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 March 31, 2004 (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: May 4, 2004

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.