<PAGE>   1
===============================================================================

                                  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 JUNE 30, 1998

                                       OR

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

           FOR THE TRANSITION PERIOD FROM              TO             
                                          -------------  -------------
                          COMMISSION FILE 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 August 11, 1998, 23,896,340 shares of Common Stock, par value
$.01 per share, were outstanding.


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



<PAGE>   2




                         THE HOUSTON EXPLORATION COMPANY

                                TABLE OF CONTENTS

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

PART I.       FINANCIAL INFORMATION

Item 1.       Consolidated Financial Statements (unaudited)

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

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

              Consolidated Statements of Cash Flows -- Six Month Periods Ended
                  June 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>
                                                                                 JUNE 30,     DECEMBER  31,
                                                                                   1998           1997
                                                                              ------------    -------------
                                                                                (UNAUDITED)
<S>                                                                           <C>             <C>         
ASSETS:
Cash and cash equivalents.................................................... $      4,063    $      4,745
Accounts receivable..........................................................       25,581          37,898
Accounts receivable-- Brooklyn Union.........................................          357           1,303
Inventories..................................................................        1,423           1,265
Prepayments and other........................................................        1,226             645
                                                                              ------------    ------------
          Total current assets...............................................       32,650          45,856
Natural gas and oil properties, full cost method
  Unevaluated properties.....................................................      121,449         104,075
  Properties subject to amortization.........................................      679,420         566,868
Other property and equipment.................................................        9,296           9,341
                                                                              ------------    ------------
                                                                                   810,165         680,284
Less: Accumulated depreciation, depletion and amortization...................     (275,986)       (236,546)
                                                                              -------------   ------------
                                                                                   534,179         443,738
Other assets.................................................................        3,414           1,797
                                                                              ------------    ------------
          TOTAL ASSETS....................................................... $    570,243    $    491,391
                                                                              ============    ============

LIABILITIES:
Accounts payable and accrued expenses........................................ $     31,052    $     42,432
Deferred stock obligation....................................................           --           8,825
                                                                              ------------    ------------
          Total current liabilities..........................................       31,052          51,257
Long-term debt...............................................................      188,000         113,000
Deferred federal income taxes................................................       75,865          70,741
Other deferred liabilities...................................................          151             206
                                                                              ------------    ------------
          TOTAL LIABILITIES..................................................      295,068         235,204

COMMITMENTS AND CONTINGENCIES (SEE NOTE 4)

STOCKHOLDERS' EQUITY:
  Common Stock, $.01 par value, 50,000 shares authorized and 23,893 shares
     issued and outstanding at June 30, 1998 and 23,361 shares issued and
     outstanding at
  December 31, 1997..........................................................

                                                                                       239             234
  Additional paid-in capital.................................................      230,861         221,907
  Retained earnings..........................................................       44,075          34,046
                                                                              ------------    ------------
          TOTAL STOCKHOLDERS' EQUITY.........................................      275,175         256,187
                                                                              ------------    ------------
          TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY......................... $    570,243    $    491,391
                                                                              ============    ============
</TABLE>




