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                                                     EXHIBIT 10.1


                    Enserch Exploration, Inc.
            Non-Employee Directors' Phantom Stock Plan


Article 1.  Establishment, Purpose, and Duration

     1.1       Establishment of the Plan.  Enserch Exploration,
Inc., a Texas corporation (hereinafter referred to as "EEX" or the
"Company") hereby establishes a non-employee Directors' compensation
plan to be known as the Enserch Exploration, Inc. Non-Employee 
Directors' Phantom Stock Plan (hereinafter referred to as
the "Plan"), as set forth in this document.

     The Plan shall become effective as of October 22, 1996 (the
"Effective Date") and shall remain in effect until terminated by
the Board of Directors pursuant to Section 3.3 herein.

     1.2       Purposes.  The purposes of the Plan are to align the
economic interests of EEX's Directors with those of shareholders by
linking part of the compensation of Directors to increases in value
of EEX; and to provide a financial incentive that will help attract
and retain Directors of outstanding competence.

Article 2.  Definitions

     Whenever used in the Plan, the following terms shall have the
meanings set forth below and, when the meaning is intended, the
initial letter of the word is capitalized:

     2.1       "Award" means, individually or collectively, a grant
of Phantom Stock Units under the Plan.

     2.2       "Award Value" shall mean, with respect to each
Phantom Stock Unit, the value on the date of grant equivalent to
the average of the high and the low selling prices of one share of
common stock as reported in the New York Stock Exchange Composite
Transactions Report (or any other consolidated transactions
reporting system which subsequently may replace such Composite
Transactions Report) for the New York Stock Exchange as of the date
such Unit is deemed to be granted, or if there is no sale on the
relevant date, then on the last previous day on which a sale was
reported.

     2.3       "Board of Directors" or "Board" means the Board of
Directors of EEX.

     2.4       "Change in Control" of EEX means one or more of the
following events:  

        (a)  Any person within the meaning of Section 13(d) and
     14(d) of the Exchange Act, other than the Company (including
     its subsidiaries), has become the beneficial owner, within the
     meaning of Rule 13d-3 under the 1934 Act, of 20% or more of
     the combined voting power of the Company's then outstanding
     Common Stock or equivalent in voting power of any class or
     classes of the Company's outstanding securities ordinarily
     entitled to vote in elections of directors ("voting
     securities"), or

        (b)  Shares representing 20% or more of the combined
     voting power of the Company's voting securities are purchased
     pursuant to a tender offer or exchange offer (other than an
     offer by the Company or its subsidiaries or affiliates), or

        (c)  the shareholders of the Company have:

               (i)  approved an agreement to merge or consolidate
        with or into another corporation or an agreement to sell
        or otherwise dispose of all or substantially all of the
        Company's assets (including a plan of liquidation), or

               (ii)  elected two or more persons to serve as
        directors of the Company who were not nominated and
        approved by the Board or a committee of the Board.

        (d)  For the purposes of this Section 2.4, no "change in
     control" shall be deemed to have occurred as a result of any
     action taken on transactions (including any Director or
     shareholder approvals thereof) or changes in the ownership of
     the Common Stock of the Company arising out of, or in
     connection with, (1) the merger of the Company with Lone Star
     Energy Plant Operations, Inc. ("LSEPO"); and (2) the spinoff
     by ENSERCH Corporation to its shareholders of its entire
     interest in the Company or any successor to the Company,
     following such merger with LSEPO.

     2.5       "Company" means Enserch Exploration, Inc., Texas
corporation, (including any and all subsidiaries), and any
successor thereto, as provided in Section 10.3 hereof.

     2.6       "Director" means an individual who is a member of
the Board of Directors of the Company.

     2.7       "Exchange Act" means the Securities Exchange Act of
1934, as amended from time to time, or any successor thereto.

     2.8       "Non-Employee Director" means a Director of the
Company who is ineligible to receive (or has waived any rights to
receive) any benefit or benefits under any Company-sponsored
pension or retirement plan.

