Highwoods Realty Limited Partnership 10-Q 2004 Q3 Quarterly report

Exhibit 32.1

CERTIFICATION PURSUANT TO SECTION 906

OF THE SARBANES-OXLEY ACT

In connection with the Quarterly Report of Highwoods Realty Limited Partnership (the “Operating Partnership”) on Form 10-Q for the period ended September 30, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Edward J. Fritsch, President and Chief Executive Officer of Highwoods Properties, Inc., general partner of the Operating Partnership, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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

/s/ EDWARD J. FRITSCH

Edward J. Fritsch

President and Chief Executive Officer of the General Partner

January 19, 2005