<PAGE>

                                                                   EXHIBIT 10.32


                              EMPLOYMENT AGREEMENT


         THIS EMPLOYMENT AGREEMENT (this "AGREEMENT") is dated as of October 22,
2001 (the "EFFECTIVE DATE"), and is entered into by and between THE HOUSTON
EXPLORATION COMPANY, a Delaware corporation (the "COMPANY"), and Steven L.
Mueller (the "EXECUTIVE").

                                   WITNESSETH:

         WHEREAS, the Company desires to employ the Executive upon the terms and
conditions and in the capacities set forth herein; and

         WHEREAS, the Company and the Executive desire to enter into this
Agreement according to the terms and conditions contained 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. EMPLOYMENT AND TERM OF EMPLOYMENT. Subject to the terms and
conditions of this Agreement, the Company hereby agrees to employ the Executive,
and the Executive hereby agrees to serve the Company as Senior Vice President
and General Manager-Onshore Division for a term (the "TERM OF EMPLOYMENT")
beginning on the Effective Date and ending on the Expiration Date (defined
below). As used herein, "EXPIRATION DATE" means the third anniversary of the
Effective Date, provided that on the first anniversary of the Effective Date and
on each subsequent anniversary of the Effective Date (such first anniversary
date and each such subsequent anniversary date being referred to as a "RENEWAL
DATE"), the Expiration Date shall be automatically extended one additional year
unless, not less than ninety (90) days prior to the relevant Renewal Date, (i)
either party shall have given written notice to the other that no such automatic
extension shall occur after the date of such notice or (ii) either party shall
have given a Notice of Termination to the other pursuant to Section 7 hereof.
Notwithstanding the foregoing, if either party gives a valid Notice of
Termination pursuant to Section 7 hereof, the Term of Employment shall not
extend beyond the termination date specified in such Notice of Termination.

         2. SCOPE OF EMPLOYMENT.

                  (a) During the Term of Employment, the Executive agrees to (i)
         serve as Senior Vice President and General Manager-Onshore Division of
         the Company and shall have and may exercise all the powers, duties and
         functions as are normal and customary to such positions and that are
         consistent with the responsibilities set forth with respect to such
         positions in the Company's by-laws and (ii) perform such other duties
         not inconsistent with his position as are assigned to him, from time to
         time, by the Board of Directors of the Company (the "BOARD"). During
         the Term of Employment, the Executive shall (i) report directly and
         exclusively to the President and Chief Executive Officer and (ii)
         devote substantially all of his business time, attention, skill and
         efforts to the faithful performance of his duties hereunder. Subject to
         Section 6, the foregoing shall not be construed to prevent the
         Executive from making investments in businesses or enterprises so long
         as such investments do not require any services on the part of the
         Executive in the operation of such business or enterprises of a nature
         or magnitude that would interfere materially with the performance of
         his duties hereunder.

                  (b) During the Term of Employment, the Executive agrees to
         serve, if elected, as an officer or director of any subsidiary or
         affiliate of the Company so long as such service is commensurate with
         the Executive's duties and responsibilities to the Company.



                                      -1-
<PAGE>

                  (c) The Executive's place of employment hereunder shall be at
         the Company's principal executive offices in the greater Houston, Texas
         metropolitan area. Moreover, the Company agrees that it will provide
         immunity and indemnity for the Executive to the fullest extent allowed
         by law, that if necessary it will amend its certificate of
         incorporation and bylaws to so provide, and that it will obtain errors
         and omissions insurance in the amount of no less than Ten Million
         Dollars ($10,000,000) naming the Executive as an additional insured.

         3. COMPENSATION. During the Term of Employment, in consideration of the
Executive's services hereunder, including, without limitation, service as an
officer or director of the Company or of any subsidiary or affiliate thereof,
and in consideration of the Executive's covenants regarding confidentiality in
Section 5 hereof and noncompetition in Section 6 hereof, the Executive shall
receive a salary at the rate of Two Hundred Thirty Thousand Dollars ($230,000)
per year (payable at such regular intervals as other employees of the Company
are compensated in accordance with the Company's employment practices), which
amount shall be subject to review annually by the Board and may be adjusted at
its discretion, provided that such salary may not be reduced at any time. In
addition, the Executive shall be entitled to participate in such bonus,
incentive compensation or other programs as are created or approved by the Board
from time to time, including, but not limited to, the benefits described on
EXHIBIT A attached hereto.

         4. ADDITIONAL COMPENSATION AND BENEFITS.

                  (a) As additional compensation for the Executive's services
         under this Agreement, the Executive's covenants regarding
         confidentiality in Section 5 hereof and noncompetition in Section 6
         hereof, during the Term of Employment, the Company agrees to provide
         the Executive with the non-cash benefits being provided by the Company
         to its other officers and key employees as they may exist from time to
         time, including, but not limited to, the benefits described on EXHIBIT
         A attached hereto. Such benefits shall include leave or vacation time
         (not less than five (5) weeks per year), medical and dental insurance,
         life insurance and other health care benefits, retirement and
         disability benefits as may hereafter be provided by the Company in
         accordance with its policies as well as any stock option plan or
         similar employee benefit program for which key executives are or shall
         become eligible. The Executive's participation in each employee benefit
         plan or program provided to officers or other senior executives of the
         Company in general shall be at least as favorable to the Executive as
         the most highly benefited employee thereunder.