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


                                       -4-

<PAGE>   5



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



<TABLE>
<CAPTION>
                                                             THREE MONTHS ENDED,                SIX MONTHS ENDED,
                                                                   JUNE 30,                         JUNE 30,
                                                        ----------------------------      ----------------------------
                                                             1998          1997                1998          1997
                                                        -------------- -------------      -------------- -------------
                                                                                 (UNAUDITED)
<S>                                                     <C>            <C>                <C>            <C>          
REVENUES:
  Natural gas and oil revenues......................... $       35,141 $      22,050      $       68,025 $      47,064
  Other................................................            370           170                 570           484
                                                        -------------- -------------      -------------- -------------
          Total revenues...............................         35,511        22,220              68,595        47,548
OPERATING COSTS AND EXPENSES:
  Lease operating......................................          3,563         3,134               7,432         6,277
  Severance tax........................................          1,350           630               2,468         1,736
  Depreciation, depletion and amortization.............         20,191        12,573              39,505        23,955
  General and administrative, net......................          1,707         1,546               3,282         2,956
                                                        -------------- -------------      -------------- -------------
          Total operating expenses.....................         26,811        17,883              52,687        34,924
Income from operations.................................          8,700         4,337              15,908        12,624
Interest expense, net..................................            950           286               1,250           429
                                                        -------------- -------------      -------------- -------------
Net income before income taxes.........................          7,750         4,051              14,658        12,195
Provision for federal income taxes.....................          2,444           609               4,629         3,060
                                                        -------------- -------------      -------------- -------------
NET INCOME ............................................ $        5,306 $       3,442      $       10,029 $       9,135
                                                        ============== =============      ============== =============

Net income per share................................... $         0.22 $        0.15      $         0.42 $        0.39
                                                        ============== =============      ============== =============
Net income per share-- assuming dilution............... $         0.22 $        0.14      $         0.42 $        0.38
                                                        ============== =============      ============== =============

Weighted average shares outstanding....................         23,890        23,333              23,639        23,333
Weighted average shares outstanding-- assuming
    dilution...........................................
                                                                24,288        23,901              23,927        23,953
</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>
                                                                       SIX MONTHS ENDED JUNE 30,
                                                                       -------------------------
                                                                         1998            1997
                                                                       ---------      ----------
                                                                              (UNAUDITED)
<S>                                                                    <C>            <C>      
OPERATING ACTIVITIES:
Net income .......................................................     $  10,029      $   9,135
Adjustments to reconcile net income to net cash
  provided by operating activities:
  Depreciation, depletion and amortization .......................        39,505         23,955
  Deferred income tax expense ....................................         5,124          5,305
  Changes in operating assets and liabilities:
     Decrease in accounts receivable .............................        13,263            239
     Increase in inventories .....................................          (158)          (464)
     Decrease (increase) in prepayments ..........................          (581)           461
     Decrease (increase) in other assets and liabilities .........        (1,672)           833
     Decrease in accounts payable and accrued expenses ...........       (11,380)        (6,790)
                                                                       ---------      ---------

Net cash provided by operating activities ........................        54,130         32,674

INVESTING ACTIVITIES:
Investment in property and equipment .............................      (129,949)       (55,767)
Dispositions and other ...........................................            --          1,360
                                                                       ---------      ---------

Net cash used in investing activities ............................      (129,949)       (54,407)

FINANCING ACTIVITIES:
Proceeds from long term borrowings ...............................       175,000         35,500
Repayments of long term borrowings ...............................      (100,000)       (14,000)
Proceeds from issuance of common stock, net of offering costs ....           137           (141)
                                                                       ---------      ---------

Net cash provided by financing activities ........................        75,137         21,359
                                                                       ---------      ---------

Decrease in cash and cash equivalents ............................          (682)          (374)

Cash and cash equivalents, beginning of period ...................         4,745          2,851
                                                                       ---------      ---------

Cash and cash equivalents, end of period .........................     $   4,063      $   2,477
                                                                       =========      =========

Cash paid for interest ...........................................     $   3,210      $   2,487
                                                                       =========      =========

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 an indirect wholly-owned subsidiary of
MarketSpan Corporation on May 29, 1998 through the combination of Brooklyn
Union's former 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 June 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 June 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

