . . . . . . . . . . . .         24,173       23,912           24,009       24,030
</TABLE>





              The accompanying notes are an integral part of these
                       consolidated financial statements





                                      -5-
<PAGE>   6
                        THE HOUSTON EXPLORATION COMPANY
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)


<TABLE>
<CAPTION>
                                                                                 NINE MONTHS ENDED SEPTEMBER 30, 
                                                                                 --------------------------------
                                                                                      1998             1997      
                                                                                 ---------------  ---------------
                                                                                           (UNAUDITED)
        <S>                                                                      <C>              <C>
        OPERATING ACTIVITIES:
        Net income  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    $   12,032       $    14,660
        Adjustments to reconcile net income to net cash
          provided by operating activities:
          Depreciation, depletion and amortization  . . . . . . . . . . . . .        59,264            39,472
          Deferred income tax expense . . . . . . . . . . . . . . . . . . . .         6,049             8,963
          Changes in operating assets and liabilities:
             Decrease in accounts receivable  . . . . . . . . . . . . . . . .        16,374             1,647
             Decrease (increase) in inventories . . . . . . . . . . . . . . .            12              (630)
             Increase in prepayments  . . . . . . . . . . . . . . . . . . . .          (523)             (842)
             Decrease (increase) in other assets and liabilities  . . . . . .        (1,752)              935
             Increase (decrease) in accounts payable and accrued expenses . .        (7,107)              609
                                                                                 -----------      -----------
        Net cash provided by operating activities . . . . . . . . . . . . . .        84,349            64,814

        INVESTING ACTIVITIES:
        Investment in property and equipment  . . . . . . . . . . . . . . . .      (166,482)          (98,530)
        Dispositions and other  . . . . . . . . . . . . . . . . . . . . . . .             --            1,360
                                                                                 -----------      -----------
        Net cash used in investing activities . . . . . . . . . . . . . . . .      (166,482)          (97,170)

        FINANCING ACTIVITIES:
        Proceeds from long term borrowings  . . . . . . . . . . . . . . . . .       187,000            50,000
        Repayments of long term borrowings  . . . . . . . . . . . . . . . . .      (109,000)          (17,000)
        Proceeds from issuance of common stock, net of offering costs . . . .           198              (141)
                                                                                 ----------       ------------
        Net cash provided by financing activities . . . . . . . . . . . . . .        78,198            32,859
                                                                                 ----------       -----------
        Increase (decrease) in cash and cash equivalents  . . . . . . . . . .        (3,935)              503
        Cash and cash equivalents, beginning of period  . . . . . . . . . . .         4,745             2,851
                                                                                 ----------       -----------
        Cash and cash equivalents, end of period  . . . . . . . . . . . . . .    $      810       $     3,354
                                                                                 ==========       ===========
        Cash paid for interest  . . . . . . . . . . . . . . . . . . . . . . .    $    7,661       $     4,021
                                                                                 ==========       ===========
        Cash paid for taxes . . . . . . . . . . . . . . . . . . . . . . . . .    $       --       $        --
                                                                                 ==========       ===========
</TABLE>


              The accompanying notes are an integral part of these
                       consolidated financial statements.





                                      -6-
<PAGE>   7
                        THE HOUSTON EXPLORATION COMPANY
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                  (UNAUDITED)

NOTE 1 -- SUMMARY OF ORGANIZATION AND SIGNIFICANT ACCOUNTING POLICIES

         Organization

         The Houston Exploration Company ("Houston Exploration" or the
"Company"), a Delaware corporation, was incorporated in December 1985 and began
operations in January 1986 for the purpose of conducting certain natural gas and
oil exploration and development activities for The Brooklyn Union Gas Company
("Brooklyn Union"). Brooklyn Union became a subsidiary of MarketSpan Corporation
on May 29, 1998 through the combination of Brooklyn Union's parent company,
KeySpan Energy Corporation, and Long Island Lighting Company. Effective February
29, 1996, Brooklyn Union implemented a reorganization of its exploration and
production assets by transferring to Houston Exploration certain onshore
producing properties and developed and undeveloped acreage. On July 2, 1996, the
Company acquired certain natural gas and oil properties and associated pipelines
located in Zapata County, Texas (the "TransTexas Acquisition") from TransTexas
Gas Corporation and TransTexas Transmission Corporation (together,
"TransTexas"). In September 1996, the Company completed its initial public
offering ("IPO") of 7,130,000 shares of its Common Stock at $15.50 per share,
resulting in net cash proceeds of approximately $101.0 million. Concurrently
with the completion of the IPO, the Company completed the acquisition (the
"Soxco Acquisition") of substantially all of the natural gas and oil properties
and related assets of Smith Offshore Exploration Company ("Soxco"). As of
September 30, 1998, THEC Holdings Corp., a wholly-owned subsidiary of Brooklyn
Union, holds approximately 64% of the outstanding shares of the Company's common
stock. The Company's operations focus on the exploration, development and
acquisition of domestic natural gas and oil properties offshore in the Gulf of
Mexico and onshore in South Texas, the Arkoma Basin, East Texas, West Virginia
and South Louisiana.

         Principles of Consolidation

         The consolidated financial statements include the accounts of The
Houston Exploration Company and its wholly- owned subsidiary, Seneca Upshur
Petroleum Company (collectively the "Company").  All significant intercompany
balances and transactions have been eliminated.

         Interim Financial Statements

         The balance sheet of the Company at September 30, 1998 and the
statements of operations and cash flows for the periods indicated herein have
been prepared by the Company without audit, pursuant to the rules and
regulations of the Securities and Exchange Commission.  Certain information and
footnote disclosures normally included in financial statements prepared in
accordance with generally accepted accounting principles have been condensed or
omitted, although the Company believes that the disclosures contained herein
are adequate to make the information presented not misleading.  The balance
sheet at December 31, 1997 is derived from the December 31, 1997 audited
financial statements, but does not include all disclosures required by
generally accepted accounting principles.  The Interim Financial Statements
should be read in conjunction with the Consolidated Financial Statements and
Notes thereto included in the Company's Annual Report on Form 10-K for the year
ended December 31, 1997.

         In the opinion of management, all adjustments, consisting of normal
recurring accruals, necessary to present fairly the information in the
accompanying financial statements have been included.  The results of
operations for such interim periods are not necessarily indicative of the
results for the full year.

