SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  SCHEDULE 13D
                               (Amendment No. 13)

                   Under the Securities Exchange Act of 1934

                        THE HALLWOOD GROUP INCORPORATED
                                (Name of Issuer)


                    Common Stock, $0.10 par value per share
                         (Title of Class of Securities)


                                   406364307
                                 (CUSIP Number)

                              W. Alan Kailer, Esq.
                Jenkens & Gilchrist, a Professional Corporation
                          1445 Ross Avenue, Suite 3200
                            Dallas, Texas 75202-2799
                                 (214) 855-4500
                      (Name, Address and Telephone Number
                        of Person Authorized to Receive
                          Notices and Communications)


                                  July 6, 2004
            (Date of Event which Requires Filing of this Statement)

If the filing person has previously  filed a statement on Schedule 13G to report
the  acquisition  that is the subject of this  Schedule  13D, and is filing this
schedule because of Section  240.13d-1(e),  240.13d-1(f) or 240.13d-1(g),  check
the following box.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the  Securities  Exchange  Act of
1934 ("Act") or otherwise  subject to the liabilities of that section of the Act
but  shall be  subject  to all other  provisions  of the Act  (however,  see the
Notes).



CUSIP No. 406364307

     1.   Names of  Reporting  Persons  S.S.  or I.R.S.  Identification  Nos. of
          Persons:  Alpha Trust

     2.   Check the  Appropriate  Box if a Member of a Group (See  Instructions)
          (a) [    ]     (b) [    ]

     3.   SEC Use Only

     4.   Source of Funds (See instructions) OO

     5.   Check box if Disclosure of Legal  Proceedings is Required  Pursuant to
          Items 2(d) or 2(e) [    ]

     6.   Citizenship or Place of Organization:
          Island of Jersey, Channel Islands


                        7.   Sole Voting Power                        0
Number of Units
Beneficially Owned      8.   Shared Voting Power                   851,575
by Each Reporting
Person with:            9.   Sole Dispositive Power                   0

                        10.  Shared Dispositive Power              851,575


     11.  Aggregate Amount Beneficially Owned by Each Reporting Person: 851,575

     12.  Check if the  Aggregate  Amount in Row 11 Excludes  Certain Units (See
          Instructions) [    ]

     13.  Percent of Class Represented by Amount in Row 11.         64.20%

     14.  Type of Reporting Person (See Instructions):                OO



CUSIP No. 406364307

     1.   Names of  Reporting  Persons  S.S.  or I.R.S.  Identification  Nos. of
          Persons:  Anthony J. Gumbiner

     2.   Check the  Appropriate  Box if a Member of a Group (See  Instructions)
          (a) [    ]     (b) [    ]

     3.   SEC Use Only

     4.   Source of Funds (See instructions) OO

     5.   Check box if Disclosure of Legal  Proceedings is Required  Pursuant to
          Items 2(d) or 2(e) [    ]

     6.   Citizenship or Place of Organization:
          United Kingdom


                        7.   Sole Voting Power                     150,000
Number of Units
Beneficially Owned      8.   Shared Voting Power                   851,575
by Each Reporting
Person with:            9.   Sole Dispositive Power                150,000

                        10.  Shared Dispositive Power              851,575


     11.  Aggregate Amount Beneficially Owned by Each Reporting Person:
          1,001,575

     12.  Check if the  Aggregate  Amount in Row 11 Excludes  Certain Units (See
          Instructions) [    ]

     13.  Percent of Class Represented by Amount in Row 11.         67.84%

     14.  Type of Reporting Person (See Instructions):                00






                                  Schedule 13D

     This  Amendment  No.  13 to  Schedule  13D  amends  the  Schedule  13D (the
"Schedule  13D"),  filed by Alpha  Trust,  a trust  formed under the laws of the
Island of Jersey,  Channel Islands (the "Trust"), and is being filed pursuant to
Rule 13d-2 of the General Rules and  Regulations  under the Securities  Exchange
Act of 1934, as amended. Unless otherwise indicated, all capitalized terms used,
but not defined herein, have the meanings ascribed to such terms in the Schedule
13D. "No material  changes" means no material changes to the response  contained
in the Trust's Schedule 13D previously filed.

Item 1.   Security and Issuer.

          No material changes.