     2.9       "Participant" means any eligible Director who has
received an Award under this Plan.

     2.10      "Payout Date" means the date of the earlier to occur
of: (i) a Directors' Retirement Date; (ii) a Director's death, or
(iii) a Change in Control.

     2.11      "Payout Value" means the aggregate value of the
Phantom Stock Units in a Participant's Account at the Payout Date
based on the value of EEX's common stock determined from the
average of the high and the low selling prices of shares of common
stock of EEX for each day during the ten (10) days immediately
preceding and following the Payout Date in which securities are
traded on the New York Stock Exchange as reported in the New York
Stock Exchange Composite Transactions Report (or any other
consolidated transactions reporting system which subsequently may
replace such Composite Transactions Report).

     2.12      "Phantom Stock Unit" or "Unit" means an Award
granted to a Participant as a measure of participation under the
Plan.

     2.13      "Plan" means the Enserch Exploration, Inc. Non-Employee 
Directors' Phantom Stock Plan, as set forth herein.

     2.14      "Retirement Date" shall mean the date a Director
terminates service as a member of the Board of Directors.

Article 3. Administration

     3.1       The Board.  The Plan shall be administered by the
Board of Directors.

     3.2       Authority of the Board.  Subject to the provisions
herein, except as limited by law or by the Company's Articles of
Incorporation or Bylaws, the Board shall have full power to:
(i) determine the eligibility of Directors to participate in the
Plan; (ii) determine the terms and conditions of each grant in a
manner consistent with the provisions of the Plan; (iii) construe
and interpret the Plan and any agreement or instrument entered into
under the Plan; (iv) establish, amend, rescind, or waive rules and
regulations for the Plan's administration; and (v) (subject to the
provisions of Section 3.3 herein) amend, modify, and/or terminate
the Plan.  Further, the Board shall have the full power to make all
other determinations which may be necessary or advisable for the
administration of the Plan to the extent consistent with the Plan.

     Except as limited by applicable law, the Board, at its
discretion, has the right to delegate any or all of its
administrative duties to a committee of the Board or to any
employee or employees of the Company; and to rely on outside
counsel, independent accountants, or other consultants to render
advice and/or assistance in fulfilling any of its administrative
duties hereunder.

     3.3       Amendment, Modification, and Termination.  The
Board, at its discretion, without prior notice, at any time and
from time to time, may modify or amend, in whole or in part, any or
all of the provisions of the Plan, or may suspend or terminate the
Plan at any time.

     Notwithstanding the foregoing, other than as permitted by the
Plan, no such amendment, modification, suspension, or termination
by the Board may materially and adversely affect any outstanding
Phantom Stock Unit or the rights of a Participant hereunder,
without the written consent of the Participant (or a Participant's
beneficiary, as appropriate).

     3.4       Decisions Binding.  All determinations and decisions
made by the Board of Directors pursuant to the provisions of the
Plan and all related orders or resolutions of the Board shall be
final, conclusive, and binding on all persons, including the
Company, Participants, and any other person claiming an interest
under the Plan.

Article 4. Eligibility and Participation

     4.1       Eligibility.  Eligibility for participation in the
Plan shall be limited to Non-Employee Directors.

     4.2       Participation.  Each Non-Employee Director shall
automatically participate in the Plan; provided however, that the
Board may, in its sole discretion, determine that an otherwise
eligible Director shall not participate in a grant of Phantom Stock
Units.

Article 5. Establishment of Phantom Stock Units

     5.1       Value of Phantom Stock Units.  Each Phantom Stock
Unit shall have a value on the date of grant which is equal to
Award Value as defined in Section 2.2.

     Subsequent to the date of grant, the value of the Phantom
Stock Units in a Participant's Account shall be the equivalent of
the Payout Value as such term is defined in Section 2.11 hereof. 
The Board, subject to the terms and limitations of the Plan, shall
establish such rules and procedures which it deems appropriate to
further govern the value of Phantom Stock Units granted hereunder.