         Reclassifications and Use of Estimates

         The preparation of the 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 dates of the financial
statements and the reported amounts of revenues and expenses during the
reporting periods. The Company's most significant financial estimates are based
on remaining





                                      -7-
<PAGE>   8
proved natural gas and oil reserves.  Because there are numerous uncertainties
inherent in the estimation process, actual results could differ from the
estimates. Certain reclassifications for prior years have been made to conform
with current year presentation.

         Net Income Per Share

         Basic earnings per share ("EPS") is calculated by dividing net income
by the weighted average number of shares of common stock outstanding during the
period.  No dilution for any potentially dilutive securities is included.
Diluted EPS assumes the conversion of all potentially dilutive securities and
is calculated by dividing net income by the weighted average number of shares
common stock outstanding plus all potentially dilutive securities.

         Under the requirements of Statement of Financial Accounting Standards
("SFAS") No. 128, the Company's EPS are as follows:

<TABLE>
<CAPTION>
                                                                   THREE MONTHS ENDED,        NINE MONTHS ENDED,
                                                                     SEPTEMBER 30,               SEPTEMBER 30,                   
                                                                  --------------------      --------------------
                                                                   1998         1997         1998         1997                  
                                                                  -------      -------      -------      -------
                                                                     (IN THOUSANDS, EXCEPT PER SHARE DATA)
<S>                                                               <C>          <C>          <C>          <C>    
     Net income ............................................      $ 2,003      $ 5,525      $12,032      $14,660
                                                                  =======      =======      =======      =======
     Denominator:
     Weighted average shares outstanding ...................       23,896       23,333       23,725       23,333
     Add: dilutive securities ..............................
           Options .........................................          277          185          284          153
           Contingent shares ...............................           --          394           --          544
                                                                  -------      -------      -------      -------
     Total weighted average shares outstanding and dilutive
       securities ..........................................       24,173       23,912       24,009       24,030
                                                                  =======      =======      =======      =======

     Net income per share ..................................      $  0.08      $  0.24      $  0.50      $  0.63
                                                                  =======      =======      =======      =======
     Net income per share -- assuming dilution .............      $  0.08      $  0.23      $  0.50      $  0.61
                                                                  =======      =======      =======      =======
 </TABLE>


         New Accounting Pronouncements

         In June 1998, the Financial Accounting Standards Board ("FASB") issued
SFAS No. 133, "Accounting for Derivative Instruments and Hedging Activities."
This statement broadens the definition of a derivative instrument and
establishes accounting and reporting standards requiring that every derivative
instrument, including certain derivative instruments embedded in other
contracts, be recorded in the balance sheet as either an asset or liability
measured at its fair market value.  The statement requires that changes in the
derivative instrument's fair value be recognized currently in earnings unless
specific hedge accounting criteria are met.  Special accounting for qualifying
hedges allows a derivative instrument's gains and losses to offset related
results on the hedged item in the income statement, and requires that a company
must formally document, designate and assess the effectiveness of transactions
that receive hedge accounting.  The statement cannot be applied retroactively
and must be applied to (i) derivative instruments and (ii) certain derivative
instruments embedded in hybrid contracts that were issued, acquired or
substantively modified after December 31, 1997.  The Company plans to adopt
SFAS No. 133 effective January 1, 2000.  Currently, the Company cannot estimate
the impact of the statement on results of future operations; however, it
believes that the impact will not be material.





                                      -8-
<PAGE>   9
NOTE 2 -- LONG-TERM DEBT

         Long-term debt consisted of the following:

<TABLE>
<CAPTION>
                                                             SEPTEMBER 30,  DECEMBER 31,
                                                                 1998           1997    
                                                            -------------   ------------
                                                                    (IN THOUSANDS)
           <S>                                              <C>             <C>
           Bank revolving credit facility ................      $ 91,000      $113,000
           8 5/8% Senior Subordinated Notes, due 2008 ....       100,000            --
                                                                --------      --------
               Total long-term debt ......................      $191,000      $113,000
                                                                ========      ========
 </TABLE>


         Credit Facility

         The Company has entered into a revolving credit facility ("Credit
Facility") with a syndicate of lenders led by Chase Bank of Texas, National
Association ("Chase"), which provides a maximum commitment of $150 million,
subject to borrowing base limitations.  The Credit Facility was amended in
March 1998 in connection with the Company's private placement of $100 million
of senior subordinated notes and as of September 30, 1998, the available
borrowing base was $135 million.  In addition, up to $5 million of the Credit
Facility is available for the issuance of letters of credit to support
performance guarantees.  The Credit Facility matures on July 1, 2000 and is
unsecured.  At September 30, 1998, $91.0 million was outstanding under the
Credit Facility and $0.4 million was outstanding in letter of credit
obligations.  Subsequent to September 30, 1998, the Company borrowed an
additional $28.5 million under the Credit Facility to fund the acquisition of
additional properties in South Louisiana and to make a downpayment of $8.5
million on the pending acquisition of certain properties in the Gulf of Mexico
(see Note 6 -- Acquisitions).  The Company intends to amend the Credit Facility
prior to December 1, 1998 so that the $85.3 million purchase price of the
pending acquisition of such properties, if completed, can be financed with
borrowings under the Credit Facility.

         Interest is payable on borrowings under the Credit Facility, at the
Company's option, at (i) a fluctuating rate ("Base Rate") equal to the greater
of the Federal Funds rate plus 0.5% or Chase's prime rate, or (ii) a fixed rate
("Fixed Rate") equal to a quoted LIBOR rate plus a margin of 0.375% to 1.125%,
depending on the amount outstanding under the Credit Facility.  Interest is
payable at calendar quarters for Base Rate loans and at the earlier of maturity
or three months from the date of the loan for Fixed Rate loans. In addition,
the Credit Facility requires a commitment fee of: (i) between 0.20% and 0.375%
per annum on the unused portion of the Designated Borrowing Base, and (ii) 33%
of the fee in (i) above on the difference between the lower of the Facility
Amount or the Borrowing Base and the Designated Borrowing Base.

         The Credit Facility, as amended, contains covenants of the Company,
including certain restrictions on liens and financial covenants which require
the Company to, among other things, maintain (i) an interest coverage ratio of
2.5 to 1.0 of earnings before interest, taxes and depreciation ("EBITDA") to
cash interest and (ii) a total debt to capitalization ratio of less than 60%.
In addition to maintenance of certain financial ratios, cash dividends and/or
purchase or redemption of the Company's stock is restricted as well as the
encumbering of the Company's gas and oil assets or the pledging of the assets
as collateral. As of September 30, 1998, the Company was in compliance with all
such covenants.

