<PAGE>

                                                                    EXHIBIT 10.1

                      SECOND AMENDMENT TO CREDIT AGREEMENT

         THIS SECOND AMENDMENT TO CREDIT AGREEMENT (this "Second Amendment")
dated effective as of September 3, 2003 (the "Second Amendment Effective Date"),
among THE HOUSTON EXPLORATION COMPANY, a Delaware corporation (the "Company");
the lenders party hereto (the "Lenders"); WACHOVIA BANK, NATIONAL ASSOCIATION,
as Issuing Bank and as Administrative Agent (in its capacity as Administrative
Agent, the "Administrative Agent"); THE BANK OF NOVA SCOTIA and FLEET NATIONAL
BANK, as Co-Syndication Agents; and BNP PARIBAS, as Documentation Agent.

                                R E C I T A L S:

         A.       The Company, the Lenders, the Administrative Agent, the
Co-Syndication Agents and the Documentation Agent are parties to that certain
Credit Agreement dated as of July 15, 2002 (said Credit Agreement, as amended by
First Amendment to Credit Agreement dated as of June 5, 2003, the "Credit
Agreement").

         B.       The parties to the Credit Agreement intend to amend Section
9.18 (Hedging Agreements).

         C.       Therefore, in consideration of the mutual covenants and
agreements herein contained, the parties hereto hereby agree as follows:

         SECTION 1. Defined Terms. Except as amended hereby, terms used herein
when defined in the Credit Agreement shall have the same meanings herein unless
the context otherwise requires.

         SECTION 2. Amendments to Credit Agreement.

                  (a)      Definitions. The term "Agreement", defined in Section
1.02 of the Credit Agreement, is hereby amended in its entirety to read as
follows:

                  "Agreement" shall mean this Credit Agreement, as amended by
         the First Amendment, as further amended by the Second Amendment, and as
         the same may be further amended, supplemented, waived or otherwise
         modified from time to time in accordance herewith.

                  (b)      New Definition. Section 1.02 of the Credit Agreement
is hereby further amended by adding thereto the following new definition in its
appropriate alphabetical order:

                           "Second Amendment" shall mean that certain Second
         Amendment to Credit Agreement dated effective as of September 3, 2003,
         among the Company, the Lenders party thereto, the Administrative Agent,
         the Issuing Bank, the Co-Syndication Agents and the Documentation
         Agent.

                  (c)      Negative Covenants. Section 9.18 of the Credit
Agreement is hereby amended in its entirety to read as follows:

                  "Section 9.18 Hedging Agreements. Except for those Hedging
         Agreements described in Schedule 9.18, the Company will not enter into
         or become obligated under, or permit any of its Subsidiaries to enter
         into or become obligated under any Hedging Agreement except for such
         agreements which in the aggregate do not cover at any time a volume of
         oil and gas (on a barrel of oil equivalent basis) equal to more than
         (i) 80% for any 12-month period during the period beginning July 15,
         2002 through and including December 31, 2004, and (ii) 70% for any
         12-month period thereafter, of the projected production for such period
         of oil and gas (on a barrel of oil equivalent basis) from the Oil and
         Gas Properties included in the Borrowing Base and such

                                        1

<PAGE>

         contracts are for delivery or settlement on or before the end of the
         second calendar year after the calendar year of the date of such
         contract."

         SECTION 3. Conditions Precedent; Effectiveness. (a) This Second
Amendment shall become effective as of the date hereof when the Administrative
Agent shall have received counterparts hereof duly executed by the Company and
the Required Lenders (or, in the case of any party as to which an executed
counterpart shall not have been received, telegraphic, telex, or other written
confirmation from such party of execution of a counterpart hereof by such
party).

         SECTION 4. Reaffirmation of Representations and Warranties. To induce
the Lenders, the Administrative Agent and the Issuing Bank to enter into this
Second Amendment, the Company hereby reaffirms, as of the date hereof, its
representations and warranties in their entirety contained in Article VII of the
Credit Agreement and in all other documents executed pursuant thereto (except to
the extent such representations and warranties relate solely to an earlier
date).

         SECTION 5. Reaffirmation of Credit Agreement. This Second Amendment
shall be deemed to be an amendment to the Credit Agreement, and the Credit
Agreement, as amended hereby, is hereby ratified, approved and confirmed in each
and every respect. All references to the Credit Agreement herein and in any
other document, instrument, agreement or writing shall hereafter be deemed to
refer to the Credit Agreement, as amended hereby.

         SECTION 6. Governing Law; Entire Agreement. This Second Amendment shall
be governed by, and construed in accordance with, the laws of the State of
Texas. The Credit Agreement, as amended by this Second Amendment, the Notes and
the other Loan Documents constitute the entire understanding among the parties
hereto with respect to the subject matter hereof and supersede any prior
agreements, written or oral, with respect thereto.

