Exhibit 32.1

                            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 Annual Report of American Tax Credit Properties III L.P.
(the "Registrant") on Form 10-K for the year ended March 30, 2005 as filed with
the Securities and Exchange Commission on the date hereof (the "Report"), I,
David Salzman, Chief Executive Officer of Richman Housing Credits Inc., general
partner of Richman Tax Credit Properties III L.P., general partner of the
Registrant, certify, pursuant to 18 U.S.C. (S) 1350, as adopted pursuant to (S)
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 Registrant.

/s/  David Salzman
- ---------------------------------------
David Salzman
Chief Executive Officer of Richman
Housing Credits Inc., general partner
of Richman Tax Credit Properties III
L.P., General Partner of the Registrant
August 11, 2005

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