Item 2.   Identity and Background.

          The person on whose  behalf this  statement  is filed is the Trust,  a
          trust formed under the laws of the Island of Jersey,  Channel Islands.
          The trustee of the Trust is Hallwood  Company  Limited,  a corporation
          filed under the laws of Nevis ("HCL").  Mr.  Anthony J. Gumbiner,  his
          wife Mylene  Gumbiner  and his  children  Celine  Gumbiner and Charles
          Gumbiner are directors of HCL.

Item 3.   Source and Amount of Funds or Other Consideration.

          Anthony J. Gumbiner,  the trustee and a  discretionary  beneficiary of
          the Trust contributed 851,575 shares (the "Shares") of common stock of
          The Hallwood  Group  Incorporated  (the  "Company") to the Trust.  The
          Trust, in turn, contributed the Shares to Hallwood Investments Limited
          ("HIL"), a corporation  organized under the laws of the British Virgin
          Islands and wholly-owned by the Trust.

Item 4.   Purpose of Transaction.

          The Trust  intends to hold the Shares for  investment  and  intends to
          review  its  investment  in the  Company  on a  continuing  basis and,
          depending  on  market  conditions  and  other  factors,   may  acquire
          additional securities, dispose of all or any portion of the securities
          he now owns or may hereafter acquire,  seek to engage in extraordinary
          corporate  transactions,  such as a  merger  or  other  reorganization
          involving  the Company or a  purchase,  sale or transfer of a material
          amount of the assets of the Company or any of its subsidiaries  (which
          extraordinary  transaction  could  involve  one or more of the matters
          described  in clauses (a)  through  (j) of Schedule  13D) and take any
          other action that he may deem to be appropriate in the  circumstances.
          Whether the Trust takes any of the foregoing  actions will depend upon
          its evaluation of pertinent factors, including without limitation, the
          availability  of shares of common stock for purchase or acquisition at
          particular price levels or upon particular terms; the capital needs of
          the Company; the business and prospects of each of the Company and the
          Trust;  economic,  stock market,  and money market  conditions;  other
          business  and  investment   opportunities   available  to  the  Trust;
          regulatory   requirements;   other  circumstances  that  may  make  it
          advantageous to the Trust to either increase or decrease its ownership
          of the Company's securities and other requirements of the Trust.




Item 5.   Interest in Securities of the Issuer.

          (a)  As of the date  hereof,  the Trust,  through  HIL,  owns  851,575
               shares  of common  stock  representing  64.20%  of the  Company's
               outstanding  common  stock,  based on 1,326,343  shares of common
               stock outstanding,  as reported in the Company's Quarterly Report
               on Form 10-Q for the fiscal  quarter  ended March 31,  2004.  Mr.
               Gumbiner holds currently  exercisable  options (the "Options") to
               purchase   150,000   shares  of  the   Company's   common  stock,
               representing  approximately  10% of the  Company's  common stock,
               which, in addition to the Shares  beneficially  owned through the
               Trust,  give Mr. Gumbiner  beneficial  ownership of approximately
               67.84% of the Company's common stock.

          (b)  The Shares are owned directly by HIL and indirectly by the Trust.
               Mr.   Anthony   Gumbiner   and  his  family   are   discretionary
               beneficiaries of the Trust. Because Mr. Gumbiner is the principal
               director  and officer of HIL,  Mr.  Gumbiner and the Trust may be
               deemed to share voting and dispositive power over the Shares. Mr.
               Gumbiner  has sole voting and  dispositive  power with respect to
               the Options.

          (c)  Not applicable.

          (d)  Not applicable.

          (e)  Not applicable.

Item 6.   Contracts, Arrangements, Understandings or Relationships with Respect
          to Securities of the Issuer.

          None.

Item 7.   Materials Filed as Exhibits.

          None.





                                   SIGNATURE


     After reasonable inquiry and to the best of their knowledge and belief, the
undersigned  certify that the  information  set forth in this statement is true,
complete and correct.


Date: July 6, 2004                      THE ALPHA TRUST

                                        By:     Hallwood Company Limited,
                                                Trustee


                                        By:     /s/ Anthony J. Gumbiner
                                                ---------------------------
                                        Name:   Anthony J. Gumbiner
                                        Title:  Director