                                       -7-

<PAGE>   8



expenses during the reporting periods. The Company's most significant financial
estimates are based on remaining 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,               SIX MONTHS ENDED,
                                                                     JUNE 30,                         JUNE 30,
                                                           ---------------------------      ---------------------------
                                                               1998          1997               1998          1997
                                                           ------------- -------------      ------------- -------------
                                                                       (IN THOUSANDS, EXCEPT PER SHARE DATA)
<S>                                                        <C>           <C>                <C>           <C>          
Net income ............................................... $       5,306 $       3,442      $      10,029 $       9,135
                                                           ============= =============      ============= =============
Denominator:
Weighted average shares outstanding.......................        23,890        23,333             23,639        23,333
Add: dilutive securities
      Options.............................................           398             1                288            --
      Contingent shares...................................            --           567                 --           620
                                                           ------------- -------------      ------------- -------------
Total weighted average shares outstanding and dilutive
 securities...............................................        24,288        23,901             23,927        23,953
                                                           ============= =============      ============= =============
Net income per share......................................

Net income per share-- assuming dilution.................. $        0.22 $        0.15      $        0.42 $        0.39
                                                           ============= =============      ============= =============
                                                           $        0.22 $        0.14      $        0.42 $        0.38
                                                           ============= =============      ============= =============
</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 and is currently evaluating the impact of the
statement.


                                       -8-

<PAGE>   9



NOTE 2 -- LONG-TERM DEBT

         As of June 30, 1998, long-term debt consisted of the following:


<TABLE>
<CAPTION>
                                                            JUNE 30,  DECEMBER 31,
                                                              1998        1997
                                                            --------  ------------
                                                                (IN THOUSANDS)
          <S>                                               <C>       <C>         
          SENIOR DEBT:

          Bank revolving credit facility .................. $ 88,000  $    113,000
          8 5/8% Senior Subordinated Notes, due 2008.......  100,000            --
                                                            --------  ------------
              Total long-term debt......................... $188,000  $    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 June 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
June 30, 1998, $88 million was outstanding under the Credit Facility and $0.4
million was outstanding in letter of credit obligations.

         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 June 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 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

                                       -9-

<PAGE>   10


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. The natural gas and oil properties acquired in the Soxco
Acquisition consisted solely of working interests in properties located in the
Gulf of Mexico that are operated by the Company or in which the Company also has
a working interest. 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 June 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 June 30, 1998 and 1997 was a
reduction to income tax expense of $0.3 million and $0.5 million, respectively,
and $0.5 million and $0.9 million, respectively, for the six months ended June
30, 1998 and 1997, representing benefits received from the Section 29 tax
credits.

NOTE 6 -- ACQUISITION

         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 June 1998 attributable to such properties was approximately 14
MMcfe per day, net to the interest acquired by the Company. The purchase price
of $53.9 million

                                      -10-

<PAGE>   11



will be adjusted for production revenues and operating expenses related to the
acquired properties between November 1, 1997 and the April 29, 1998 effective
date of the South Louisiana Acquisition. The purchase price of the South
Louisiana Acquisition was paid in cash, financed with borrowings under the
Credit Facility.


                                      -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 six months ended June 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 an indirect wholly-owned
subsidiary of MarketSpan Corporation on May 29, 1998 through the combination of
Brooklyn Union's former 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, 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 June 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 June 30, 1998, the Company estimates, using prices in effect as
of such date, that the ceiling limitation imposed under full cost accounting
rules on total capitalized natural gas and oil property costs exceeded actual
capitalized costs. Natural gas prices have declined substantially since June 30,
1998. The Company may be required

                                      -12-

<PAGE>   13



to write down the carrying value of its natural gas and oil properties at the
end of the third quarter of 1998, depending upon natural gas prices and the
results of the Company's drilling programs.

         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 and is currently evaluating the impact of the
statement.

         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 similar normal business.