         Senior Subordinated Notes

         On March 2, 1998, the Company issued $100 million of 8 5/8% Senior
Subordinated Notes (the "Notes") due January 1, 2008 in a private placement to
qualified institutional buyers.  The Notes bear interest at a rate of 8 5/8%
per annum with interest payable semi-annually on January 1 and July 1,
commencing July 1, 1998.  The Notes are redeemable at the option of the
Company, in whole or in part, at any time on or after January 1, 2003 at a
price equal to 100% of the principal amount plus accrued and unpaid interest,
if any, plus a specified premium if the Notes are redeemed prior to January 1,
2006.  Notwithstanding the foregoing, any time prior to January 1, 2001, the
Company may redeem up to 35% of the original aggregate principal amount of the
Notes with the net proceeds of any equity offering, provided that at least 65%
of the original aggregate principal amount of the Notes remains outstanding
immediately after the occurrence of such redemption.  Upon the occurrence of a
change of control (as defined), the Company will be





                                      -9-
<PAGE>   10
required to offer to purchase the Notes at a purchase price equal to 101% of
the aggregate principal amount thereof, plus accrued and unpaid interest, if
any.  The Notes are general unsecured obligations of the Company and rank
subordinate in right of payment to all existing and future senior debt,
including the Credit Facility, and will rank senior or pari passu in right of
payment to all existing and future subordinated indebtedness.

NOTE 3 -- STOCKHOLDERS' EQUITY

         Soxco Deferred Purchase Price

           On September 25, 1996, the Company completed the Soxco Acquisition
and acquired substantially all of the natural gas and oil properties and
related assets of Soxco.  Pursuant to the Soxco Acquisition, the Company paid
Soxco cash in the aggregate amount of $20.3 million (net of $3.4 million for
certain purchase price adjustments), and issued to Soxco 762,387 shares of
common stock with an aggregate value (determined by reference to the IPO price)
of $11.8 million. The cash portion of the purchase price was funded with the
proceeds of the IPO.  In addition to the foregoing, on March 27, 1998, the
Company issued 520,777 shares of common stock with an aggregate value
(determined by reference to the average price of the Company's common stock
over a specified period of 20 trading days) of $8.8 million to Soxco in payment
of the deferred purchase price.

NOTE 4 -- COMMITMENTS AND CONTINGENCIES

         The Company is involved from time to time in various claims and
lawsuits incidental to its business.  In the opinion of management, the
ultimate liability thereunder, if any, will not have a material adverse effect
on the financial position or results of operations of the Company.

NOTE 5 -- RELATED PARTY TRANSACTIONS

         Sale of Section 29 Tax Credits

         Effective January 1, 1997, the Company entered into an agreement to
sell to a subsidiary of Brooklyn Union certain interests in onshore producing
wells of the Company that produce from formations that qualify for tax credits
under Section 29 of the Internal Revenue Code ("Section 29"). Section 29
provides for a tax credit from non-conventional fuel sources such as oil
produced from shale and tar sands and natural gas produced from geopressured
brine, Devonian shale, coal seams and tight sands formations. Brooklyn Union
acquired an economic interest in wells that are qualified for the tax credits
and in exchange, the Company (i) retained a volumetric production payment and a
net profits interest of 100% in the properties, (ii) received a cash down
payment of $1.4 million and (iii) receives a quarterly payment of $0.75 for
every dollar of tax credit utilized. The Company will manage and administer the
daily operations of the properties in exchange for an annual management fee of
$100,000. At December 31, 1997, the balance sheet effect of this transaction
was a $1.4 million reduction to the full cost pool for the down payment. The
income statement effect for the three months ended September 30, 1998 and 1997
was a reduction to income tax expense of $0.3 million and $0.3 million,
respectively, and $0.8 million and $1.2 million, respectively, for the nine
months ended September 30, 1998 and 1997, representing benefits received from
the Section 29 tax credits.

NOTE 6 -- ACQUISITIONS

         South Louisiana Acquisition

         On April 29, 1998, the Company completed the acquisition of certain
natural gas and oil properties and associated gathering pipelines and
equipment, together with developed and undeveloped acreage, located in South
Louisiana (the "South Louisiana Acquisition").  The properties and acreage
acquired are located primarily in the South Lake Arthur and Lake Pagie Fields,
located primarily in Vermilion Parish and Terrebonne Parish, respectively.  The
properties purchased represented approximately 41 Bcfe of net proved reserves
as of November 1, 1997, and currently contain approximately 64 producing wells.
The average net production in September 1998 attributable to such properties
was approximately 11 MMcfe per day, net to the interest acquired by the
Company.  The purchase price of  $53.2 million





                                      -10-
<PAGE>   11
(net of approximately $0.7 million for certain purchase price adjustments) was
paid in cash, financed with borrowings under the Credit Facility.

         On October 16, 1998, the Company completed the acquisition of
additional working interests in approximately 25 wells located in the South
Lake Arthur Field.  The natural gas and oil properties acquired consisted
solely of incremental working interests in properties in which the Company had
acquired a working interest via the South Louisiana Acquisition.  The working
interests acquired represented approximately 18 Bcfe of net proved reserves as
of September 1, 1998.  During September 1998, production averaged approximately
5 MMcfe per day, net to the interest acquired by the Company.  The purchase
price of $20.0 million will be adjusted for production revenues and operating
expenses related to the acquired working interests between the September 1,
1998 effective date of the acquisition and the October 16, 1998 closing date.
The purchase price was paid in cash, financed with borrowings under the Credit
Facility.

         Pending Acquisition

         On November 5, 1998, the Company entered into an agreement to acquire
from Chevron U.S.A. Production Company ("Chevron") a 100% working interest in
Chevron's Mustang Island A-31 Field in the Gulf of Mexico (the "Pending
Acquisition").  The Mustang Island A-31 Field is comprised of three adjacent
blocks:  Mustang Island A-22, A-31 and A- 32.  The field has nine producing
wells and three platforms.  The Company expects to complete the Pending
Acquisition effective December 1, 1998.  The Company expects that the estimated
net proved reserves associated with the properties to be acquired in the
Pending Acquisition will be approximately 69 Bcfe as of the December 1, 1998
effective date, and that daily production, net to the interest to be acquired,
will be approximately 37 MMcfe per day.  The purchase price of $85.3 million
will be paid in cash, financed by borrowings under the Credit Facility.  The
completion of the Pending Acquisition is subject to numerous conditions,
including the completion of due diligence and the negotiation and execution of
binding agreements, among others; accordingly, no assurances can be made that
the Pending Acquisition will be consummated.





