Nasdaq (NDAQ) 10-Q 2004 Q3 Quarterly report

Exhibit 32.1

Certification of CEO and CFO 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 Quarterly Report on Form 10-Q of The Nasdaq Stock Market, Inc. (the “Company”) for the quarter ended September 30, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Robert Greifeld, as President and Chief Executive Officer of the Company and David P. Warren, as Executive Vice President and Chief Financial Officer of the Company, each hereby certifies, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that, to the best of his knowledge:

(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 represents, in all material respects, the financial condition and results of the operations of the Company.

/s/ ROBERT GREIFELD

Name: Robert Greifeld

Title: Chief Executive Officer and President

Date: November 5, 2004

/s/ DAVID P. WARREN

Name: David P. Warren

Title: Executive Vice President and Chief Financial Officer

Date: November 5, 2004

This certification accompanies the Report pursuant to § 906 of the Sarbanes-Oxley Act of 2002 and shall not, except to the extent required by the Sarbanes-Oxley Act of 2002, be deemed filed by the Company for purposes of § 18 of the Securities Exchange Act of 1934, as amended.