         The Company is in the process of assessing all financial and
operational systems and equipment to ensure year 2000 compliance and plans to
complete the assessment by December 31, 1998. 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,       SIX MONTHS ENDED,
                                                                 JUNE 30,                 JUNE 30,
                                                           -------------------       ------------------
                                                            1998         1997         1998        1997
                                                           ------       ------       ------      ------
<S>                                                        <C>          <C>          <C>         <C>
PRODUCTION:
    Natural gas (MMcf).........................            15,861       11,246       30,996      21,817
    Oil (MBbls)................................                57           39          104          72
    Total (MMcfe)..............................            16,203       11,480       31,620      22,249

AVERAGE SALES PRICES:
    Natural gas (per Mcf) realized(1) .........            $ 2.17       $ 1.90       $ 2.15      $ 2.09
    Natural gas (per Mcf) unhedged.............              2.13         1.96         2.09        2.36
    Oil (per Bbl)..............................             13.14        17.62        13.61       19.21

EXPENSES (PER MCFE):
    Lease operating............................            $ 0.22 $       0.27       $ 0.24      $ 0.28
    Severance tax..............................              0.08         0.06         0.08        0.08
    Depreciation, depletion and amortization...              1.25         1.10         1.25        1.08
    General and administrative, net............              0.11         0.13         0.10        0.13
</TABLE>
---------------------------

(1)      Reflects the effects of hedging.


RECENT FINANCIAL AND OPERATING RESULTS

COMPARISON OF THREE MONTHS ENDED JUNE 30, 1997 AND 1998

         Production. Houston Exploration's production increased 41% from 11,480
MMcfe for the three months ended June 30, 1997 to 16,203 MMcfe for the three
months ended June 30, 1998. The increase in production was primarily
attributable to the Company's continued successful development drilling program
in the Charco Field. The Charco Field in South Texas was acquired in July of
1996. Since the beginning of 1997, the Company has successfully completed and
brought on-line 31 new wells in the Charco Field, 25 of these since June 30,
1997. Production in the Charco Field has increased 97% from 3,821 MMcfe, or 42
MMcfe per day, in the second quarter of 1997 to 7,535 MMcfe, or 83 MMcfe per
day, in the second quarter of 1998. Adding to the significant increase in
production from the Charco Field is new production from offshore wells brought
on-line since June 1997 and wells acquired in the South Louisiana Acquisition,
which was completed on April 29, 1998.

         Natural Gas and Oil Revenues. Natural gas and oil revenues increased
59% from $22.1 million for the three months ended June 30, 1997 to $35.1 million
for the three months ended June 30, 1998 as a result of the 41% increase in
production combined with a 14% increase in average realized natural gas prices,
from $1.90 per Mcf for the three months ended June 30, 1997 to $2.17 per Mcf for
the three months ended June 30, 1998.

         As a result of hedging activities, the Company realized an average gas
price of $2.17 per Mcf for the three months ended June 30, 1998, which was 102%
of the unhedged natural gas price of $2.13 per Mcf that otherwise would have
been received, resulting in a $0.7 million increase in natural gas revenues for
the three months ended June 30, 1998. For the corresponding three month period
of 1997, the average realized gas price was $1.90 per Mcf, which was 97% of the
unhedged average gas price of $1.96 per Mcf, resulting in a decrease in natural
gas revenues of $0.7 million for the three months ended June 30, 1997.


                                      -14-

<PAGE>   15



         Lease Operating Expenses and Severance Tax. Lease operating expenses
increased 16% from $3.1 million for the three months ended June 30, 1997 to $3.6
million for the three months ended June 30, 1998. On an Mcfe basis, lease
operating expenses decreased from $0.27 for the three months ended June 30, 1997
to $0.22 for the three months ended June 30, 1998. The increase in lease
operating expenses during the second quarter 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 substantial increase in production during the three months
ended June 30, 1998 as compared to the corresponding period of 1997. Severance
tax, which is a function of volume and revenues generated from onshore
production, increased from $0.6 million for the three months ended June 30, 1997
to $1.4 million for the three months ended June 30, 1998. On an Mcfe basis,
severance tax increased from $0.06 per Mcfe, for the three months of 1997 to
$0.08 per Mcfe, for the first three months of 1998. The increase in both the
severance tax expense and the rate per Mcfe is due to higher natural gas prices
received during the second quarter of 1998 as compared to prices received during
the second quarter of 1997, combined with the addition of the onshore South
Louisiana properties acquired in April 1998.