                                      -11-
<PAGE>   12
Item 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
RESULTS OF OPERATIONS

         The following discussion is intended to assist in an understanding of
the Company's historical financial position and results of operations for the
three months and the nine months ended September 30, 1997 and 1998.  The
Company's consolidated financial statements and notes thereto included
elsewhere in this report contain detailed information that should be referred
to in conjunction with the following discussion.

GENERAL

         The Houston Exploration Company ("Houston Exploration" or the
"Company") was incorporated in December 1985 to conduct certain of the natural
gas and oil exploration and development activities of The Brooklyn Union Gas
Company ("Brooklyn Union").  Brooklyn Union became a subsidiary of MarketSpan
Corporation on May 29, 1998 through the combination of Brooklyn Union's parent
company, KeySpan Energy Corporation, and Long Island Lighting Company.  The
Company initially focused primarily on the exploration and development of high
potential prospects in the Gulf of Mexico.  Effective February 29, 1996,
Brooklyn Union implemented a reorganization of its exploration and production
assets by transferring to Houston Exploration certain onshore producing
properties and developed and undeveloped acreage.  Subsequent to the
reorganization, the Company has expanded its focus to include lower risk
exploitation and development drilling on the onshore properties transferred or
acquired, in addition to seeking opportunistic acquisitions both onshore and
offshore.  On July 2, 1996, the Company acquired certain natural gas and oil
properties and associated pipelines located in Zapata County, Texas (the
"TransTexas Acquisition") from TransTexas Gas Corporation and TransTexas
Transmission Corporation (together, "TransTexas").  In September 1996, the
Company completed its initial public offering ("IPO") of 7,130,000 shares of
its Common Stock at $15.50 per share, resulting in net cash proceeds of
approximately $101.0 million.  Concurrently with the completion of the IPO, the
Company completed the acquisition (the "Soxco Acquisition") of substantially
all of the natural gas and oil properties and related assets of Smith Offshore
Exploration Company ("Soxco").  On April 29, 1998 and October 16, 1998, the
Company completed the acquisition (the "South Louisiana Acquisition") of
certain natural gas and oil properties and associated gathering pipelines and
equipment, together with developed and undeveloped acreage located in the South
Lake Arthur and Lake Pagie Fields in South Louisiana.  As of September 30,
1998, THEC Holdings Corp., a wholly owned subsidiary of Brooklyn Union, owned
approximately 64% of the outstanding shares of the Company's common stock.  At
December 31, 1997, the Company had net proved reserves of 337 Bcfe, 98% of
which were natural gas and 78% of which were classified as proved developed.

         The Company's revenue, profitability and future rate of growth are
substantially dependent upon prevailing prices for natural gas, oil and
condensate, which are dependent upon numerous factors beyond the Company's
control, such as economic, political and regulatory developments and
competition from other sources of energy.  The energy markets have historically
been highly volatile, and future decreases in natural gas and oil prices could
have a material adverse effect on the Company's financial position, results of
operations, quantities of natural gas and oil reserves that may be economically
produced, and access to capital.

         The Company uses the full cost method of accounting for its investment
in natural gas and oil properties.  Under the full cost method of accounting,
all costs of acquisition, exploration and development of natural gas and oil
reserves are capitalized into a "full cost pool" as incurred, and properties in
the pool are depleted and charged to operations using the unit-of-production
method based on the ratio of current production to total proved natural gas and
oil reserves.  To the extent that such capitalized costs (net of accumulated
depreciation, depletion and amortization and related deferred taxes) exceed the
present value (using a 10% discount rate) of estimated future net after tax
cash flows from proved natural gas and oil reserves and the lower of cost or
fair value of unproved properties, such excess costs are charged to operations.
If a write-down is required, it would result in a charge to earnings but would
not have an impact on cash flows from operating activities.  Once incurred, a
write-down of oil and gas properties is not reversible at a later date even if
oil and gas prices increase.

         As of September 30, 1998, the Company estimates, using September
prices, that actual capitalized costs of natural gas and oil properties
exceeded the ceiling limitation imposed under full cost accounting rules by
approximately $58.6 million, after taxes.  Subsequent to September 30, 1998,
however, natural gas prices increased substantially, such that the Company
estimates, using October prices, that the ceiling limitation exceeded actual
capitalized costs of natural





                                      -12-
<PAGE>   13
gas and oil properties by approximately $5.6 million, after taxes.  As a
result, the Company is not required to write down of the carrying value of its
natural gas and oil properties as of September 30, 1998.  However, natural gas
prices continue to experience volatility; thus, depending upon the strength of
natural gas prices and the results of the Company's current drilling programs,
the Company may be required to write down the carrying value of its natural gas
and oil properties at the end of the fourth quarter of 1998.

         In June 1998, the Financial Accounting Standards Board ("FASB") issued
SFAS No. 133, "Accounting for Derivative Instruments and Hedging Activities."
This statement broadens the definition of a derivative instrument and
establishes accounting and reporting standards requiring that every derivative
instrument, including certain derivative instruments embedded in other
contracts, be recorded in the balance sheet as either an asset or liability
measured at its fair market value.  The statement requires that changes in the
derivative instrument's fair value be recognized currently in earnings unless
specific hedge accounting criteria are met.  Special accounting for qualifying
hedges allows a derivative instrument's gains and losses to offset related
results on the hedged item in the income statement, and requires that a company
must formally document, designate and assess the effectiveness of transactions
that receive hedge accounting.  The statement cannot be applied retroactively
and must be applied to (i) derivative instruments and (ii) certain derivative
instruments embedded in hybrid contracts that were issued, acquired or
substantively modified after December 31, 1997.  The Company plans to adopt
SFAS No. 133 effective January 1, 2000.  Currently, the Company cannot estimate
the impact of the statement on results of future operations; however, it
believes that the impact will not be material.

         Year 2000 issues result from the inability of computer programs or
computerized equipment to accurately calculate, store or use a date subsequent
to December 31, 1999.  The erroneous date can be interpreted in a number of
different ways; typically the year 2000 is represented as the year 1900.  This
could result in a system failure or miscalculations causing disruptions of
operations, including, among other things, a temporary inability to process
transactions, send invoices or engage in normal business.