         SECTION 7. Severability of Provisions. Any provision in this Second
Amendment that is held to be inoperative, unenforceable, or invalid in any
jurisdiction shall, as to that jurisdiction, be inoperative, unenforceable, or
invalid without affecting the remaining provisions in that jurisdiction or the
operation, enforceability, or validity of that provision in any other
jurisdiction, and to this end the provisions of this Second Amendment are
declared to be severable.

         SECTION 8. Counterparts. This Second Amendment may be executed in any
number of counterparts, all of which taken together shall constitute one
agreement, and any of the parties hereto may execute this Second Amendment by
signing any such counterpart.

         SECTION 9. Headings. Article and section headings in this Second
Amendment are for convenience of reference only, and shall not govern the
interpretation of any of the provisions of this Second Amendment.

         SECTION 10. Successors and Assigns. This Second Amendment shall be
binding upon and inure to the benefit of the parties hereto and their respective
successors and assigns.

                         [Signatures begin on next page]

                                        2

<PAGE>

         IN WITNESS WHEREOF, the parties hereto have executed this Second
Amendment effective as of the Second Amendment Effective Date.

COMPANY:                               THE HOUSTON EXPLORATION COMPANY

                                       By:    /s/ John H. Karnes
                                              ----------------------------------
                                       Name:  John H. Karnes
                                       Title: Sr. Vice President and Chief
                                              Financial

Officer

AGENTS AND LENDERS:                    WACHOVIA BANK, NATIONAL ASSOCIATION,
                                       Individually, as Issuing Bank and as
                                       Administrative Agent

                                       By:    /s/ David E. Humphreys
                                              ----------------------------------
                                       Name:  David E. Humphreys
                                       Title: Vice President

                                       THE BANK OF NOVA SCOTIA, Individually and
                                       as Co-Syndication Agent

                                       By:    /s/ V. Gibson
                                              ----------------------------------
                                       Name:  V. Gibson
                                       Title: Assistant Agent

                                       FLEET NATIONAL BANK, Individually and as
                                       Co-Syndication Agent

                                       By:    /s/ Allison I. Rossi
                                              ----------------------------------
                                       Name:  Allison I. Rossi

                                       Title: Director

                                       BNP PARIBAS, Individually and as
                                       Documentation Agent

                                       By:    /s/ Betsy Jocher
                                              ----------------------------------
                                       Name:  Betsy Jocher

                                       Title: Vice President

                                       By:    /s/ Polly Schott
                                              ----------------------------------
                                       Name:  Polly Schott
                                       Title: Vice President

                                       COMERICA BANK-TEXAS

                                       By:    /s/ H. Vadgama
                                              ----------------------------------
                                       Name:  Huma Vadgama
                                       Title: Assistant Vice President

                      [Signature Page to Second Amendment]

<PAGE>

                                       FORTIS CAPITAL CORP.

                                       By:    /s/ David Montgomery
                                              ----------------------------------
                                       Name:  David Montgomery
                                       Title: Senior Vice President

                                       By:    /s/ Darrell W. Holley
                                              ----------------------------------
                                       Name:  Darrell W. Holley
                                       Title: Managing Director

                                       UNION BANK OF CALIFORNIA, N.A.

                                       By:    /s/ Sean Murphy
                                              ----------------------------------
                                       Name:  Sean Murphy
                                       Title: Vice President

                                       THE BANK OF NEW YORK

                                       By:    /s/ Peter W. Keller
                                              ----------------------------------
                                       Name:  Peter W. Keller
                                       Title: Vice President

                                       WASHINGTON MUTUAL BANK, F.A.

                                       By:    /s/ Mark Isensee
                                              ----------------------------------
                                       Name:  Mark Isensee
                                       Title: Vice President

                                       WELLS FARGO BANK TEXAS, N.A.

                                       By:    /s/ Paul Squires
                                              ----------------------------------
                                       Name:  Paul Squires
                                       Title: Vice President

                                       NATEXIS BANQUES POPULAIRES

                                       By:    /s/ Renaud d'Herbes
                                              ----------------------------------
                                       Name:  Renaud d'Herbes
                                       Title: Senior Vice President & Regional
                                              Manager

                                       By:    /s/ Daniel Payer
                                              ----------------------------------
                                       Name:  Daniel Payer
                                       Title: Vice President

                                       HIBERNIA NATIONAL BANK

                                       By:    /s/ David R. Reid
                                              ----------------------------------
                                       Name:  David R. Reid
                                       Title: Senior Vice President

                      [Signature Page to Second Amendment]
<PAGE>

                                       COMPASS BANK

                                       By:    /s/ Murray E. Brasseux
                                       Name:  Murray E. Brasseux
                                       Title: Executive Vice President

                                       SOUTHWEST BANK OF TEXAS, N.A.

                                       By:    /s/ W. Bryan Chapman
                                              ----------------------------------
                                       Name:  W Bryan Chapman
                                       Title: Vice President, Energy Lending

                      [Signature Page to Second Amendment]