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                                                                   EXHIBIT 10.20

                       [NATIONAL ENERGY GROUP, INC. LOGO]




                                  May 19, 1998



VIA HAND DELIVERY

Mr. Gene W. Anderson
5990 Lindenshire, #130
Dallas, TX 75230

         Re:  Separation Agreement

Dear Gene:

National Energy Group, Inc. (the "Company") recognizes your service as an
employee of the Company. This letter confirms the discussions we have held
concerning the termination of your employment from the Company, and the
Company's offer and your acceptance of this proposed separation agreement (this
"Separation Agreement") on the terms set forth below.

1.    Resignation; Termination of Employment. Your employment with the Company
      as Vice President-Land is terminated effective May 19, 1998 (hereinafter
      the "Separation Date"), at which time your Employment Agreement dated
      March 20, 1997 (the "Employment Agreement") shall also terminate.

2.    Salary and Benefits. In accordance with the Company's existing policies,
      you have received, will receive, or are receiving with this letter the
      following payments and benefits pursuant to your employment with the
      Company and your participation in the Company's benefit plans:

      (a)   Payment of your regular base salary through May 19, 1998, less all
            legal deductions;

      (b)   Payment of accrued and unused vacation leave, if any, through the
            Separation Date, less all legally required deductions; and

      (c)   Payment of two (2) weeks of your base salary for each year of
            employment you have completed with the Company in the amount of
            $4,038.50.
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Mr. Gene W. Anderson
May 19, 1998
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      The amounts paid in accordance with subparagraphs (a), (b) and (c) of
      this Paragraph 2 are gross amounts, subject to lawful deductions,
      including any deductions you have previously authorized or authorize
      prior to your Separation Date.

      Your paid group health insurance benefits are paid through May 19, 1998.
      After the Separation Date, you are entitled at your option to continue
      your group health insurance coverage at your expense in accordance with
      applicable law. Please complete the COBRA election form which will be
      furnished to you if you elect to continue such insurance coverage.

      Payment of any benefits to which you have vested entitlements under the
      terms of the employee benefit plans established by the Company (including
      but not limited to the Company 401(k) Plan and Employee Stock Purchase
      Plan) shall be paid to you in accordance with the provisions of such
      plans.

      The Company will settle promptly all authorized reimbursable business
      expenses, if any, when you have submitted appropriate expense reports
      along with the required receipts and documenting information. To be
      eligible for reimbursement of these expenses, they must be submitted by
      the close of business on or before May 26, 1998.

3.    Special Separation Benefits. In consideration of the General Release,
      the Confidentiality of Separation Agreement and Nondisparagement
      provision, and the Agreement Regarding Solicitation of Employees and
      Consultants set forth in this Separation Agreement, and contingent upon
      your acceptance of the terms contained herein, the Company offers you the
      following Special Separation Benefits, in addition to the benefits you
      will receive pursuant to Paragraph 2:

      (a)   Termination Allowance. A termination allowance in the amount of
            $26,250.00, which is equivalent to your base salary for three (3)
            months, payable concurrently with the execution and delivery to the
            Company of both this Separation Agreement and the Reaffirmation of
            Separation Agreement described in Paragraph 13 hereof.

      (b)   Additional Benefits.

            (i)   The Company shall continue to pay your group health insurance
            benefits through May 31, 1998; and


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Mr. Gene W. Anderson
May 19, 1998
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            (ii)  For a period of ninety (90) days following your
            Separation Date through August 19, 1998, you shall have the right
            to exercise Stock Options of the Company granted to you which have
            vested as of your Separation Date.

4.    Return of Property. Whether or not you accept the terms of this
      Separation Agreement, you must return to the Company any and all items of
      its property, including without limitation: automobiles, telephones,
      office keys, security access cards, computers, equipment, credit cards,
      forms, files, manuals, correspondence, business records, personnel data,
      lists of employees, salary and benefits information, work product, maps,
      data and files relating to wells, leases, partners and/or contractors,
      seismic data and files, contracts, contract information, Prospect
      information and plans for future Prospects, brochures, catalogs, computer
      tapes and diskettes, and data processing reports, and any and all other
      documents or property which you have had possession of or control over
      during the course of your employment, and which you have not already
      returned to the Company. You agree that you will return such property to
      the Company by no later than the close of business on or before May 26,
      1998, or as soon thereafter as is possible with respect to any items not
      then immediately available or which you later find in your possession.
      The provisions of this Paragraph 4 do not prohibit the maintenance by you
      of copies of any non-confidential, non-proprietary information, such as
      reading files, work papers, calculations, flowcharts and other similar
      information reflecting the performance of your job duties and
      responsibilities.

