Level 3 Parent (LVLT) 10-Q 2004 Q3 Quarterly report

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Exhibit 32.1

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 Level 3 Communications, Inc. (the "Company") on Form 10-Q for the three months ended September 30, 2004 as filed with the Securities and Exchange Commission on the date hereof (the "Report"), I, James Q. Crowe, 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.

/s/  JAMES Q. CROWE      James Q. Crowe
Chief Executive Officer

November 8, 2004

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Exhibit 32.1