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                                                                    EXHIBIT 10.2
                              EMPLOYMENT AGREEMENT


         THIS EMPLOYMENT AGREEMENT (this "Agreement") dated as of May 1, 1998 by
and between THE HOUSTON EXPLORATION COMPANY a Delaware corporation (the
"Company"), and THOMAS E. SCHWARTZ, (the "Executive").

                                   WITNESSETH:

         WHEREAS, the Executive has been providing services to the Company and
the Company has been compensating the Executive; and

         WHEREAS, the Company desires to continue to employ the Executive upon
the terms and conditions and in the capacities 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. 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 Vice President,
Geophysics for a term (the "Term of Employment") beginning on the Effective Date
(defined below) and ending on the Expiration Date (defined below). As used
herein, "Effective Date" means May 1, 1998. As used in this Agreement,
"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 60 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 Vice President, Geophysics 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 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 Employee's duties
and,responsibilities to the Company.

         (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



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incorporation and by-laws to so provide, and that it will obtain errors and
omissions insurance in the amount of no less than $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 $160,000 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, without
limitation, those set forth on Exhibit A 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 to him on the date of this
Agreement (or the equivalent of such benefits) and, without duplication, any
other noncash benefits provided by the Company to its other officers and key
employees as they may exist from time to time. Such benefits shall include leave
or vacation time (not less than four weeks), 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 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 $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 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



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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 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) Definitions: 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 and for the period of one year thereafter, 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 l 2 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 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.




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         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 l 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 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 Section 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 60% of annual salary at the date of disability (to continue until at
least age 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 180 consecutive days during any
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



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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 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 described in Section 2 hereof 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 positions (and attributes thereof) described in Section 2 hereof, (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 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 if, within one year
thereafter, the Company shall:

                  (1) fail to continue in effect (x) any material benefit or
         compensation plan in which the Executive is participating immediately
         prior to such Change of Control or (y) a plan providing the Executive
         with substantially similar benefits;

                  (2) take any action that would materially adversely affect the
         Executive's participation in or reduce the Executive's benefits under
         any of the plans referred to in clause (i) above, but excluding any
         such action by the Company that is required by law;

                  (3) amend, modify or repeal any provision of its certificate
         of incorporation or bylaws that was in effect immediately prior to such
         Change of Control, if such amendment, modification or repeal would
         materially adversely affect the Executive's rights to indemnification
         by the Company; or

                  (4) violate or breach any obligation of the Company in effect
         immediately prior to such Change of Control (regardless whether such
         obligation shall be set forth in the bylaws of the Company or
         elsewhere) to indemnify the Executive against any claim, loss, expense
         or liability sustained or incurred by the Executive by reason, in whole
         or in part, of the fact that the Executive is or was an officer,
         director or employee of the Company or any subsidiary or affiliate of
         the Company.

As used in this Agreement, a "Change of Control" shall mean:


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                  (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 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, (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) (I) 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 60 percent 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 60
         percent 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, 20 percent 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.

         (f) Insurance and Other Special Benefits. To the extent the Executive
is eligible thereunder, for a period of 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 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



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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 12-month period or at any other time.

         (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 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 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 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:

                  (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



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                  (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 by the Internal
Revenue Service or other taxing authority 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 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 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 resolved 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 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. NONEXCLUSIVITY 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.



<PAGE>   9



         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 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 30 days of the disputing
party's notice, or if the parties fail to meet within 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 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 nonbinding means as provided in Section 9(a) within 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 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 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



<PAGE>   10



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/ Thomas E. Schwartz
                             ---------------------- 
                               Thomas E. Schwartz




                             THE HOUSTON EXPLORATION COMPANY




                              By:/s/ James G. Floyd
                                 -------------------------
                                Name:   James G. Floyd
                                Title: President




<PAGE>   11



                                                              THOMAS E. SCHWARTZ


                                    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 and the other senior
executives of the Company will be:

<TABLE>
<CAPTION>
                                                 Percentage of Salary
                                                for Target Annual Bonus
                                                -----------------------
<S>                                                      <C>
         Thomas E. Schwartz,                             55%
         Vice President,
         Geophysics
</TABLE>


Moreover, if the Company performs better or worse than the Target, the bonus
will be directly affected. A schedule of Target 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>



<PAGE>   12

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 equalled 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. 

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 non-qualified stock options for the
remainder. On May 1, 1998, a grant of options with an exercise price at the
market trading price per share shall be granted in amounts described as follows:
                                                                             
<TABLE>
<CAPTION>
                                                       Shares
                                                       ------
         <S>                         <C>     
         Thomas E. Schwartz          30,000 shares @ $22.9375
</TABLE>


**As approved by the Compensation Committee, the Executive has been granted the
option to purchase 30,000 shares at $22.9375 per share effective May 1, 1998.

         These options will have a term of ten years and will vest in one-fifth
increments over five 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, (ii) on the termination of the Executive's
employment on the Disability of the Executive after the Executive had already
vested 60% or more of the option grant, or (iii) on the termination of the
Executive's employment by the Company without Cause or by the Executive for Good
Reason, or after the third anniversary of the date granted for any reason by the
Company other than for Cause.

         Thereafter, and during the Term of Employment, each year on the
anniversary of his Employment Agreement, the Executive shall be eligible for
consideration in accordance with the Company's performance and the terms of the



<PAGE>   13


Plan 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>
                  <S>                                        <C>
                                                              Target Percentage of Base Salary
                                                              --------------------------------
                  Thomas E. Schwartz                                         50
</TABLE>

These options will vest in accordance with the Plan at the rate of one-third per
year of the number of option shares beginning with the first anniversary of the
award and each anniversary thereafter with accelerated vesting as provided
above. These options will have a ten year term.