5.    Use of Confidential Information. You acknowledge and agree that, except
      for your knowledge and training to compete in the marketplace and except
      for information which is now or in the future becomes available in the
      public domain, all of the non-public documents and information to which
      you have had access during your employment, including but not limited to
      all information pertaining to any specific business transactions in which
      the Company or any other Company Released Parties (as defined in
      Paragraph 6(a) below) were, are, or may be involved, all information
      concerning salary and benefits paid to employees of the Company or any of
      the other Company Released Parties, all personnel information relating in
      any way to current or former employees of the Company or any of the other
      Company Released Parties, all non-public information obtained in the
      course of employment pertaining to acquisitions, divestitures, wells,
      Prospects and development plans of the Company or any of the other
      Company Released Parties, lease holdings and lease block bid information
      and strategies, all financial budgetary information, all other
      information specified in Paragraph 4 above, and in general, the business
      and operations of the Company or any of the other Company Released
      Parties in addition to any other work product, calculations, files, maps,
      logs, flowcharts and other related and/or similar information to which
      you had access through the Company, its partners or consultants are
      considered confidential and are not to be disseminated or disclosed by
      you to any other parties, except 

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Mr. Gene W. Anderson
May 19, 1998
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      as may be required by law or judicial process. In the event you are
      required to disclose such information to any other party, you shall
      provide the Company immediate written notice to enable the Company to
      seek, at the Company's discretion and expense, a protective order or take
      other such action as the Company in its sole discretion deems advisable
      or necessary. You further agree that in the event it appears that you
      will be compelled by law or judicial process to disclose such
      confidential information, you will notify Mr. Philip D. Devlin, General
      Counsel, in writing at 4925 Greenville Avenue, Suite 1400, Dallas, Texas,
      75206, immediately upon your receipt of any such notice, a subpoena or
      other legal process.

6.    General Release.

      (a)   Except for the obligations of the Company and the Company Released
            Parties to be performed hereunder and in consideration of the
            Special Separation Benefits described above, you and your family
            members, heirs, successors, and assigns (collectively, the
            "Employee Released Parties") hereby release, acquit, and forever
            discharge any and all claims and demands of whatever kind or
            character, whether vicarious, derivative, or direct, that you or
            they, individually, collectively, or otherwise, may have or assert
            against (i) National Energy Group, Inc. or (ii) any officer,
            director, stockholder, fiduciary, agent, employee, representative,
            insurer, attorney, or any successors and assigns of National Energy
            Group, Inc. (collectively, the "Company Released Parties"). This
            Separation Agreement includes but is not limited to any claim or
            demand based on any federal, state, or local statutory or common
            law that applies or is asserted to apply, directly or indirectly,
            to the formation of your employment relationship, your employment
            relationship, or the termination of your employment relationship
            with the Company. Thus, you and the other Employee Released Parties
            agree not to make any claims or demands against the Company or any
            of the other Company Released Parties such as for wrongful
            discharge; unlawful employment discrimination; retaliation; breach
            of contract (express or implied); breach of the duty of good faith
            and fair dealing; violation of the public policy of the United
            States, the State of Texas, or any other state; intentional or
            negligent infliction of emotional distress; tortious interference
            with contract; promissory estoppel; detrimental reliance;
            defamation of character; duress; negligent misrepresentation;
            intentional misrepresentation or fraud; invasion of privacy; loss
            of consortium; assault; battery; conspiracy; bad faith; negligent
            hiring or supervision; any intentional or negligent act of personal
            injury; any alleged act of harassment or intimidation; or any other
            intentional or negligent tort; or any alleged violation of the Age
            Discrimination in Employment Act of 1967; Title VII of the Civil
            Rights Act of 1964; the Americans with Disabilities Act of 1990;
            the Employee Retirement Income Security Act of 1974; the Fair Labor
            Standards Act; the Fair 

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Mr. Gene W. Anderson
May 19, 1998
Page 5


            Credit Reporting Act; the Texas Commission on Human Rights Act; or
            the Texas Wage Payment Statute, Tex. Rev. Civ. Stat. Ann. art.
            5155.