                  (b) The Executive is authorized to incur reasonable business
         expenses for promoting the business and reputation of the Company,
         including (without limitation) reasonable expenditures for travel,
         lodging, club memberships, meals and client, patron, customer and/or
         business associate entertainment. The Company shall reimburse within
         thirty (30) days the Executive for reasonable expenses incurred by the
         Executive in furtherance of the Company's business, provided that such
         expenses are incurred in accordance with the Company's policies and
         upon presentation of documentation in accordance with expense
         reimbursement policies of the Company as they may exist from time to
         time, and submission to the Company of adequate documentation in
         accordance with federal income tax regulations and administrative
         pronouncements.

                  (c) During the Term of Employment, the Company shall pay to
         the Executive an automobile allowance of Seven Hundred Dollars ($700)
         per month. The Board shall review the amount of such monthly allowance
         at least annually and may increase the same at any time as the Board
         deems appropriate.

         5. CONFIDENTIALITY AND OTHER MATTERS.

                  (a) Confidentiality. The Executive shall hold in a fiduciary
         capacity for the benefit of the Company all maps, data, reports,
         including results of exploration, drilling, drill cores, cuttings, and
         other samples, and other information relating to the business of the
         Company which comes into the possession of the Executive during the
         Term of Employment (such information being collectively referred to
         herein as the "CONFIDENTIAL INFORMATION"). During the Term of
         Employment and after termination of the



                                      -2-
<PAGE>

         Executive's employment hereunder, the Executive agrees: (i) to take all
         such precautions as may be reasonably necessary to prevent the
         disclosure to any third party of any of the Confidential Information;
         (ii) not to use for the Executive's own benefit any of the Confidential
         Information; and (iii) not to aid any other person or entity in the use
         of the Confidential Information in competition with the Company,
         provided that nothing in this Agreement shall prohibit the Executive
         from disclosing or using any Confidential Information (A) in the
         performance of his duties hereunder, (B) as required by applicable law,
         (C) in connection with the enforcement of his rights under this
         Agreement or any other agreement with the Company, (D) in connection
         with the defense or settlement of any claim, suit or action brought or
         threatened against the Executive by or in the right of the Company or
         (E) with the prior written consent of the Board. Notwithstanding any
         provision contained herein to the contrary, the term "CONFIDENTIAL
         INFORMATION" shall not be deemed to include any general knowledge,
         skills or experience acquired by the Executive or any knowledge or
         information known or available to the public in general. The Executive
         further agrees that, if requested by the Company in writing at any time
         within ninety (90) days after termination of his employment for any
         reason, he will surrender to the Company all Confidential Information,
         and any copies thereof, in his possession and agrees that all such
         materials, and copies thereof, are at all times the property of the
         Company. Notwithstanding the foregoing, the Executive shall be
         permitted to retain copies of, or have access to, all such Confidential
         Information relating to any disagreement, dispute or litigation
         (pending or threatened) involving the Executive.

                  (b) Remedies. For purposes of this Section 5, the "COMPANY"
         shall be defined as the Company and its affiliated companies including
         (without limitation) its successors and assigns and its subsidiaries
         and each of their respective successors and assigns. In the event of a
         breach or threatened breach by the Executive of the provisions of this
         Section 5, the Company shall be entitled to an injunction restraining
         the Executive from violating such provisions without the necessity of
         posting a bond therefor. Nothing herein shall be construed as
         prohibiting the Company from pursuing any other remedies available to
         it at law or in equity. Except as specifically set forth herein, the
         parties agree that the provisions of this Section 5 shall survive the
         earlier termination of the Executive's employment with the Company, as
         the continuation of this covenant is necessary for the protection of
         the Company.

         6. NONCOMPETITION.

                  (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 a competing business in 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 if the Executive's employment
         is terminated during the Term of Employment by the Executive for Good
         Reason (defined in Section 7 hereof) or by the Company for any reason
         other than Cause (defined in Section 7 hereof) 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).

                  (b) Scope. In the event that the provisions of this Section 6
         should ever be deemed to exceed the time, geographic or activity
         related limitations permitted by applicable law, then such provisions
         shall be reformed to the maximum time, geographic or activity related
         limitations permitted by applicable law. In the event of a breach or
         threatened breach by the Executive of the provisions of this Section 6,
         the Company shall be entitled to an injunction restraining the
         Executive from violating such provisions without the necessity of
         posting a bond therefor. Nothing herein shall be construed as
         prohibiting the Company



                                      -3-
<PAGE>

         from pursuing any other remedies available to it at law or in equity.
         Except as specifically set forth herein, the parties agree that this
         Section 6 shall remain in effect for its full term notwithstanding the
         earlier termination of the Executive's employment with the Company, as
         the continuation of this covenant is necessary for the protection of
         the Company. For purposes of this Section 6, the "COMPANY" shall be
         defined as the Company and its affiliated companies, including (without
         limitation) its successors and assigns and its subsidiaries and each of
         their respective successors and assigns.

