Exhibit 32.1

CERTIFICATION PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, Manuel D. Medina, hereby certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, that:

     (1) The accompanying quarterly report on Form 10-Q for the fiscal quarter ended June 30, 2004 fully complies with the requirements of Section 13(a) or Section 15(d) of the Securities Exchange Act of 1934, as amended; and

     (2) The information contained in such report fairly presents, in all material respects, the financial condition and result of operations of Terremark Worldwide, Inc.

/s/ MANUEL D. MEDINA  

Manuel D. Medina, Chairman of the Board

President and Chief Executive Officer
(Chief Executive Officer) 

Date: August 9, 2004