      (b)   Except for your obligations to be performed hereunder, the Company
            and the other Company Released Parties hereby release, acquit, and
            forever discharge any and all claims and demands of whatever kind
            or character, whether vicarious, derivative, or direct, that it or
            they, individually, collectively, or otherwise may have or assert
            against you or any of the other Employee Released Parties. This
            Separation Agreement includes, but is not limited to, any claim or
            demand based on any federal, state, or local statutory or common
            law that applies or is asserted to apply, directly or indirectly,
            to the formation of your employment relationship, your employment,
            or the termination of your employment relationship with the
            Company.

      (c)   Except as otherwise provided herein, the effect of this Separation
            Agreement is to mutually release, acquit, and forever discharge any
            and all claims and demands of whatever kind or character, that
            either party, the Employee Released Parties, or the Company
            Released Parties may now have, or hereafter have or assert against
            each other arising out of the employment relationship (including
            the formation and termination thereof) which has existed between
            you and the Company. It is further agreed that each of you and the
            Company agree to indemnify and hold harmless the other for any
            breach of the provisions of this Separation Agreement by the
            respective Employee Released Parties or Company Released Parties
            which results in damage to the other or to the respective parties
            hereto. This mutual general release does not include: (i) the
            executory obligations of either party yet to be performed, or (ii)
            any rights, claims or obligations which may accrue as between the
            parties after the date of this Separation Agreement.

7.    Confidentiality of this Separation Agreement and Nondisparagement. In
      consideration of the Special Separation Benefits described above, each of
      the Company and you agree that the terms of this Separation Agreement
      shall be and remain confidential, and shall not be disclosed by you and
      the other Employee Release Parties or the Company and the other Company
      Released Parties to any party other than your spouse, attorney,
      accountant or tax return preparer; provided such persons have agreed to
      keep such information confidential, and except as may be required by law
      or judicial process. Each of the Company and you further agree, except as
      compelled by law or judicial process, not to cooperate or supply
      information of any kind in any proceeding, investigation, or inquiring
      raising issues under the Age Discrimination in Employment Act of 1967,
      Title VII of the Civil Rights Act of 1964, the Americans with
      Disabilities Act of 1990, the Employee Retirement Income Security Act of
      1974, the Fair Labor Standards Act, the Fair Credit Reporting Act, the
      Texas 


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Mr. Gene W. Anderson
May 19, 1998
Page 6


      Commission on Human Rights Act, or the Texas Wage Payment Statute, Tex.
      Rev. Civ. Stat. Ann. art. 5155, or any other federal, state, or local
      law, involving the formation of your employment relationship, your
      employment relationship, the termination of your employment relationship,
      or the employment of other persons by the Company or any of the Company
      Released Parties. In the event it appears that either party hereto shall
      be compelled by law or judicial process to disclose the terms and
      conditions of this Separation Agreement, such party shall immediately
      notify the other party in writing and provide a copy of any notice that
      such disclosure is being requested or required so that such party at its
      sole discretion and expense may seek a protective order or take other
      such action as such party in its sole discretion deems advisable or
      necessary.

      You and the other Employee Released Parties further agree not to make any
      statement, oral or written, which directly or indirectly impugns the
      quality or integrity of the Company's or any of the Company Released
      Parties' business practices, or to make any other disparaging or
      derogatory remarks or statements, oral or written, about the Company or
      any of the Company Released Parties, their officers, directors,
      stockholders, managerial personnel, or other employees or their partners
      and consultants to any other parties. You agree and acknowledge that
      should you breach this obligation, in addition to any other remedy the
      Company may have at law or in equity, you may be required to repay the
      Special Separation Benefits provided to you pursuant to this Separation
      Agreement, but all other provisions of this Separation Agreement shall
      remain in full force and effect.

      In consideration of the General Release, the Confidentiality of
      Separation Agreement and Nondisparagement provision, and the Agreement
      Regarding Solicitation of Employees and Consultants, set forth herein,
      the Company and the Company Released Parties agree that it and they,
      respectively, shall instruct its officers, directors, managerial
      personnel, or other employees not to make any statement, oral or written,
      which directly or indirectly impugns the quality or integrity of you or
      any of the Employee Released Parties' business practices, or to make any
      other disparaging or derogatory remarks or statements, oral or written,
      about you or your employment with the Company.