         To ensure year 2000 compliance, the Company has implemented a year
2000 review of all financial and operational systems and equipment.  The
assessment phase has been completed, and the Company is currently in the
remediation phase and plans to begin testing systems and equipment in the first
quarter of 1999.  Based on reviews to date and preliminary information, the
Company does not anticipate that it will incur any significant costs relating
to the assessment and remediation of year 2000 issues.  The Company believes
that the potential impact, if any, of its systems not being year 2000 compliant
should not affect the Company's ability to continue exploration, drilling,
production and sales activities.  However, there can be no guarantee that the
Company, its business partners, vendors or customers will successfully be able
to identify and remedy all potential year 2000 problems and that a resulting
system failure would not have a material adverse effect on the Company.





                                      -13-
<PAGE>   14
RESULTS OF OPERATIONS

         The following table sets forth the Company's historical natural gas
and oil production data during the periods indicated:

<TABLE>
<CAPTION>
                                                            THREE MONTHS ENDED,              NINE MONTHS ENDED,
                                                               SEPTEMBER 30,                    SEPTEMBER 30,    
                                                         --------------------------      --------------------------
                                                            1998            1997            1998            1997   
                                                         ----------      ----------      ----------      ----------
<S>                                                      <C>             <C>             <C>             <C>   
          PRODUCTION:
              Natural gas (MMcfe) .................          15,122          13,330          46,118          35,147
              Oil (MBbls) .........................              60              39             164             111
              Total (MMcfe) .......................          15,482          13,564          47,102          35,813

          AVERAGE SALES PRICES:
              Natural gas (per Mcf) realized(1) ...      $     1.98      $     2.13      $     2.09      $     2.11
              Natural gas (per Mcf) unhedged ......            1.84            2.25            2.01            2.31
              Oil (per Bbl) .......................           11.00           17.79           12.65           18.71

          EXPENSES (PER MCFE):
              Lease operating .....................      $     0.29      $     0.25      $     0.25      $     0.27
              Severance tax .......................            0.08            0.07            0.08            0.07
              Depreciation, depletion and
                amortization ......................            1.28            1.14            1.26            1.10
              General and administrative, net .....            0.09            0.10            0.10            0.12
 </TABLE>

----------

(1)      Reflects the effects of hedging.


RECENT FINANCIAL AND OPERATING RESULTS

COMPARISON OF THREE MONTHS ENDED SEPTEMBER 30, 1997 AND 1998

         Production.  Houston Exploration's production increased 14% from
13,564 MMcfe for the three months ended September 30, 1997 to 15,482 MMcfe for
the three months ended September 30, 1998.  The increase in production was
primarily attributable to the Company's continued successful development
drilling program in the Charco Field and the addition of new production from
wells acquired in the South Louisiana Acquisition completed April 29, 1998.
The Company has brought on-line 21 new Charco wells since September 30, 1997
and daily production has increased approximately 40% from 58 MMcfe/day during
the third quarter of 1997, to 81 MMcfe/day during the third quarter of 1998.
The onshore production growth, however, was offset by offshore production
curtailments caused by tropical storms Charlie and Frances and hurricanes Earl
and Georges during August and September 1998.  In addition to shut-ins for
tropical weather, High Island 38 encountered mechanical problems and was
shut-in the first week of August 1998.  High Island 38 came on-line in January
1998 and was producing approximately 10 MMcfe/day, net to the Company's
interest.  Because of hurricanes Earl and Georges during September, the
workover was interrupted.  The Company expects the High Island 38 workover to
be completed by the first half of November 1998.

         Natural Gas and Oil Revenues.  Natural gas and oil revenues increased
5% from $29.1 million for the three months ended September 30, 1997 to $30.5
million for the three months ended September 30, 1998 as a result of the 14%
increase in production offset in part by a 7% decrease in average realized
natural gas prices, from $2.13 per Mcf for the three months ended September 30,
1997 to $1.98 per Mcf for the three months ended September 30, 1998.

         As a result of hedging activities, the Company realized an average gas
price of $1.98 per Mcf for the three months ended September 30, 1998, which was
108% of the unhedged natural gas price of $1.84 per Mcf that otherwise would
have been received, resulting in a $2.1 million increase in natural gas
revenues for the three months ended September 30, 1998.  For the corresponding
three month period of 1997, the average realized gas price was $2.13 per





                                      -14-
<PAGE>   15
Mcf, which was 95% of the unhedged average gas price of $2.25 per Mcf,
resulting in a decrease in natural gas revenues of $1.6 million for the three
months ended September 30, 1997.

         Lease Operating Expenses and Severance Tax.  Lease operating expenses
increased 29% from $3.4 million for the three months ended September 30, 1997
to $4.4 million for the three months ended September 30, 1998.  On an Mcfe
basis, lease operating expenses increased 16% from $0.25 for the three months
ended September 30, 1997 to $0.29 for the three months ended September 30,
1998. The increase in lease operating expenses during the third quarter of 1998
is attributable to the continued expansion of operations in the Charco Field,
combined with new offshore producing properties and the addition of the South
Louisiana properties acquired in April 1998.  On a per unit basis, the increase
lease operating expenses reflects the addition of new producing properties as
well as the effect of curtailed offshore production caused by tropical storms
and hurricanes in the Gulf of Mexico during August and September 1998.
Severance tax, which is a function of volume and revenues generated from
onshore production, increased 33% from $0.9 million for the three months ended
September 30, 1997 to $1.2 million for the three months ended September 30,
1998.  On an Mcfe basis, severance tax increased from $0.07 per Mcfe, for the
three months of 1997 to $0.08 per Mcfe, for the third quarter of 1998.  The
increase in both the severance tax expense and the rate per Mcfe is due to the
increase in the Company's onshore production from the Charco Field and the
addition of the onshore South Louisiana properties acquired in April 1998.

         Depreciation, Depletion and Amortization.  Depreciation, depletion and
amortization expense increased 27% from $15.5 million for the three months
ended September 30, 1997 to $19.7 million for the three months ended September
30, 1998.  Depreciation, depletion and amortization expense per Mcfe increased
12% from $1.14 for the three months ended September 30, 1997 to $1.28 for the
corresponding three months of 1998.  The increase in depreciation, depletion
and amortization expense was a result of the increased production from
newly-developed properties combined with an increased depletion rate.  The
increase in the depletion rate is attributable a higher level of capital
spending in 1998 as compared to 1997.

