Exhibit 32(b)

CERTIFICATION OF CHIEF FINANCIAL OFFICER

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 of Schlumberger N.V. (Schlumberger Limited) (the “Company”) on Form 10-K for the year ended December 31, 2003 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Jean-Marc Perraud, Executive Vice President and Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report 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 Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

Date: March 3, 2004	/s/    Jean-Marc Perraud
	Jean-Marc Perraud Executive Vice President and Chief Financial Officer

A signed original of this written statement required by section 906 has been provided to Schlumberger Limited and will be retained by Schlumberger Limited and furnished to the Securities and Exchange Commission or its staff upon request.

This certification accompanies the report pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 and shall not be deemed filed by the Company for purposes of Section 18 of the Exchange Act of 1934, as amended.

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