         7. TERMINATION.

                  (a) General. The Executive's employment hereunder shall
         automatically terminate on the earlier of his death or the Expiration
         Date. The Executive may, at any time prior to the Expiration Date,
         terminate his employment hereunder for any reason by delivering a
         Notice of Termination (defined below) to the Board. The Company may, at
         any time prior to the Expiration Date, terminate the Executive's
         employment hereunder for any reason by delivering a Notice of
         Termination to the Executive, provided that in no event shall the
         Company be entitled to terminate the Executive's employment prior to
         the Expiration Date unless the Board shall duly adopt, by the
         affirmative vote of a least a majority of the entire membership of the
         Board, a resolution authorizing such termination and stating whether
         such termination is for Cause (defined below). The giving of a notice
         pursuant to clause (i) of the proviso contained in the penultimate
         sentence of Section 1 hereof shall not be deemed a termination of the
         Executive's employment by the party giving such notice. As used in this
         Agreement, "NOTICE OF TERMINATION" means a notice in writing purporting
         to terminate the Executive's employment in accordance with this Section
         7, which notice shall (i) specify the effective date of such
         termination (not prior to the date of such notice) and (ii) in the case
         of a termination by the Company for Cause or Disability or a
         termination by the Executive for Good Reason or Disability, set forth
         in reasonable detail the reason for such termination and the facts and
         circumstances claimed to provide a basis for such termination.

                  (b) Automatic Termination on Expiration Date. In the event the
         Executive's employment hereunder shall automatically terminate on the
         Expiration Date for any reason other than death, the Executive shall
         only be entitled to receive (i) all unpaid compensation accrued as of
         the termination date pursuant to Section 3 hereof, (ii) all unused
         vacation time accrued by the Executive as of the termination date,
         (iii) all amounts owing to the Executive under Sections 4(b) and 4(c)
         hereof and (iv) those benefits under Section 4 which are required under
         the Employee Retirement Income Security Act of 1974, as amended
         ("ERISA"), or other laws. The amounts described in clauses (i), (ii)
         and (iii) of the foregoing sentence shall be paid to the Executive in a
         lump sum payment promptly after the Expiration Date.

                  (c) Termination by Company for Cause. If the Company
         terminates the Executive's employment for Cause, the Executive shall
         only be entitled to receive the compensation and other payments
         described in paragraph (b) above, such compensation and other payments
         to be paid as if the Executive's employment had automatically
         terminated without the giving of any Notice of Termination. As used in
         this Agreement, "CAUSE" shall mean (i) any material failure of the
         Executive to perform his duties specified in Section 2 of this
         Agreement (other than any such failure resulting from the Executive's
         incapacity due to illness or other disability) after written notice of
         such failure has been given to the Executive by the Board and such
         failure shall have continued for thirty (30) days after receipt of such
         notice, (ii) gross or willful negligence or intentional wrongdoing or
         misconduct, (iii) a material breach by the Executive of Sections 5 or 6
         of this Agreement, or (iv) conviction of the Executive of a felony
         offense involving moral turpitude, any of which has or have a material
         adverse effect on the Executive's ability to perform the duties of his
         position or on the financial condition or profitability of the Company.

                  (d) Death or Disability. To provide for the event the
         Executive's employment is automatically terminated on account of his
         death or is terminated by either the Company or the Executive on
         account of Disability (defined below), the Company shall purchase and
         provide for the Executive life insurance in the amount of one times
         annual salary and shall purchase and provide for the Executive
         supplemental executive long-term disability benefits (to the extent
         necessary to provide the total benefits described herein, net of the
         Company's existing group long-term disability plan) to provide salary
         replacement in the amount of sixty percent (60%) of annual salary at
         the date of disability (to continue until



                                      -4-
<PAGE>

         at least age sixty-five (65), or for life if reasonably practicable).
         As used herein, "DISABILITY" means any physical or mental condition of
         the Executive that (i) prevents the Executive from being able to
         perform the services required under this Agreement, (ii) has continued
         for at least one hundred eighty (180) consecutive days during any
         twelve (12)-month period and (iii) is reasonably expected to continue.
         The Company's obligation to provide to the Executive long-term
         disability benefits hereunder shall be defined by the long-term
         disability benefits contract it is able to procure from an unrelated
         third party. For that purpose, the definition of disability shall be as
         stated in the contract. The Company and the Executive recognize that
         the definition of Disability hereunder may differ from the contract
         definition and the benefits payable shall be those as stated in the
         contract. The Company, however, agrees to obtain a contract with a
         definition of disability as similar as possible to the definition
         stated hereunder. Moreover, the Company and the Executive agree that
         for purposes of the other provisions of this Agreement, the definition
         of Disability as stated herein shall control.

