EXHIBIT 13.1

                                  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 on Form 20-F for the fiscal year ended June
30, 2005 of Harmony Gold Mining Company Limited (the "Company") as filed with
the U.S. Securities and Exchange Commission (the "Commission") on the date
hereof (the "Report") and pursuant to 18 U.S.C. Section 1350, as adopted
pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, I, Zacharias
Bernardus Swanepoel, Chief Executive Officer of the Company, certify, that:

      (1) the Report fully complies with the requirements of Section 13(a) or
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
Company.

Date: November 2, 2005

                                 /s/ Zacharias Bernardus Swanepoel
                                 -----------------------------------------------
                                 Zacharias Bernardus Swanepoel
                                 Chief Executive Officer

A signed original of this written statement required by Section 906 has been
provided to it and will be retained by it and furnished to the Commission or its
staff upon request.