Exhibit 32.1

Certification Under Section 906 of the Sarbanes-Oxley Act of 2002

(United States Code, Title 18, Chapter 63, Section 1350)

Accompanying Annual Report on Form 10-K of

MarketAxess Holdings Inc. for the Year Ended December 31, 2004

      In connection with the Annual Report Form 10-K on MarketAxess Holdings Inc. (the “Company”) for the year ended December 31, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Richard M. McVey, Chief Executive Officer of the Company, hereby certify, pursuant to 18 U.S.C. Section 1350, that:

      (1) The Report fully complies with the requirements of Section 13(a) or 15(d), as applicable, 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 Company.

/s/ Richard M. McVey

Richard M. McVey

Chief Executive Officer

March 30, 2005

      This certification shall not be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, or otherwise subject to the liability of that section, nor shall it be deemed to be incorporated by reference into any filing under the Securities Act of 1933 or the Securities Exchange Act of 1934, except to the extent the Company specifically incorporates it by reference.

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