                  (e) Termination by Company Without Cause or by the Executive
         with Good Reason. If either the Company terminates the Executive's
         employment for any reason other than for Cause or on account of
         Disability or the Executive terminates his employment for Good Reason
         (as hereinafter defined), the Company shall:

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

                           (ii) pay the Executive any accrued but unpaid
                  compensation as of the date of the termination of employment;
                  and

                           (iii) continue until the first anniversary of the
                  termination of the Executive's employment, or such longer
                  period as any plan, program or policy or ERISA or other laws
                  may provide, benefits to the Executive as set forth in Section
                  7(f) below.

         As used in this Agreement, "GOOD REASON" shall mean: (A) the failure by
         the Company to elect or re-elect or to appoint or re-appoint the
         Executive to the office of Senior Vice President and General
         Manager-Onshore Division of the Company without Cause; (B) a material
         change in the powers, duties, responsibilities or functions of the
         Executive as described in Section 2 hereof, including (without
         limitation) any change which would alter the Executive's reporting
         responsibilities or cause the Executive's position with the Company to
         be of less dignity, responsibility, importance or scope than the
         position (and attributes thereof) of Senior Vice President and General
         Manager-Onshore Division of the Company, (C) without the Executive's
         prior written consent, the relocation of the Company's principal
         executive offices outside the greater Houston, Texas metropolitan area
         or requiring the Executive to be based other than at such principal
         executive offices, (D) the failure of the Company to obtain any
         assumption agreement required by Section 16 hereof, (E) the failure by
         the Company to pay the Executive within ten (10) days after a written
         demand therefor any installment of any previous award of or deferred
         compensation, if any, under any employee benefit plan or any deferred
         compensation program in effect in which the Executive may have
         participated, (F) any other material breach of this Agreement by the
         Company, or (G) the occurrence of a Change of Control.

         As used in this Agreement, a "CHANGE OF CONTROL" shall mean:

                           (i) the acquisition after the Effective Date by any
                  individual, entity or group (within the meaning of Section
                  13(d)(3) or 14(d)(2) of the Securities Exchange Act of 1934,
                  as amended) (a "PERSON") of beneficial ownership of twenty
                  percent (20%) or more of either (i) the then outstanding
                  shares of common stock of the Company (the "OUTSTANDING COMMON
                  STOCK") or (ii) the combined voting power of the then
                  outstanding voting securities of the Company entitled to vote
                  generally in the election of directors (the "OUTSTANDING
                  VOTING SECURITIES"), provided that for purposes of this
                  subsection (i), the following acquisitions shall not
                  constitute a Change of Control: (A) any acquisition directly
                  from the Company, (B) any acquisition by the Company,



                                      -5-
<PAGE>

                  (C) any acquisition by any employee benefit plan (or related
                  trust) sponsored or maintained by the Company or any
                  corporation controlled by the Company, or (D) any acquisition
                  by any corporation pursuant to a transaction which complies
                  with clauses (A), (B) and (C) of subsection (iii) hereof; or

                           (ii) individuals, who, as of the Effective Date,
                  constitute the Board (the "INCUMBENT BOARD") cease for any
                  reason to constitute at least a majority of the Board,
                  provided that any individual becoming a director subsequent to
                  the Effective Date whose election, or nomination for election
                  by the Company's shareholders, was approved by a vote of at
                  least a majority of the directors then comprising the
                  Incumbent Board shall be considered as though such individual
                  was a member of the Incumbent Board, but excluding, for this
                  purpose, any such individual whose initial assumption of
                  office occurs as a result of an actual or threatened election
                  contest with respect to the election or removal of directors
                  or other actual or threatened solicitation of proxies or
                  consents by or on behalf of a Person other than the Board; or

                           (iii) consummation after the Effective Date of a
                  reorganization, merger or consolidation or sale or other
                  disposition of all or substantially all of the assets of the
                  Company (a "CORPORATE Transaction") in each case, unless,
                  following such Corporate Transaction, (A) (1) all or
                  substantially all of the persons who were the beneficial
                  owners of the Outstanding Common Stock immediately prior to
                  such Corporate Transaction beneficially own, directly or
                  indirectly, more than sixty percent (60%) of the then
                  outstanding shares of common stock of the corporation
                  resulting from such Corporate Transaction, and (2) all or
                  substantially all of the persons who were the beneficial
                  owners of the Outstanding Voting Securities immediately prior
                  to such Corporate Transaction beneficially own, directly or
                  indirectly, more than sixty percent (60%) of the combined
                  voting power of the then outstanding voting securities
                  entitled to vote generally in the election of directors of the
                  corporation resulting from such Corporate Transaction
                  (including, without limitation, a corporation which as a
                  result of such transaction owns the Company or all or
                  substantially all of the Company's assets either directly or
                  through one or more subsidiaries) in substantially the same
                  proportions as their ownership of the Outstanding Common Stock
                  and the Outstanding Voting Securities immediately prior to
                  such Corporate Transaction, as the case may be, (B) no Person
                  (excluding (l) any corporation resulting from such Corporate
                  Transaction or any employee benefit plan (or related trust) of
                  the Company or such corporation resulting from such Corporate
                  Transaction and (2) any Person approved by the Incumbent
                  Board) beneficially owns, directly or indirectly, twenty
                  percent (20%) or more of the then outstanding shares of common
                  stock of the corporation resulting from such Corporate
                  Transaction or the combined voting power of the then
                  outstanding voting securities of such corporation except to
                  the extent that such ownership existed prior to such Corporate
                  Transaction and (C) at least a majority of the members of the
                  board of directors of the corporation resulting from such
                  Corporate Transaction were members of the Incumbent Board at
                  the time of the execution of the initial agreement or of the
                  action of the Board providing for such Corporate Transaction.

