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                                                                    EXHIBIT 10.2

                     FIRST AMENDMENT TO EMPLOYMENT AGREEMENT

     THIS FIRST AMENDMENT TO EMPLOYMENT AGREEMENT (this "FIRST AMENDMENT") dated
as of May 17, 2002 (the "AMENDMENT EFFECTIVE DATE") by and between The Houston
Exploration Company, a Delaware corporation (the "Company"), and William G.
Hargett (the "EXECUTIVE").

                                   WITNESSETH:

     WHEREAS, the Company and the Executive entered into an Employment Agreement
dated as of April 8, 2001 (the "AGREEMENT"); and

     WHEREAS, the Company and the Executive hereby desire to amend the Agreement
as set forth herein;

     NOW, THEREFORE, in consideration of the premises and for other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the Company and the Executive hereby agree as follows:

     1. The Agreement shall be amended to clarify the term "reasonable
compensation" in Section 4(d). Section 4(d) shall be amended to read in its
entirety as follows:

               (d) In the event of the sale of all or substantially all of the
          assets of the Company or the acquisition by any person other than
          KeySpan Corporation doing business as KeySpan Energy or its affiliates
          ("KeySpan") of a majority of the outstanding common stock of the
          Company, the Company agrees to award Reasonable Compensation to the
          Executive in recognition of his services in consummating such
          transaction.

               As used in this Section 4(d), the term "Reasonable Compensation"
          shall mean an amount between $3,000,000 and $7,500,000, based on the
          value received for the Company's stock or assets in an acquisition,
          using the following formula:

<Table>
<Caption>
                                     PERCENTAGE OF           APPROXIMATE
 ACQUISITION STOCK PRICE           TRANSACTION VALUE            BONUS
 -----------------------           -----------------         -----------
<S>                                <C>                       <C>
  Up to $30.41 per share                  .25%                $3,000,000

$30.41 to $31.93 per share                .30%                $3,700,000

$31.93 to $33.45 per share                .40%                $5,200,000

$33.45 to $34.97 per share                .55%                $7,500,000
</Table>

               As used in this Agreement, the term "Transaction Value" shall
          mean (i) in the event of a stock acquisition, the sum of (a) the per
          share value in cash, securities, and other assets received by the
          Company's shareholders multiplied by the number of Company shares
          outstanding at the time of the acquisition, and (b) the principal
          amount of all indebtedness as set forth on the consolidated balance
          sheet of the Company upon the consummation of any such acquisition;
          and (ii) in the event of an asset acquisition, the amount paid for the
          assets of the Company acquired in any such transaction, and including,
          without limitation, the principal amount of all indebtedness assumed
          by the purchaser in any such transaction. In the event of an asset
          acquisition, the Transaction Value shall be multiplied by .30% to
          determine the amount of Reasonable Compensation under this Section
          4(d).

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     2. The Agreement shall be amended by modifying the second sentence of
Section 6(a) to provide that the termination of the Agreement will also
terminate the non-compete provisions contained therein. As amended, Section 6(a)
now reads in its entirety as follows:

               (a) Noncompetition Activities. The Executive acknowledges that
          the nature of the employment under this Agreement is such as will
          bring the Executive in personal contact with patrons or customers of
          the Company and will enable him to acquire valuable information as to
          the nature and character of the business of the Company, thereby
          enabling him, by engaging in the competing business on his own behalf,
          or for another, to take advantage of such knowledge and thereby gain
          an unfair advantage. Accordingly, the Executive covenants and agrees
          that he will not, without the prior written consent of the Company
          during the Term of Employment, engage directly or indirectly for
          himself, or as an agent, representative, officer, director or employee
          of others, in the exploration for or production of hydrocarbons in
          waters offshore from the States of Texas and Louisiana, provided that
          the foregoing restriction shall not apply at any time after the
          Executive's Term of Employment and, provided further, that nothing in
          this Agreement shall prohibit the Executive from acquiring or holding
          any issue of stock or securities of any entity registered under
          Section 12 of the Securities and Exchange Act of 1934 (as amended),
          listed on a national securities exchange or quoted on the automated
          quotation system of the National Association of Securities Dealers,
          Inc., so long as the Executive is not deemed to be an "affiliate" of
          such entity, as such term is used in paragraphs (c) and (d) of Rule
          145 under the Securities Act of 1933 (as amended).

     3. The Agreement shall be amended to clarify the scope of the term "total
compensation" in Section 7(e). Section 7(e)(i) shall be amended to read in its
entirety as follows:

               (i) pay to the Executive, within thirty (30) days after the date
          of such termination, a lump sum payment equal to 2.99 times the
          Executive's then-current annual rate of Total Compensation;

The following provision shall be added to the end of Section 7(e):

               As used in this Agreement, the term "Total Compensation" shall
          mean the sum of the following:

               (i) the current annual salary of the Executive referenced in
          Section 3;

               (ii) the current car allowance provided by the Company to the
          Executive referenced in Section 4(c); and

               (iii) the Executive's annual bonus, calculated as though the
          Company's financial targets had been met at one hundred percent (100%)
          referenced in Section 3 and Exhibit A hereto.

     4. The Agreement shall be amended by modifying Section 14 to read in its
entirety as follows:

               14. Entire Agreement. This Agreement, as amended by the First
          Amendment, constitutes the sole agreement between the parties with
          respect to the employment of the Executive by the Company and
          supersedes any and all other agreements, oral or written, between the
          parties.

     5. Except as expressly amended hereby, the Company and the Executive ratify
and confirm all terms and conditions of the Agreement as continuing in full
force and effect.

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     IN WITNESS WHEREOF, the parties hereto have duly executed this First
Amendment as of the date first above written.

                                       THE HOUSTON EXPLORATION COMPANY
Addresses:

1100 Louisiana, Suite 2000
Houston, Texas 77002                   By: /s/ Robert B. Catell
                                           -------------------------------------
                                       Name:  Robert B. Catell
                                       Title: Chairman, Compensation Committee

1100 Louisiana, Suite 2000
Houston, Texas  77002                  /s/ William G. Hargett
                                       -----------------------------------------
                                       William G. Hargett

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