Global Crossing (GBLXQ) 10-Q 2008 Q3 Quarterly report

Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER

CERTIFICATION 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 of Global Crossing Limited (the “Company”) on Form 10-Q for the period ending September 30, 2008 as filed with the Securities and Exchange Commission on the date hereof (the “report”), I, John J. Legere, Chief Executive 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 results of operations of the Company.

Date: November 6, 2008

/S/ JOHN J. LEGERE

John J. Legere

Chief Executive Officer