         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.

                  (f) Insurance and Other Special Benefits. To the extent the
         Executive is eligible thereunder, for a period of twelve (12) months
         following termination pursuant to Section 7(e) hereof, the Executive
         shall continue to be provided life insurance policies provided to the
         Executive on the date hereof or such successor policies in effect at
         the time of the Executive's termination, and shall also continue to be
         covered



                                      -6-
<PAGE>

         for the applicable period by each other insurance, health or other
         benefit program, plan or policy (excluding long-term disability) by
         which he was covered at the time of the Executive's termination. In the
         event the Executive is ineligible to continue to be so covered under
         the terms of any such life insurance, health or other benefit program,
         plan or policy, the Company shall provide to the Executive through
         other sources such benefits (excluding long-term disability), including
         such additional benefits, as may be necessary to make the benefits
         applicable to the Executive substantially equivalent to those in effect
         immediately prior to such termination, provided that if during such
         period the Executive should enter into the employ of another company or
         firm which provides to the Executive substantially similar benefit
         coverage, the Executive's participation in the comparable benefits
         provided by the Company, either directly or through such other sources,
         shall cease. Nothing contained in this paragraph shall be deemed to
         require or permit termination or restriction of any of the Executive's
         coverage under any plan or program of the Company or any of its
         subsidiaries or any successor plan or program thereto to which the
         Executive is entitled under the terms of such plan or program, whether
         at the end of the aforementioned twelve (12)-month period or at any
         other time. Upon termination of the Executive's employment under
         Section 7(d) or 7(e) hereof, any vesting, lapse of time or similar
         requirement under any stock option plan, restricted stock plan or other
         employee benefit or deferred compensation plan or program in which the
         Executive may participate shall be accelerated to the date of such
         termination and any conditions to the Executive's entitlement to any
         benefits under any of such plans or programs shall be deemed to have
         been satisfied.

                  (g) Certain Additional Payments by the Company. Anything in
         this Agreement to the contrary notwithstanding, in the event it shall
         be determined that any payment or distribution by the Company to or for
         the benefit of the Executive, whether paid or payable or distributed or
         distributable pursuant to the terms of this Agreement or otherwise (a
         "PAYMENT"), would be subject to the excise tax imposed by Section 4999
         of the Code or any interest or penalties with respect to such excise
         tax (such excise tax, together with any such interest and penalties,
         are hereinafter collectively referred to as the "EXCISE TAX"), then the
         Executive shall be entitled to receive an additional payment (a
         "GROSS-UP PAYMENT") in an amount such that after payment by the
         Executive of all taxes (including any interest or penalties imposed
         with respect to such taxes), including any Excise Tax imposed upon the
         Gross-Up Payment, the Executive retains an amount of the Gross-Up
         Payment equal to the Excise Tax imposed upon the Payments. Subject to
         the provisions of this Section 7(g), all determinations required to be
         made hereunder, including whether a Gross-Up Payment is required and
         the amount of such Gross-Up Payment, shall be made by Arthur Andersen
         L.L.P. or such other accounting firm which at the time audits the
         financial statements of the Company (the "ACCOUNTING FIRM") at the sole
         expense of the Company, which shall provide detailed supporting
         calculations both to the Company and the Executive within fifteen (15)
         business days of the date of termination of the Executive's employment
         under this Agreement, if applicable, or such earlier time as is
         requested by the Company. If the Accounting Firm determines that no
         Excise Tax is payable by the Executive, the Accounting Firm shall
         furnish the Executive with an opinion that he has substantial authority
         not to report any Excise Tax on his federal income tax return. Any
         determination by the Accounting Firm shall be binding upon the Company
         and the Executive. As a result of the uncertainty in the application of
         Section 4999 of the Code at the time of the initial determination by
         the Accounting Firm hereunder, it is possible that Gross-Up Payments,
         which will not have been made by the Company should have been made (an
         "UNDERPAYMENT"), consistent with the calculations required to be made
         hereunder. If the Company exhausts its remedies pursuant hereto and the
         Executive thereafter is required to make a payment of any Excise Tax,
         the Accounting Firm shall determine the amount of the Underpayment that
         has occurred and any such Underpayment shall be promptly paid by the
         Company to or for the benefit of the Executive.

