EXHIBIT 32

    CERTIFICATION BY THE CHIEF EXECUTIVE OFFICER AND CHIEF FINANCIAL OFFICER
                       PURSUANT TO 18 U.S.C. SECTION 1350,
      AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

         I, Richard B. Handler, Chief Executive Officer, and I, Joseph A.
Schenk, Chief Financial Officer, of Jefferies Group, Inc, a Delaware corporation
(the "Company"), each hereby certifies, pursuant to 18 U.S.C. section 1350, as
adopted pursuant to section 906 of the Sarbanes-Oxley Act of 2002, that to my
knowledge:

         (1)      The Company's periodic report on Form 10-Q for the period
ended September 26, 2003 (the "Form 10-Q") 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 Form 10-Q fairly presents, in
all material respects, the financial condition and results of operations of the
Company.

                                      * * *

CHIEF EXECUTIVE OFFICER                      CHIEF FINANCIAL OFFICER

 /s/ Richard B. Handler                       /s/ Joseph A. Schenk
- ------------------------------------         -----------------------------------
     Richard B. Handler                           Joseph A. Schenk

Date: November 7, 2003                       Date: November 7, 2003

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

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