EXHIBIT 32

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


      In connection with the Annual Report of Aastrom Biosciences, Inc. (the
"Company") on Form 10-K for the year ended June 30, 2003, as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I, R.
Douglas Armstrong, President and Chief Executive 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 ("Section 906"), that:

      (1)   The Report fully complies with the requirements of section 13(a) of
            the Securities Exchange Act of 1934 (15 U.S.C. 78m); and

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

Date: September 8, 2003

                                            /s/ R. Douglas Armstrong, Ph.D.
                                       -----------------------------------------
                                              R. Douglas Armstrong, Ph.D.
                                         President and Chief Executive Officer

A signed original of this written statement required by Section 906, or other
document authenticating, acknowledging, or otherwise adopting the signature that
appears in typed form within the electronic version of this written statement
required by Section 906, has been provided to Aastrom Biosciences, Inc. and will
be retained by Aastrom Biosciences, Inc. and furnished to the Securities and
Exchange Commission or its staff upon request.

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


      In connection with the Annual Report of Aastrom Biosciences, Inc. (the
"Company") on Form 10-K for the year ended June 30, 2003, as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I, Alan M.
Wright, Senior Vice President and 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 ("Section 906"), that:

      (1)   The Report fully complies with the requirements of section 13(a) of
            the Securities Exchange Act of 1934 (15 U.S.C. 78m); and

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

Date: September 8, 2003

                                                   /s/ Alan M. Wright
                                       -----------------------------------------
                                                     Alan M. Wright
                                         Senior Vice President, Administrative
                                               and Financial Operations
                                             and Chief Financial Officer

A signed original of this written statement required by Section 906, or other
document authenticating, acknowledging, or otherwise adopting the signature that
appears in typed form within the electronic version of this written statement
required by Section 906, has been provided to Aastrom Biosciences, Inc. and will
be retained by Aastrom Biosciences, Inc. and furnished to the Securities and
Exchange Commission or its staff upon request.