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                                                                   Exhibit 10.26


                              EMPLOYMENT AGREEMENT


         THIS EMPLOYMENT AGREEMENT (this "Agreement") dated as of September 19,
1996 by and between THE HOUSTON EXPLORATION COMPANY a Delaware corporation (the
"Company"), and CHARLES W. ADCOCK (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, Project Development 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 the closing date of
the offering of shares of Common Stock of the Company registered under the
Securities Act of 1933 (as amended) pursuant to a Registration Statement on
Form S-1 (Reg. No. 333-4437).  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, Project Development 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

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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 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 $125,000 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





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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 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.





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         (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).





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         (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.

         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.





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         (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 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.





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         (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,





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         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:

                 (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





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         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 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.





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         (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,





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                 (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 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.





                                      -11-
<PAGE>   12
         (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 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.      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 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.





                                      -12-
<PAGE>   13
         (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 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





                                      -13-
<PAGE>   14
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.





                                      -14-
<PAGE>   15
         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/ Charles W. Adcock            
                                           -------------------------------
                                           Charles W. Adcock




                                           THE HOUSTON EXPLORATION COMPANY


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





                                      -15-