EXHIBIT 32.2

                            CERTIFICATION PURSUANT TO
                            18 U. S. C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of GTx, Inc. (the "Company") on Form
10-Q for the period ending June 30, 2004, as filed with the Securities and
Exchange Commission on the date hereof (the "Report"), I, Mark E. Mosteller,
Chief Financial Officer of the Company certify, pursuant to 18 U.S.C. Section
1350, as adopted pursuant to Section 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 Company.

/s/ Mark E. Mosteller
-----------------------------------
Mark E. Mosteller
Chief Financial Officer

July 30, 2004