         Depreciation, Depletion and Amortization. Depreciation, depletion and
amortization expense increased 60% from $12.6 million for the three months ended
June 30, 1997 to $20.2 million for the three months ended June 30, 1998.
Depreciation, depletion and amortization expense per Mcfe increased 14% from
$1.10 for the three months ended June 30, 1997 to $1.25 for the corresponding
three months in 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 combination of higher drilling and development costs and an over
all 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 $0.2 million for both the three month periods ended June 30, 1997 and
1998, increased 13% from $1.5 million for the three months ended June 30, 1997
to $1.7 million for the three months ended June 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 $1.6
million and $1.9 million, respectively, for the three months ended June 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 Company's incentive compensation plan. On an Mcfe basis, general and
administrative expenses decreased 15% from $0.13 for the three months ended June
30, 1997 to $0.11 for the three months ended June 30, 1998. The lower rate per
Mcfe during the second quarter of 1998 reflects the increase in the Company's
production.

         Interest Expense, Net. Interest expense, net of capitalized interest,
increased from $0.3 million for the three months ended June 30, 1997 to $1.0
million for the three ended June 30, 1998. Capitalized interest increased from
$1.2 million for three months ended June 30, 1997 to $2.5 million for the three
months ended June 30, 1998. The increase in aggregate interest expense was
attributable to higher average debt levels during the second 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 increased 300%
from an expense of $0.6 for the first three months of 1997 to an expense of $2.4
million for the first three months of 1998. The increase in income tax expense
for the three months ended June 30, 1998 as compared to the corresponding period
of 1997 is due to the 90% increase in pretax income for the three months ended
June 30, 1998.

         Operating Income and Net Income. As a result of the significant
increase in natural gas production and the increase in natural gas prices,
operating income increased 102% from $4.3 million for the three months ended
June 30, 1997 to $8.7 million for the three months ended June 30, 1998. Net
income increased 56% from $3.4 million for the three months ended June 30, 1997
to $5.3 million for the three months ended June 30, 1998.


                                      -15-

<PAGE>   16



Comparison of Six Months Ended June 30, 1997 and 1998

         Production. Houston Exploration's production increased 42% from 22,249
MMcfe for the six months ended June 30, 1997 to 31,620 MMcfe for the six months
ended June 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
44% from $47.1 million for the six months ended June 30, 1997 to $68.0 million
for the six months ended June 30, 1998 as a result of the 42% increase in
production combined with a slight 3% increase in average realized natural gas
prices, from $2.09 per Mcf in the six months ended June 30, 1997 to $2.15 per
Mcf in the six months ended June 30, 1998.

         As a result of hedging activities, the Company realized an average gas
price of $2.15 per Mcf for the six months ended June 30, 1998, which was 103% of
the unhedged natural gas price of $2.09 per Mcf that otherwise would have been
received, resulting in a $1.8 million increase in natural gas revenues for the
six month period. For the six months ended June 30, 1997, the average realized
gas price was $2.09 per Mcf, which was 89% of the unhedged average gas price of
$2.36, resulting in a decrease to natural gas revenues of $5.7 million for the
six month period.

         Lease Operating Expenses and Severance Tax. Lease operating expenses
increased 17% from $6.3 million for the six months ended June 30, 1997 to $7.4
million for the six months ended June 30, 1998. On an Mcfe basis, lease
operating expenses decreased from $0.28 for the six first months of 1997 to
$0.24 for the first six months of 1998. The increase in lease operating expenses
during the first half 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 substantial
increase in production during the first six 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 from $1.7 million for the
six months ended June 30, 1997 to $2.5 million for the six months ended June 30,
1998. On an Mcfe basis, severance tax remained unchanged at $0.08 per Mcfe for
the six month periods ended June 30, 1998 and 1997. The increase in severance
tax expense reflects the added onshore production both at Charco and in South
Louisiana and the flat rate per Mcfe reflects comparatively flat natural gas
prices the first half of 1998 as compared to the corresponding period of 1997.