8.    Agreement Regarding Solicitation of Employees. In consideration of the
      monetary payments and other benefits provided to you or on your behalf by
      the Company in this Separation Agreement, you acknowledge and agree that
      for a period of two (2) years following the termination of your
      employment with the Company, you will not, directly or indirectly, for
      your own account or for the benefit of any other person or party,
      solicit, induce, entice, or attempt to entice any employee, or
      independent contractor of the Company to terminate his or her employment
      relationship, agreements or contracts with the Company.


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Mr. Gene W. Anderson
May 19, 1998
Page 7


9.    Nonadmission of Liability and Wrongdoing. It is acknowledged that this
      Separation Agreement does not in any manner constitute an admission of
      liability or wrongdoing on your part or that of the Company, but that you
      and the Company expressly deny any such liability or wrongdoing, and
      enter into this Separation Agreement for the sole purpose of avoiding
      further trouble and expense; and, except to the extent necessary to
      enforce this Separation Agreement, neither this Separation Agreement, nor
      any part of it may be construed, used, or admitted into evidence in any
      judicial, administrative, or arbitral proceedings as an admission of any
      kind by the Company, the Company Released Parties, or you or any of the
      Employee Released Parties.

10.   Authority to Execute. Each of the parties hereto warrants and agrees that
      it (i) has full power and authority to execute, deliver and perform the
      obligations contained in this Separation Agreement, (ii) is a legally
      binding and enforceable agreement in accordance with its terms and
      conditions, (iii) has the power and authority to bind its respective
      Released Parties, (iv) does not violate, conflict with or constitute a
      breach or default under any statute, rule, ordinance, regulation or
      administrative order of any federal, state, county or municipal court,
      board, office, agency or commission, and (v) is not contemplating, nor
      are any bankruptcy or insolvency proceedings threatened against such
      party of which it is aware.

11.   GOVERNING LAW AND INTERPRETATION. THIS SEPARATION AGREEMENT AND THE
      RIGHTS AND DUTIES OF THE PARTIES UNDER IT SHALL BE GOVERNED BY AND
      CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF TEXAS AND PERFORMED
      IN DALLAS COUNTY, TEXAS. If any provision of this Separation Agreement is
      held to be unenforceable, such provision shall be considered separate,
      distinct, and severable from the other remaining provisions and shall not
      affect the validity or enforceability of such other remaining provisions,
      and that, in all other respects, this Separation Agreement shall remain
      in full force and effect. If any provision of this Separation Agreement
      is held to be unenforceable as written and may be made to be enforceable
      by limitation thereof, then such provision shall be enforceable to the
      maximum extent permitted by applicable law and to the extent the
      remaining provisions further accomplish the goals, benefits and intent of
      this Separation Agreement. The language of all parts of this Separation
      Agreement shall in all cases be construed as a whole, according to its
      fair meaning, and not strictly for or against any of the parties.

12.   Expiration of Offer. The Company's offer of the proposed Special
      Separation Benefits will expire at midnight on the 21st day (the
      "Expiration of Offer") following the date of this correspondence, i.e.,
      on June 9, 1998. You may accept this offer at any time before the
      Expiration of Offer by executing this Separation Agreement and returning
      it to the designated representative of the Company. Whether or not you
      execute this Separation Agreement, you 


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Mr. Gene W. Anderson
May 19, 1998
Page 8


      will receive the items set forth in Paragraph 2(a), (b) and (c) and are
      required to follow the obligations set forth in Paragraphs 4 and 5
      hereof.

13.   The Effective Date. This Separation Agreement will become effective and
      enforceable seven (7) days after your execution hereof (the "Effective
      Date"). At any time prior to the Effective Date, you may revoke your
      acceptance of this Separation Agreement by delivering written notice
      thereof to the Company. You further agree to execute and deliver to the
      Company the Reaffirmation of this Separation Agreement, attached hereto
      as Exhibit "A", within seven (7) days of the execution and delivery of
      this Separation Agreement.

14.   Consultation With Counsel. You have the right to consult, and are
      encouraged by the Company to consult, an attorney before executing this
      Separation Agreement.

15.   Voluntary Agreement. You and the Company acknowledge that execution of
      this Separation Agreement is knowing and voluntary, that you and the
      Company have had reasonable time to deliberate regarding its terms, and
      that you and the Company have had the right to consult with an attorney.

