Jefferies 10-Q 2004 Q1 Quarterly report

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 March 26, 2004 (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:	May 4, 2004	Date:	May 4, 2004

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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