         Depreciation, Depletion and Amortization. Depreciation, depletion and
amortization expense increased 65% from $23.9 million for the six months ended
June 30, 1997 to $39.5 million for the six months ended June 30, 1998.
Depreciation, depletion and amortization expense per Mcfe increased 16% from
$1.08 for the six months ended June 30, 1997 to $1.25 for the six months ended
June 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 higher
drilling and development costs and 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 $0.5 million for both the six month periods ended June 30, 1997 and
1998, increased 14% from $2.9 million for the six months ended June 30, 1997 to
$3.3 million for the six months ended June 30, 1998. The Company capitalized
general and administrative expenses directly related to oil and gas exploration
and development activities of $3.4 million and $3.9 million, respectively, for
the six months ended June 30, 1997 and 1998. The increase in aggregate general
and administrative expense reflects the overall 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 23% from $0.13 for the
six months ended June 30, 1997 to $0.10 for the six months ended June 30, 1998.
The lower rate per Mcfe during the first half of 1998 reflects the increase in
the Company's production.


                                      -16-

<PAGE>   17



         Interest Expense, Net. Interest expense, net of capitalized interest,
increased from $0.4 million for the six months ended June 30, 1997 to $1.3
million for the six ended June 30, 1998. Capitalized interest increased from
$2.4 million for six months ended June 30, 1997 to $4.5 million for the six
months ended June 30, 1998. The increase in aggregate interest expense was
attributable to higher average debt levels during the first half 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 increased 48% from
an expense of $3.1 million for the first six months of 1997 to an expense of
$4.6 million for the first six months of 1998 due to the increase in pretax
income, offset in part by a decrease in the benefit received from Section 29 tax
credits.

         Operating Income and Net Income. As a result of the significant
increase in natural gas production, combined with the slight increase in natural
gas prices offset by the increase in operating costs, operating income increased
26% from $12.6 million for the six months ended June 30, 1997 to $15.9 million
for the six months ended June 30, 1998. Net income increased 10% from $9.1
million for the six months ended June 30, 1997 to $10.0 million for the six
months ended June 30, 1998 and reflects higher interest expense and taxes during
the first six 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 June 30, 1998, the Company had a working capital of $1.6 million
and $46.6 million of available borrowing base under the Credit Facility. Net
cash provided by operating activities for the six months ended June 30, 1998 was
$54.1 million compared to $32.7 million for the six months ended June 30, 1997.
The increase in net cash flows from operations is due to higher net income
caused by increases in production and natural gas prices, and changes in
operating assets and liabilities. The Company's cash position was increased
during the six months ended June 30, 1998 by a net increase in long-term debt of
$75 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 $25 million in borrowings under the Credit Facility. Funds used in
investing activities consisted of $129.9 million for investments in property and
equipment, including the $53.9 million purchase price of the South Louisiana
Acquisition. As a result of these activities, cash and cash equivalents
decreased $0.7 million from $4.7 million at December 31, 1997 to $4.0 million at
June 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 June 30, 1998, the Company had spent $74 million on exploration and
development and $55 million on acquisitions, including $53.9 million for the
South Louisiana Acquisition and $1.2 million for an incremental working interest
in a producing offshore property. 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 the year. No significant abandonment or
dismantlement costs are anticipated through 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

                                      -17-

<PAGE>   18



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 June 30,
1998. At June 30, 1998, $88 million was borrowed and $0.4 million was committed
under outstanding letter of credit obligations. 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 June 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 has traditionally employed swaps, collars and
options, although the only hedging instruments in place as of June 30, 1998
consisted of collars. 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.