         General and Administrative Expenses.  General and administrative
expenses, net of overhead reimbursements received from other working interest
owners of $0.2 million and $0.3 million for the three months ended September
30, 1997 and 1998, respectively, increased 7% from $1.4 million for the three
months ended September 30, 1997 to $1.5 million for the three months ended
September 30, 1998.  The increase in general and administrative expenses
reflects the continued growth and expansion of the Company and its operations.
As the Company continues to grow and expand its workforce, the Company expects
aggregate general and administrative expenses to increase.  The Company
capitalized general and administrative expenses directly related to oil and gas
exploration and development activities of $1.8 million and $2.0 million,
respectively, for the three months ended September 30, 1997 and 1998.  The
increase in capitalized general and administrative expenses directly
corresponds with the growth of the Company's technical workforce and the
continued expansion of exploration and drilling operations.  On an Mcfe basis,
general and administrative expenses decreased 10% from $0.10 for the three
months ended September 30, 1997 to $0.09 for the three months ended September
30, 1998.  The lower rate per Mcfe during the third quarter of 1998 is
attributable to the increase in the Company's production.

         Interest Expense, Net.  Interest expense, net of capitalized interest,
increased from $0.1 million for the three months ended September 30, 1997 to
$1.3 million for the three ended September 30, 1998.  Capitalized interest
increased from $1.7 million for three months ended September 30, 1997 to $2.5
million for the three months ended September 30, 1998.  The increase in
aggregate interest expense was attributable to higher average debt levels
during the third quarter of 1998.  With the issuance of $100 million of senior
subordinated indebtedness in March 1998, the Company expects its 1998 average
debt levels to exceed those in 1997 and, accordingly, expects an increase in
net interest expense.

         Income Tax Provision.  The provision for income taxes decreased 76%
from an expense of $2.5 million for the three months ended September 30, 1997
to an expense of $0.6 million for the corresponding period of 1998.  The
decrease in income tax expense for the three months ended September 30, 1998 as
compared to the corresponding period of 1997 is due to the 68% decrease in
pretax income for the three months ended September 30, 1998.

         Operating Income and Net Income.  Although production increased 14%
for the quarter ended September 30, 1998 as compared to the corresponding
quarter of 1997, natural gas prices decreased 7% and operating expenses





                                      -15-
<PAGE>   16
increased 27%, causing operating income to decrease 52% from $8.1 million for
the three months ended September 30, 1997 to $3.9 million for the three months
ended September 30, 1998.  Net income decreased 64% from $5.5 million for the
three months ended September 30, 1997 to $2.0 million for the three months
ended September 30, 1998, reflecting higher interest expense during the third
quarter of 1998.


Comparison of Nine Months Ended September 30, 1997 and 1998

         Production.  Houston Exploration's production increased 32% from
35,813 MMcfe for the nine months ended September 30, 1997 to 47,102 MMcfe for
the nine months ended September 30, 1998.  The increase in production was
primarily attributable to significant newly-developed production in the Charco
Field, combined with new offshore production brought on-line since June 1997
and added production from wells acquired in the South Louisiana Acquisition,
which was completed in April 1998.

         Natural Gas and Oil Revenues.  Natural gas and oil revenues increased
30% from $76.1 million for the nine months ended September 30, 1997 to $98.6
million for the nine months ended September 30, 1998 as a result of the 32%
increase in production combined with a 1% decrease in average realized natural
gas prices, from $2.11 per Mcf in the nine months ended September 30, 1997 to
$2.09 per Mcf in the nine months ended September 30, 1998.

         As a result of hedging activities, the Company realized an average gas
price of $2.09 per Mcf for the nine months ended September 30, 1998, which was
104% of the unhedged natural gas price of $2.01 per Mcf that otherwise would
have been received, resulting in a $3.9 million increase in natural gas
revenues for the nine month period.  For the nine months ended September 30,
1997, the average realized gas price was $2.11 per Mcf, which was 91% of the
unhedged average gas price of $2.31, resulting in a decrease to natural gas
revenues of $7.3 million for the nine month period.

         Lease Operating Expenses and Severance Tax.  Lease operating expenses
increased 23% from $9.7 million for the nine months ended September 30, 1997 to
$11.9 million for the nine months ended September 30, 1998.  On an Mcfe basis,
lease operating expenses decreased 7% from $0.27 for the first nine months of
1997 to $0.25 for the first nine months of 1998.  The increase in lease
operating expenses during the first nine months of 1998 is attributable to the
significant expansion of operations in the Charco Field, combined with new
offshore producing properties and the addition of the South Louisiana
properties acquired in April 1998.  The decrease in the lease operating
expenses per Mcfe resulted from the 32% increase in production during the first
nine months of 1998 as compared to the corresponding period of 1997.  Severance
tax, which is a function of volume and revenues generated from onshore
production, increased 42% from $2.6 million for the nine months ended September
30, 1997 to $3.7 million for the nine months ended September 30, 1998.  On an
Mcfe basis, severance tax increased from $0.07 per Mcfe for the nine months
ended September 30, 197 to $0.08 per Mcfe for the nine month periods ended
September 30, 1998.  The increase in severance tax expense and the rate per
Mcfe reflects the added onshore production both at Charco and in South
Louisiana during 1998.

         Depreciation, Depletion and Amortization.  Depreciation, depletion and
amortization expense increased 50%  from $39.5 million for the nine months
ended September 30, 1997 to $59.3 million for the nine months ended September
30, 1998.  Depreciation, depletion and amortization expense per Mcfe increased
15% from $1.10 for the nine months ended September 30, 1997 to $1.26 for the
nine months ended September 30, 1998.  The increase in expense was a result of
the increased production from acquired as well as newly-developed properties
combined with an increased depletion rate.  The increase in the depletion rate
is attributable to an overall higher level of capital spending during 1998 as
compared to 1997.

         General and Administrative Expenses.  General and administrative
expenses, net of overhead reimbursements received from other working interest
owners of $0.7 million for both the nine month periods ended September 30, 1997
and 1998, increased 9% from $4.3 million for the nine months ended September
30, 1997 to $4.7 million for the nine months ended September 30, 1998.  The
Company capitalized general and administrative expenses directly related to oil
and gas exploration and development activities of $5.2 million and $5.9
million, respectively, for the nine months ended September 30, 1997 and 1998.
The increase in aggregate general and administrative expense reflects the
overall





                                      -16-
<PAGE>   17
growth and expansion of the Company's operations.  As the Company continues to
grow and expand its workforce, aggregate general and administrative expenses
are expected to increase.  On an Mcfe basis, general and administrative
expenses decreased 17% from $0.12 for the nine months ended September 30, 1997
to $0.10 for the nine months ended September 30, 1998.  The lower rate per Mcfe
during the first nine months of 1998 reflects the increase in the Company's
production.