     5.2       Adjustments.  In the event of any change in
corporate capitalization, such as a stock split or a corporate
transaction such as any merger, consolidation, separation,
including a spin-off or other distribution of stock or property of
the Company, any reorganization (whether or not such reorganization
comes within the definition of such term in Code Section 368) or
any partial or complete liquidation of the Company, such adjustment
shall be made in the number of Phantom Stock Units subject to
outstanding Awards granted under the Plan, as may be determined to
be appropriate and equitable by the Board, in its sole discretion,
to prevent dilution or enlargement of rights.

Article 6. Grant of Phantom Stock Units

     6.1       Grant of Phantom Stock Units.  Unless otherwise
determined by the Board pursuant to Section 4.2 or as provided in
this Section 6.1, 

        (a)  each Non-Employee Director who is elected between
     annual meetings of shareholders shall be granted a number of
     Phantom Stock Units determined by dividing $20,000 by the
     Award Value as of the date of such election;

        (b)  each Non-Employee Director who is elected to the
     Board at the annual meeting of shareholders of the Company
     shall be granted a number of Phantom Stock Units determined by
     dividing $20,000 by the Award Value on the date of the annual
     meeting; and

        (c)  each Non-Employee Director serving on the Effective
     Date of the Plan who is determined by the Board to be eligible
     at that time to receive Phantom Stock Units shall be granted
     an initial award of a number of Phantom Stock Units determined
     by dividing $20,000 by the Award Value on the Effective Date.

     Anything contained in this Section 6.1 to the contrary
notwithstanding, before any grant occurs, the Board may determine
that the date of grant specified in paragraphs (a), (b) or (c)
above may be postponed to a later date as may be specified by the
Board.

     6.2       Dividend Equivalents.  As of any dividend payment
date or other distribution date with respect to the Company's
common stock, each Participant's Phantom Stock Unit Account shall
be credited with additional Phantom Stock Units determined by
dividing the value of the dividend payment or other distribution
which the Director would have received had his or her Phantom Stock
Units been actual shares of common stock of the Company by the
Award Value on the Payment Date.

     6.3       Vesting of Phantom Stock Units.  A Participant's
Phantom Stock Units shall vest at the earlier of the Director's
Retirement Date, death, or a Change in Control.

     6.4       Phantom Stock Unit Account.  A Phantom Stock Unit
Account ("the Account") shall be established and maintained by the
Company for each Participant that receives an Award under the Plan. 
Each Account is maintained solely for accounting purposes and shall
be the record of the number of Phantom Stock Units granted and the
number of Phantom Stock Units granted and credited with respect to
dividend equivalents.

Article 7. Payout of Phantom Stock Units

     7.1       Amount of Payout.  Except as provided otherwise in
this Plan, the total amount payable to a Participant shall be the
aggregate Payout Value of the Participant's vested Phantom Stock
Units at the Payout Date.

     7.2       Timing of Payout.  Except as otherwise provided
herein and subject to Article 8 hereof, the Payout Value of vested
Phantom Stock Units shall be paid to Participants, in cash, as soon
as practicable following the Payout Date, but in no event later
than thirty (30) calendar days following the Payout Date.

     7.3       Common Stock Election.  Unless determined otherwise
by the Board of Directors, the Participant may elect to receive, in
lieu of cash, one share of common stock for each Phantom Stock Unit
in the Participant's Phantom Stock Account.  Such election shall be
made in writing in advance of the Payout Date.  Common stock
available for such purpose shall be treasury shares and
certificates therefor shall be delivered as soon as practicable
following the Payout Date, subject to compliance with any federal
or state securities laws.

Article 8.  Deferral of Payout

     Within thirty (30) calendar days following each Director's
initial grant of Phantom Units under the Plan, such Director may
elect to receive amounts otherwise payable under Section 7.2 in one
lump sum under the Plan in the form of two (2) through ten (10)
approximately equal annual installments beginning as soon as
practicable following the Payout Date.  An election made under this
Article 8 shall be in writing, in a form prescribed by the Board,
and shall be irrevocable.  Amounts deferred pursuant to this
Article 8 shall accrue interest commencing on the Payout Date at a
rate equal to the prime lending rate in effect as published in "The
Wall Street Journal" on the first business day of each month.