         As of June 30, 1998, the Company had entered into commodity price
hedging contracts with respect to its gas production as listed below. All such
commodity price hedging contracts in effect as of such date were "collar"
transactions. Natural gas production during the month of June 1998 was 5,483
MMcf (5,467 MMMBtu).



<TABLE>
<CAPTION>
                                         NYMEX
                      VOLUME        CONTRACT PRICE
     PERIOD          (MMMBTU)      FLOOR    CEILING
------------------   --------    --------  ---------  
<S>           <C>      <C>       <C>       <C>     
July          1998     2,480     $   2.25  $   2.70
August        1998     2,480     $   2.25  $   2.70
September     1998     2,400     $   2.25  $   2.70
October       1998       620     $   2.20  $   2.50
</TABLE>


                                      -18-

<PAGE>   19


         As of July 31, 1998, the Company had no commodity hedging contracts
extending beyond October 1998. 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 4.           SUBMISSION OF MATTERS TO A VOTE OF SHAREHOLDERS

         On April 23, 1998, the company held its annual meeting of shareholders.
All matters brought for a vote before the shareholders as listed in the
Company's proxy statement were approved:

         1.       The following eight Directors of the Company were elected to
                  serve until the Company's next annual meeting:


                  <TABLE>
                  <CAPTION>
                  DIRECTOR             VOTES FOR         VOTES WITHHELD
                  -----------------        -----------        --------------
                  <S>                       <C>                      <C>
                  James G. Floyd            22,259,839               41,089
                  Robert B. Catell          22,259,639               41,289
                  Gordon F. Ahalt           22,279,339               21,589
                  Russell D. Gordy          22,282,139               18,789
                  Craig G. Matthews         22,281,939               18,989
                  James Q. Riordan          22,258,339               42,589
                  Lester H. Smith           22,259,839               41,089
                  Donald C. Vaughn          22,281,739               19,189
                  </TABLE>

         2.       An amendment to the Company's 1996 Stock Option Plan providing
                  for the grant of options to non-employee directors of the
                  Company was approved.


                  <TABLE>
                  <CAPTION>
                   VOTES FOR     VOTES AGAINST   ABSTAINED
                  ----------     -------------   ---------
                  <S>                <C>           <C>
                  19,368,787         2,920,091     12,050
                  </TABLE>

         3.       The appointment of Arthur Andersen LLP as the Company's
                  independent public accountants for the fiscal year ending
                  December 31, 1998 was ratified and approved.


                  <TABLE>
                  <CAPTION>
                   VOTES FOR     VOTES AGAINST   ABSTAINED
                  ----------     -------------   ---------
                  <S>                    <C>         <C>
                  22,294,428             4,250       2,250
                  </TABLE>

ITEM 6.           EXHIBITS AND REPORTS ON FORM 8-K

         (a)      Exhibits:


<TABLE>
<CAPTION>
EXHIBIT NO.          DESCRIPTION
-----------          -----------
<S>  <C>             <C>                    
*    10.1**     --   Amended and Restated 1996 Stock Option Plan.
*    10.2**     --   Employment Agreement dated May 1, 1998 between The Houston 
                     Exploration Company and Thomas E. Schwartz.
*    27.1       --   Financial Data Schedule.

---------------------------


*        Filed herewith.
**       Management contract or compensation plan.

         (b)      Reports on Form 8-K:

                  None

</TABLE>

                                      -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: August 11, 1998              President and Chief Executive Officer



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


                                      -21-

<PAGE>   22

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
EXHIBIT NO.          DESCRIPTION
-----------          -----------
<S>  <C>             <C>                    
*    10.1**     --   Amended and Restated 1996 Stock Option Plan.
*    10.2**     --   Employment Agreement dated May 1, 1998 between The Houston 
                     Exploration Company and Thomas E. Schwartz.
*    27.1       --   Financial Data Schedule.

---------------------------

*        Filed herewith.
**       Management contract or compensation plan.

</TABLE>