         Interest Expense, Net.  Interest expense, net of capitalized interest,
increased from $0.5 million for the nine months ended September 30, 1997 to
$2.5 million for the nine months ended September 30, 1998.  Capitalized
interest increased from $4.0 million for nine months ended September 30, 1997
to $7.1 million for the nine months ended September 30, 1998.  The increase in
aggregate interest expense was attributable to higher average debt levels
during the first three quarters of 1998.  With the issuance of $100 million of
senior subordinated indebtedness in March 1998, the Company expects its 1998
average debt levels to exceed those in 1997 and, accordingly, expects an
increase in net interest expense.

         Income Tax Provision.  The provision for income taxes decreased 4%
from an expense of $5.5 million for the first nine months of 1997 to an expense
of $5.3 million for the first nine months of 1998 due to the decrease in pretax
income and a small decrease in the benefit received from Section 29 tax
credits.

         Operating Income and Net Income.  Although production increased 32%
for the nine months ended September 30, 1998 as compared to the corresponding
period of 1997, natural gas prices were flat and operating expenses increased
42%, causing operating income to decrease 4% from $20.7 million for the nine
months ended September 30, 1997 to $19.8 million for the nine months ended
September 30, 1998.  Net income decreased 18% from $14.7 million for the nine
months ended September 30, 1997 to $12.0 million for the nine months ended
September 30, 1998, reflecting higher interest expense during the first nine
months of 1998.


LIQUIDITY AND CAPITAL RESOURCES

         The Company has historically funded its operations, acquisitions,
capital expenditures and working capital requirements from cash flows from
operations, bank borrowings and, prior to the IPO, capital contributions from
Brooklyn Union.  On March 2, 1998, the Company issued $100 million of senior
subordinated indebtedness in a private placement to qualified institutional
buyers.  Net proceeds of approximately $97 million were used to repay a portion
of the outstanding indebtedness under the Company's revolving bank credit
facility (the "Credit Facility").

         As of September 30, 1998, the Company had a working capital deficit of
$9.3 million and $43.6 million of borrowing capacity available under the Credit
Facility.  Net cash provided by operating activities for the nine months ended
September 30, 1998 was $84.3 million compared to $64.8 million for the nine
months ended September 30, 1997.  The Company's cash position was increased
during the nine months ended September 30, 1998 by a net increase in long-term
debt of $78 million.  The net increase in long-term debt resulted from the
Company's issuance of $100 million of senior subordinated notes, offset in part
by a net decrease of $22 million in borrowings under the Credit Facility.
Funds used in investing activities consisted of $166.5 million for investments
in property and equipment, including the $53.2 million net purchase price of
the South Louisiana Acquisition.  As a result of these activities, cash and
cash equivalents decreased $3.9 million from $4.7 million at December 31, 1997
to $0.8 million at September 30, 1998.

         The Company's initial capital expenditure budget (excluding
acquisitions) for 1998 of $100 million was increased to $130 million in July
1998.  As of September 30, 1998, the Company had spent $111 million on
exploration and development and $55 million on acquisitions, which includes
$53.2 million for the South Louisiana Acquisition, $1.2 million for four
producing wells in the Charco Field and $1.2 million for an incremental working
interest in a producing offshore property.  In October 1998, the Company spent
$20.0 million to purchase additional properties in South Louisiana.  On
November 5, 1998, the Company agreed to acquire from Chevron U.S.A. Production
Company ("Chevron"), for $85.3 million in cash, a 100% working interest in
Chevron's Mustang Island A-31 Field (the "Pending Acquisition").  The Company
expects that the estimated net proved reserves associated with the properties
to be acquired in the Pending Acquisition will be approximately 69 Bcfe as of
the December 1, 1998 effective date of the acquisition, and that average daily
production, net to interest to be acquired, will be approximately 37 MMcfe per
day.  The Company





                                      -17-
<PAGE>   18
expects to complete the Pending Acquisition effective December 1, 1998.  The
budget includes amounts for development costs associated with recently acquired
properties and amounts that are contingent upon drilling success.  The Company
will continue to evaluate its capital spending plans through remainder of the
year.  No significant abandonment or dismantlement costs are anticipated
through the remainder of 1998.  Actual levels of capital expenditures may vary
significantly due to a variety of factors, including drilling results, natural
gas prices, industry conditions and outlook and future acquisitions of
properties.  The Company believes cash flows from operations and borrowings
under its Credit Facility will be sufficient to fund these expenditures.  The
Company will continue to selectively seek acquisition opportunities for proved
reserves with substantial exploration and development potential both offshore
and onshore.  The size and timing of capital requirements for acquisitions is
inherently unpredictable.

         The Company has entered into the Credit Facility with a syndicate of
lenders led by Chase Bank of Texas, National Association ("Chase"), which
provides a maximum loan amount of $150 million, subject to borrowing base
limitations, on a revolving basis.  The Credit Facility was amended in March
1998 in connection with the Company's private placement of $100 million of
senior subordinated notes, and had a borrowing base of $135 million as of
September 30, 1998.  At September 30, 1998, $91.0 million was borrowed and $0.4
million was committed under outstanding letter of credit obligations.
Subsequent to September 30, 1998,  the Company borrowed an additional $28.5
million under the Credit Facility to fund the acquisition of additional
properties in South Louisiana and to make a downpayment of $8.5 million on the
Pending Acquisition.  The Company intends to amend the Credit Facility prior to
December 1, 1998 so that the $85.3 million purchase price of the Pending
Acquisition, if completed, can be financed with borrowings under the Credit
Facility.

         The Credit Facility matures on July 1, 2000.  Advances under the
Credit Facility bear interest, at the Company's election at (i) a fluctuating
rate ("Base Rate") equal to the higher of the Federal Funds Rate plus 0.5% or
Chase's prime rate or (ii) a fixed rate ("Fixed Rate") equal to a quoted LIBOR
rate plus a margin between 0.375% and 1.125% depending on the amount
outstanding under the Credit Facility.  Interest is due at calendar quarters
for Base Rate loans and at the earlier of maturity or three months from the
date of the loan for Fixed Rate loans.  The Credit Facility contains covenants
of the Company, including certain restrictions on liens and financial covenants
which require the Company to, among other things, maintain (i) an interest
coverage ratio of 2.5 to 1.0 of earnings before interest, taxes and
depreciation ("EBIDTA") to cash interest and (ii) a total debt to
capitalization ratio of less than 60%.  The Credit Facility also restricts the
Company's ability to purchase or redeem its capital stock or to pledge its oil
and gas properties or other assets.  As of September 30, 1998 the Company was
in compliance with all Credit Facility covenants.  The borrowing base under the
Credit Facility is determined by Chase in its discretion in accordance with
Chase's then current standards and practices for similar oil and gas loans
taking into account such factors as Chase deems appropriate.