                  The Executive shall notify the Company in writing of any claim
         by the Internal Revenue Service that, if successful, would require the
         payment by the Company of the Gross-Up Payment. Such notification shall
         be given as soon as practicable but no later than ten (10) business
         days after the Executive knows of such claim and shall apprise the
         Company of the nature of such claim and the date on which such claim is
         requested to be paid. The Executive shall not pay such claim prior to
         the expiration of the thirty (30)-day period following the date on
         which it gives such notice to the Company (or such shorter period
         ending on the date that any payment of taxes with respect to such claim
         is due). If the Company notifies the Executive in writing prior to the
         expiration of such period that it desires to contest such claim, the
         Executive shall:



                                      -7-
<PAGE>

                           (i) give the Company any information reasonably
                  requested by the Company relating to such claim,

                           (ii) take such action in connection with contesting
                  such claim as the Company shall reasonably request in writing
                  from time to time, including (without limitation) accepting
                  legal representation with respect to such claim by an attorney
                  reasonably selected by the Company,

                           (iii) cooperate with the Company in good faith to
                  effectively contest such claim, and

                           (iv) permit the Company to participate in any
                  proceedings relating to such claim;

         provided that the Company shall bear and pay directly all costs and
         expenses (including additional interest and penalties) incurred in
         connection with such contest and shall indemnify and hold the Executive
         harmless, on an after-tax basis, for any Excise Tax or income tax,
         including interest and penalties with respect thereto, imposed as a
         result of such representation and payment of costs and expenses.
         Without limitation on the foregoing provisions hereof the Company shall
         control all proceedings taken in connection with such contest and, at
         its sole option, may pursue or forego any and all administrative
         appeals, proceedings, hearings and conferences with the taxing
         authority in respect of such claim and may, at its sole option, either
         direct the Executive to pay the tax claimed and sue for a refund or
         contest the claim in any permissible manner, and the Executive agrees
         to prosecute such contest to a determination before any administrative
         tribunal, in a court of initial jurisdiction and in one or more
         appellate courts, as the Company shall determine, provided that if the
         Company directs the Executive to pay such claim and sue for a refund,
         the Company shall advance the amount of such payment to the Executive,
         on an interest-free basis and shall indemnify and hold the Executive
         harmless, on an after-tax basis, from any Excise Tax or income tax,
         including interest or penalties with respect thereto, imposed with
         respect to such advance or with respect to any imputed income with
         respect to such advance, and further provided that any extension of the
         statute of limitations relating to payment of taxes for the taxable
         year of the Executive with respect to which such contested amount is
         claimed to be due is limited solely to such contested amount.
         Furthermore, the Company's control of the contest shall be limited to
         issues with respect to which a Gross-Up Payment would be payable
         hereunder and the Executive shall be entitled to settle or contest, as
         the case may be, any other issue raised by the Internal Revenue Service
         or any other taxing authority.

                  If, after the receipt by the Executive of an amount advanced
         by the Company pursuant hereto, the Executive becomes entitled to
         receive any refund with respect to such claim, the Executive shall
         (subject to the Company's complying with the requirements hereof)
         promptly pay to the Company the amount of such refund (together with
         any interest paid or credited thereon after taxes applicable thereto).
         If, after the receipt by the Executive of an amount advanced by the
         Company pursuant hereto, a determination is made that the Executive
         shall not be entitled to any refund with respect to such claim and the
         Company does not notify the Executive in writing of its intent to
         contest such denial of refund prior to the expiration of thirty (30)
         days after such determination, then such advance shall be forgiven and
         shall not be required to be repaid and the amount of such advance shall
         offset, to the extent thereof, the amount of Gross-Up Payment required
         to be paid.

                  (h) Either party may, within fifteen (15) days after receipt
         of a Notice of Termination from the other party, provide notice to the
         other party that a dispute exists concerning the termination, in which
         event the dispute shall be resolved in accordance with Section 9
         hereof. Notwithstanding the pendency of any such dispute and
         notwithstanding any provision of this Agreement to the contrary, the
         Company will (i) continue to pay the Executive the annual base salary
         described in Section 3 hereof and (ii) continue the Executive as a
         participant in all compensation and benefit plans in which the
         Executive was participating when the relevant Notice of Termination was
         given, until the dispute is finally resolved or, with respect to a
         Notice of Termination given by the Executive, the date of termination
         specified in such Notice of Termination if earlier, but, in each case,
         not past the Expiration Date. If (i) the Company gives a Notice of
         Termination to the Executive, (ii) the Executive disputes the
         termination as contemplated by this paragraph (h) and (iii) such
         dispute is finally in favor of the Company in accordance with Section 9
         hereof, the Executive shall be required to refund to the Company any
         amounts paid to the Executive under this



                                      -8-
<PAGE>

         paragraph (h) but only if, and then only to the extent, the Executive
         is not otherwise entitled to receive such amounts under this Agreement.

