EXHIBIT 32.1
                                                                    ------------

                                  Certification
                          Pursuant to Rule 13a-14(b) or
                    Rule 15d-14(b) and 18 U.S.C. Section 1350
                   (as adopted pursuant to Section 906 of the
                           Sarbanes-Oxley Act of 2002)


         Pursuant to 18 U.S.C. Section 1350 (as adopted pursuant to Section 906
of the Sarbanes-Oxley Act of 2002), the undersigned officer of The Estee Lauder
Companies Inc., a Delaware corporation (the "Company"), does hereby certify, to
such officer's knowledge, that:

         The Quarterly Report on Form 10-Q for the quarter ended September 30,
2004 (the "10-Q") of the Company fully complies with the requirements of section
13(a) or 15(d) of the Securities Exchange Act of 1934, as amended (15 U.S.C. 78m
or 78o(d)), and the information contained in the 10-Q fairly presents, in all
material respects, the financial condition and results of operations of the
Company.




Dated:  November 9, 2004


                                /s/ WILLIAM P. LAUDER
                                -----------------------
                                William P. Lauder
                                President and
                                Chief Executive Officer




         The foregoing certification is being furnished solely pursuant to 18
U.S.C. Section 1350 (as adopted pursuant to Section 906 of the Sarbanes-Oxley
Act of 2002) and for no other purpose.