     Notwithstanding the foregoing, any unpaid deferred amounts and
accumulated interest earned thereon shall be paid to the
Participant or his or her beneficiary, as applicable, in the event
of, at any time prior to full payment of such deferred amounts and
interest earned thereon: (i) the Participant's death; or (ii) a
Change in Control.  In such event, payment shall be made in a
single lump sum, in cash, within thirty (30) calendar days after
the Participant's death or the effective date of a Change in
Control, as applicable.

Article 9.  Rights of Participants

     9.1       Service.  Nothing in this Plan shall interfere with,
or limit in any way, the right of the Company to terminate any
Participant's service on the Board of Directors at any time in
accordance with applicable law, nor confer upon any Participant any
right to continue in the service of the Company.

        9.2    Nontransferability.  No Phantom Stock Unit and the
corresponding rights granted hereunder may be sold, transferred,
pledged, assigned, or otherwise alienated or hypothecated, other
than by will or by the laws of descent and distribution.

     9.3       Beneficiary Designation.  Each Participant under
this Plan may, from time to time, name any beneficiary or
beneficiaries (who may be named contingently or successively) to
whom any amount under the Plan is to be paid in case of the
Participant's death before receipt of any or all of such amounts. 
Each designation shall revoke all prior designations by the same
Participant, shall be in a form prescribed by the Board, and will
be effective only when filed by the Participant in writing with the
Board during his or her lifetime.  In the absence of any such
designation, amounts remaining unpaid at the Participant's death
shall be paid to the Participant's estate.

Article 10.  Miscellaneous Provisions

     10.1      Severability.  In the event that any provision of
the Plan shall be held illegal or invalid for any reason, the
illegality or invalidity shall not affect the remaining parts of
the Plan, and the Plan shall be construed and enforced as if the
illegal or invalid provision had not been included.

     10.2      Costs of the Plan.  All costs of the Plan including,
but not limited to, payout of Phantom Stock Units and
administrative expenses, shall be incurred by the Company out of
the Company's general assets.  Although not prohibited from doing
so, the Company is not required in any way to segregate assets in
any manner or to specifically fund the benefits provided under this
Plan.

     10.3      Successors.  All obligations of the Company under
this Plan with respect to Phantom Stock Units, and the
corresponding rights granted hereunder, shall be binding on any
successor to the Company, whether the existence of such successor
is the result of a direct or indirect purchase, merger,
consolidation, or otherwise of all or substantially all of the
voting interests, the business and/or the assets of the Company.

     10.4      Indemnification.  Each person who is or shall have
been a member of the Board shall be indemnified and held harmless
by the Company against and from any loss, cost, liability, or
expense that may be imposed upon or reasonably incurred by him or
her in connection with or resulting from any claim, action, suit,
or proceeding to which he or she may be a party or in which he or
she may be involved by reason of any action taken or failure to act
under the Plan and against and from any and all amounts paid by him
or her in settlement thereof, with the Company's approval, or paid
by him or her in satisfaction of any judgment in any such action,
suit, or proceeding against him or her, provided he or she shall
give the Company an opportunity, at its own expense, to handle and
defend the same before he or she undertakes to handle and defend it
on his or her own behalf.

     The foregoing right of indemnification shall not be exclusive
of any other rights of indemnification to which such persons may be
entitled through any authority that the Company may have to
indemnify them or hold them harmless, or by operation of law.

Article 11.  Requirements of Law

     11.1      Requirements of Law.  The granting, administration,
and payout of Phantom Stock Units under this Plan shall be subject
to all applicable laws, rules and regulations and to such approvals
by any governmental agencies or national securities exchanges as
may be required.

     11.2      Governing Law.  This Plan and all agreements
hereunder shall be construed in accordance with and governed by the
laws of the State of Texas.