EXHIBIT 32.1

                         HALLWOOD REALTY PARTNERS, L.P.

     CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


In connection with the filing of the quarterly report on Form 10-Q for the
quarter ended September 30, 2003 (the "Report") by Hallwood Realty Partners,
L.P. ("Registrant"), each of the undersigned hereby certifies that to their
knowledge:

1.    The Report fully complies with the requirements of Section 13(a) of 15(d)
      of the Securities Exchange Act of 1934, as amended, and

2.    The information contained in the Report fairly presents, in all material
      respects, the financial condition and results of operations of the
      Registrant.


                                    /s/ Anthony J. Gumbiner
                                    -----------------------
                                    Anthony J. Gumbiner
                                    Chief Executive Officer

                                    /s/ Jeffrey D. Gent
                                    -------------------
                                    Jeffrey D. Gent
                                    Vice President - Finance
                                    (Principal Financial and Accounting Officer)


Date: November 11, 2003

A signed original of this written statement required by Section 906 has been
provided to the Partnership and will be retained by the Partnership and
furnished to the Securities and Exchange Commission or its staff upon request.