16.   Entire Agreement. This Separation Agreement contains and constitutes the
      entire understanding and agreement between you and the Company and may be
      modified only by a writing of contemporaneous or subsequent date executed
      by both you and an authorized officer of the Company.

17.   In the event of a dispute between the parties to this Separation
      Agreement, the parties agree not to file any action or petition in any
      court of law or equity for any relief, but to participate in good faith
      in a minimum of four (4) hours of mediation in Dallas, Texas with an
      attorney-mediator who trained and certified by the American Arbitration
      Association, the United States Arbitration and Mediation Service, or any
      comparable organization, and to abide by the mediation procedures and
      decision of such organization. The parties agree to equally bear the
      costs of the mediation. In the event the parties cannot resolve their
      dispute through mediation as described herein, the parties agree to
      participate in binding arbitration pursuant to the rules of the American
      Arbitration Association or mutually agreeable similar organization. Such
      arbitration shall be held in Dallas, Texas, shall be binding and
      nonappealable and a judgment on the award to the prevailing party
      (inclusive of reasonable attorney's fees and costs) may be entered in any
      court having competent jurisdiction.

      If you are in agreement with the terms of this Separation Agreement,
please execute the attached duplicate of this letter in the space provided
below. By executing this Separation Agreement, you acknowledge that (a) you
have been offered at least twenty-one (21) days to consider 


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Mr. Gene W. Anderson
May 19, 1998
Page 9


the terms of this Separation Agreement, (b) you were advised by the Company to
consult with an attorney regarding the terms of this Separation Agreement, (c)
you have consulted with, or have had sufficient opportunity to consult with, an
attorney of your own choosing regarding the terms of this Separation Agreement,
(d) any and all questions regarding the terms of this Separation Agreement have
been asked and answered to your complete satisfaction, (e) you have read this
Separation Agreement and fully understand its terms and their importance, (f)
the consideration or special separation benefits described in Paragraph 3 of
this Separation Agreement is good and valuable and of a kind to which you were
not otherwise entitled, and (g) you are entering into this Separation Agreement
voluntarily, of your own free will, and without any coercion, undue influence,
threat or intimidation of any kind or type whatsoever.

Sincerely,

National Energy Group, Inc.                     ACCEPTED AND AGREED THIS
                                                9TH DAY OF JUNE, 1998.

By: /s/ CHUCK L. ELSEY                          /s/ GENE W. ANDERSON
    ------------------------------              ----------------------------
Name:   Chuck L. Elsey                          Name: Gene W. Anderson,
Title:  Executive Vice President                      an Individual
        and Chief Operating Officer

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                                  EXHIBIT "A"

                     REAFFIRMATION OF SEPARATION AGREEMENT


         I, Gene W. Anderson, acknowledge that I executed that certain
separation agreement (the "Separation Agreement") with National Energy Group,
Inc. (the "Company") and that during the seven (7) day period immediately
following my execution of the Separation Agreement, I had the right to revoke
the Separation Agreement at any time. By executing the Separation Agreement, I
also understand that I agreed that I would receive no benefits thereunder
unless and until I executed this reaffirmation agreement (this
"Reaffirmation").

         By executing this Reaffirmation, I now affirm and attest that I (a)
have not heretofore, or contemporaneously with the execution of this
Reaffirmation, revoked, or attempted to revoke the Separation Agreement, either
by notice to the Company, or otherwise, and (b) am now, by virtue of my
execution of this Reaffirmation, within seven (7) days after the execution of
the Separation Agreement, fully bound by all of the terms and conditions of the
Separation Agreement.

                      EXECUTED this 16 day of June, 1998.

                                                     /s/ GENE W. ANDERSON
                                                     ---------------------------
                                                     Gene W. Anderson,
                                                        an Individual


THE STATE OF TEXAS         )
                           )
COUNTY OF DALLAS           )

         BEFORE ME, the undersigned, a Notary Public, on this day personally
appeared Gene W. Anderson, known to me to be the person whose name is
subscribed to the foregoing instrument and acknowledged to me that he executed
the same for the purposes and consideration therein expressed.

         GIVEN UNDER MY HAND AND SEAL OF OFFICE this 16th day of June, 1998.


                                        /s/ MARILYN J. GRAHAM
[SEAL]                                  ------------------------------------
                                        Notary Public, State of Texas