EXHIBIT 32

                           SECTION 1350 CERTIFICATION*

      In connection with the Quarterly Report of Abercrombie & Fitch Co. (the
"Corporation") on Form 10-Q for the quarterly period ended May 1, 2004, as filed
with the Securities and Exchange Commission on the date hereof (the "Report"),
the undersigned Michael S. Jeffries, Chairman and Chief Executive Officer of the
Corporation, and Susan J. Riley, Senior Vice President - Chief Financial Officer
of the Corporation, certify, pursuant to Section 1350 of Chapter 63 of Title 18
of the United States Code, as adopted pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002, that, to the best of their knowledge:

      (1)   The Report fully complies with the requirements of Section 13(a) 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 Corporation.

/s/ Michael S. Jeffries                  /s/ Susan J. Riley
- ------------------------------------     ---------------------------------------
Michael S. Jeffries                      Susan J. Riley
Chairman and Chief Executive             Senior Vice President - Chief Financial
Officer                                  Officer

Dated: June 9, 2004                      Dated: June 9, 2004

*   This certification is being furnished as required by Rule 13a-14(b) under
    the Securities Exchange Act of 1934, as amended (the "Exchange Act"), and
    Section 1350 of Chapter 63 of Title 18 of the United States Code, and
    shall not be deemed "filed" for purposes of Section 18 of the Exchange Act
    or otherwise subject to the liability of that Section. This certification
    shall not be deemed to be incorporated by reference into any filing under
    the Securities Act of 1933 or the Exchange Act, except as otherwise stated
    in such filing.