         8. NON-EXCLUSIVITY OF RIGHTS. Nothing in this Agreement shall prevent
or limit the Executive's continuing or future participation in any benefit,
bonus, incentive or other plan or program provided by the Company or any of its
affiliated companies and for which the Executive may qualify, nor shall anything
herein limit or otherwise affect such rights as the Executive may have under any
stock option or other agreements with the Company or any of its affiliated
companies. Amounts which are vested benefits or which the Executive is otherwise
entitled to receive under any plan or program of the Company or any of its
affiliated companies at or subsequent to the date of termination of the
Executive's employment under this Agreement shall be payable in accordance with
such plan or program.

         9. RESOLUTION OF DISPUTES.

                  (a) Negotiation. The parties shall attempt in good faith to
         resolve any dispute arising out of or relating to this Agreement
         promptly by negotiations between the Executive and an executive officer
         of the Company who has authority to settle the controversy. Any party
         may give the other party written notice of any dispute not resolved in
         the normal course of business. Within ten (10) days after the effective
         date of such notice, the Executive and an executive officer of the
         Company shall meet at a mutually acceptable time and place within the
         Houston, Texas metropolitan area, and thereafter as often as they
         reasonably deem necessary, to exchange relevant information and to
         attempt to resolve the dispute. If the matter has not been resolved
         within thirty (30) days of the disputing party's notice, or if the
         parties fail to meet within ten (10) days, either party may initiate
         arbitration of the controversy or claim as provided hereinafter. If a
         negotiator intends to be accompanied at a meeting by an attorney, the
         other negotiator shall be given at least three (3) business days'
         notice of such intention and may also be accompanied by an attorney.
         All negotiations pursuant to this Section 9(a) shall be treated as
         compromise and settlement negotiations for the purposes of the federal
         and state rules of evidence and procedure.

                  (b) Arbitration. Any dispute arising out of or relating to
         this Agreement or the breach, termination or validity thereof, which
         has not been resolved by non-binding means as provided in Section 9(a)
         within sixty (60) days of the initiation of such procedure, shall be
         finally settled by arbitration conducted expeditiously in accordance
         with the Center for Public Resources, Inc. ("CPR") Rules for
         Non-Administered Arbitration of Business Disputes by three (3)
         independent and impartial arbitrators, of whom each party shall appoint
         one, provided that if one party has requested the other to participate
         in a non-binding procedure and the other has failed to participate, the
         requesting party may initiate arbitration before the expiration of such
         period. Any such arbitration shall take place in Harris County, Texas.
         Any arbitrator not appointed by a party shall be appointed from the CPR
         Panels of Neutrals. The arbitration shall be governed by the United
         States Arbitration Act and any judgment upon the award decided upon by
         the arbitrators may be entered by any court having jurisdiction
         thereof. Each party hereby acknowledges that compensatory damages
         include (without limitation) any benefit or right of indemnification
         given by another party to the other under this Agreement.

         10. EXPENSES. The Company shall promptly pay or reimburse the Executive
for all costs and expenses, including, without limitation, court costs and
attorneys' fees, incurred by the Executive as a result of any claim, action or
proceeding (including, without limitation a claim action or proceeding by the
Executive against the Company) arising out of, or challenging the validity or
enforceability of, this Agreement or any provision hereof.

         11. GOVERNING LAW. This Agreement shall be governed by and construed in
accordance with the internal laws of the State of Texas. Venue and jurisdiction
of any act on relating to this agreement shall lie in Harris County, Texas.

         12. NOTICE. Any notice, payment, demand or communication required or
permitted to be given by this Agreement shall be deemed to have been
sufficiently given or served for all purposes if delivered personally or if sent
by registered or certified mall, return receipt requested, postage prepaid,
addressed to such party at its address



                                      -9-
<PAGE>

set forth below such party's signature to this Agreement or to such other
address as shall have been furnished in writing by such party for whom the
communication is intended. Any such notice shall be deemed to be given on the
date so delivered.

         13. SEVERABILITY. In the event any provisions hereof shall he modified
or held ineffective by any court, such adjudication shall not invalidate or
render ineffective the balance of the provisions hereof.

         14. ENTIRE AGREEMENT. This Agreement 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.

         15. AMENDMENT AND WAIVER. This Agreement may not be modified or amended
except by a writing signed by the parties. Any waiver or breach of any of the
terms of this Agreement shall not operate as a waiver of any other breach of
such terms or conditions, or any other terms or conditions, nor shall any
failure to enforce any provisions hereof operate as a waiver of such provision
or any other provision hereof.