         On March 2, 1998, the Company issued $100 million of 8 5/8% Senior
Subordinated Notes (the "Notes") due January 1, 2008 in a private placement to
qualified institutional buyers.  The Notes bear interest at 8 5/8% annum with
interest payable semi-annually on January 1 and July 1, commencing July 1,
1998.  The Notes are redeemable at the option of the Company, in whole or in
part, at anytime on or after January 1, 2003 at a price equal to 100% of the
principal amount plus accrued and unpaid interest, if any, plus a specified
premium if the Notes are redeemed prior to January 1, 2006.  Notwithstanding
the foregoing, any time prior to January 1, 2001, the Company may redeem up to
35% of the original aggregate principal amount of the Notes with the net
proceeds of any equity offering, provided that at least 65% of the original
aggregate principal amount of the Notes remains outstanding immediately after
the occurrence of such redemption.  Upon the occurrence of a change of control
(as defined), the Company will be required to offer to purchase the Notes at a
purchase price equal to 101% of the aggregate principal amount thereof, plus
accrued and unpaid interest, if any.  The Notes are general unsecured
obligations of the Company and rank subordinate in right of payment to all
existing and future senior debt, including the Credit Facility, and will rank
senior or pari passu in right of payment to all existing and future
subordinated indebtedness.

         The Company utilizes derivative commodity instruments to hedge future
sales prices on a portion of its natural gas production to achieve a more
predictable cash flow, as well as to reduce its exposure to adverse price
fluctuations of natural gas.  While the use of these hedging arrangements
limits the downside risk of adverse price movements, they may limit future
revenues from favorable price movements.  The use of hedging transactions also
involves the risk that the counterparties will be unable to meet the financial
terms of such transactions.  The Company traditionally employs swaps, collars
and options for risk management.  The Company generally places hedging
instruments with major financial institutions that the Company believes are
minimal credit risks.  The Company accounts for these transactions as hedging
activities and, accordingly, gains or losses are included in natural gas and
oil revenues in the period the hedged production occurs.  Neither the hedging
contracts nor the unrealized gains or losses on these contracts, if any, are
recognized in the consolidated financial statements.





                                      -18-
<PAGE>   19
         As of September 30, 1998, the Company had entered into commodity price
hedging contracts with respect to its gas production as listed below.  Natural
gas production during the month of October 1998 was 5,251 MMcf (5,361 MMBtu).


<TABLE>
<CAPTION>
                   FIXED PRICE SWAPS                 COLLARS                        OPTIONS
                   ------------------      -----------------------------  ---------------------------
                               NYMEX                        NYMEX                   NYMEX
                    VOLUME   CONTRACT       VOLUME      CONTRACT PRICE    VOLUME    STRIKE
    PERIOD         (MMBTU)     PRICE       (MMBTU)     FLOOR     CEILING  MMBTU)    PRICE    PUT/CALL
 -------------     -------   --------      -------    -------   --------  ------   -------   --------
<S>                <C>       <C>           <C>        <C>       <C>       <C>      <C>       <C>
 October 1998       1,800    $  2.01        2,400     $  2.06   $  2.20   310      $  2.20   Put
                                                                          930      $  2.50   Call
 November 1998                              2,100     $  2.00   $  2.29   300      $  2.00   Put
                                                                          300      $  2.20   Call
 January 1999                                 930     $  2.50   $  3.00

 February 1999                                280     $  2.40   $  2.90
 </TABLE>


         As of October 31, 1998, the Company had no commodity hedging contracts
extending beyond February 1999.  The Company has entered into basis swaps with
respect to more than 50% of the indicated NYMEX hedged volume.

         These hedging transactions are settled based upon the average of the
reported settlement prices on the New York Mercantile Exchange (the "NYMEX")
for the last three trading days of a particular contract month (the "settlement
price").  With respect to any particular swap transaction, the counterparty is
required to make a payment to the Company in the event that the settlement
price for any settlement period is less than the swap price for such
transaction, and the Company is required to make payment to the counterparty in
the event that the settlement price for any settlement period is greater than
the swap price for such transaction.  For any particular collar transaction,
the counterparty is required to make a payment to the Company if the settlement
price for any settlement period is below the floor price for such transaction,
and the Company is required to make payment to the counterparty if the
settlement price for any settlement period is above the ceiling price for such
transaction.  For any particular floor transaction, the counterparty is
required to make a payment to the Company if the settlement price for any
settlement period is below the floor price for such transaction.  The Company
is not required to make any payment in connection with a floor transaction. For
option contracts, the Company has the option, but not the obligation, to buy
contracts at the strike price up to the day before the last trading day for
that NYMEX contract.

         The Company periodically enters into basis swaps (either as part of a
particular hedging transaction or separately) tied to a particular NYMEX-based
transaction to eliminate basis risk.  Basis risk is the risk associated with
the sales point price for natural gas production varying from the reference (or
settlement) price for a particular hedging transaction.  Because substantially
all of the Company's natural gas production is sold under spot contracts, that
have historically correlated with the swap price, the Company believes that it
has no material basis risk with respect to gas swaps that are not coupled with
basis swaps.





                                      -19-
<PAGE>   20
PART II.         OTHER INFORMATION

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

         (a)     Exhibits:

    EXHIBIT NO.                         DESCRIPTION

    *    27.1      -  Financial Data Schedule.

------------------
*        Filed herewith.

         (b)     Reports on Form 8-K:

                 None





                                      -20-
<PAGE>   21
                                   SIGNATURES

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

                                THE HOUSTON EXPLORATION COMPANY


                                  By:        /s/ James G. Floyd               
                                     -----------------------------------------
                                               James G. Floyd
Date: November 11, 1998               President and Chief Executive Officer



                                  By:        /s/ James F. Westmoreland        
                                     -----------------------------------------
                                               James F. Westmoreland
Date: November 11, 1998               Vice President, Chief Accounting Officer,
                                      Comptroller and Secretary



                                      -21-
<PAGE>   22
                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
EXHIBIT
NO.             DESCRIPTION
-------         -----------
<S>             <C>
* 27.1          Financial Data Schedule
</TABLE>

---------------------
*  Filed herewith.