         16. ASSIGNMENT. This Agreement is a personal employment contract and
the rights and interests of the Executive hereunder may not be sold,
transferred, assigned or pledged. The Company may assign its rights under this
Agreement to (i) any entity into or with which the Company is merged or
consolidated or to which the Company transfers all or substantially all of its
assets or (ii) any entity, which at the time of such assignment, controls, is
under common control with, or is controlled by the Company, provided that the
Company will require any successor (whether direct or indirect, by purchase,
merger, consolidation or otherwise) to all or substantially all of the business
and/or assets of the Company, by agreement in form and substance reasonably
acceptable to the Executive, to expressly assume and agree to perform this
Agreement in the same manner and to the same extent that the Company would be
required to perform it if not such succession had taken place.

         17. SUCCESSORS. This Agreement shall be binding upon and inure to the
benefit of the Executive and his heirs, executors, administrators and legal
representatives. This Agreement shall be binding upon and inure to the benefit
of the Company and its successors and assigns.

         18. SECTION HEADINGS. The section headings in this Agreement have been
inserted for convenience and shall not be used for interpretive purposes or to
otherwise construe this Agreement.

         19. NO MITIGATION OR SET-OFF. The provisions of this Agreement are not
intended to, nor shall they be construed to, require that the Executive mitigate
the amount of any payment provided for in this Agreement by seeking or accepting
other employment, nor shall the amount of any payment provided for in this
Agreement be reduced by any compensation earned by the Executive as a result of
his employment by another employer or otherwise. The Company's obligations to
make the payments to the Executive required under this Agreement and otherwise
to perform its obligations hereunder shall not be affected by any set off,
counterclaim, recoupment, defense or other claim, right or action that the
Company may have against the Executive.

         IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date first written above and intend that this Agreement have the effect
of a sealed instrument.


                                       /s/ Steven L. Mueller
                                       ---------------------
                                       Steven L. Mueller

                                       THE HOUSTON EXPLORATION COMPANY

                                       /s/ William G. Hargett
                                       ----------------------
                                       William G. Hargett
                                       President and Chief Executive Officer



                                      -10-
<PAGE>

                                    EXHIBIT A


ANNUAL INCENTIVE PLAN


         The Executive will participate in the Company's annual incentive bonus
plan which will be based on a target measure of profitability to be determined
by the Board of Directors from year to year ("TARGET"). If the Company reaches
100% of Target, the Executive would earn 100% of his target bonus. The target
bonus will be determined as a percentage of the Executive's annual salary. The
percentage for the annual bonus for the Executive will be:

<Table>
<Caption>
                                                                              Percentage of Salary
                                                                             for Target Annual Bonus
                                                                             -----------------------
<S>                                                                          <C>
         Steven L. Mueller - Senior Vice President                                     55%
</Table>

         Moreover, if the Company performs better or worse than the target
earnings, the bonus will be directly affected. A schedule of target earnings and
target bonus will be as follows:

<Table>
<Caption>
                         Percentage of                                     Percentage of Target Annual
                   Target Earned by Company                                  Incentive Bonus Earned
                   ------------------------                                ---------------------------
<S>                                                                        <C>
                         Less than 70%                                                  0%

                              70%                                                      40%
                              80%                                                      60%
                              90%                                                      80%
                             100%                                                     100%
                             110%                                                     120%
                             120%                                                     140%
                             130%                                                     160%
                             140%                                                     180%
                             150% and more                                            200%
</Table>

         As an example, if (1) the Target is $4,500,000, (2) an executive's
annual salary is $250,000, (3) the target annual bonus percentage is 45%, and
(4) actual results achieved reaches $4,500,000, the executive's target bonus
would be $112,500. Since actual results achieved equaled 100% of Target, he
would earn $112,500. If actual results achieved were $5,220,000 (116%), he would
be entitled to 132% of his target bonus, or $148,500.



                                      A-1
<PAGE>

LONG TERM INCENTIVE PLAN


         The Executive will participate in the Company's 1996 Stock Option Plan.
The 1996 Stock Option Plan shall be paid in Company stock options under a plan
providing for qualified incentive stock options (for federal income tax
purposes) to the extent possible and a non-qualified stock options for the
remainder.

         All options granted will have a term of ten (10) years and will vest in
one-fifth (1/5) increments over five (5) years beginning on the first
anniversary of the date granted; provided, however, that such options shall be
deemed fully vested (i) on the death of the Executive or other employee, (ii) on
the termination of the Executive's or other employee's employment on the
Disability of the Executive or other employee after the Executive or other
employee had already vested sixty percent (60%) or more of the option grant, or
(iii) on the termination of the Executive's or other employee's employment by
the Company without Cause or by the Executive or other employee for Good Reason,
or after the third anniversary of the date granted for any reason by the Company
other than for Cause.

         During the Term of Employment, each year on the anniversary of the
Initial Public Offering of the Company, the Executive shall be eligible for an
additional option grant for that number of shares equal to a percentage of the
Executive's annual salary divided by a per share option value determined under
the Black-Scholes model. The percentage of the annual Long Term Incentive grant
for the Executive will be:

<Table>
<Caption>
                                                                        Target Percentage of Base Salary
                                                                        --------------------------------
<S>                                                                     <C>
                  Steven L. Mueller                                                    50
</Table>



                                      A-2