tw telecom Inactive 10-Q2004 Q1 Quarterly report

Filed: 10 May 04, 12:00am

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Exhibit 32.1

Certification of Chief Executive Officer

Pursuant to 18 U.S.C. 1350

(as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002)

In connection with the Quarterly Report of Time Warner Telecom Inc. (the “Company”) on Form 10-Q for the period ended March 31, 2004 filed with the Securities and Exchange Commission (the “Report”), I, Larissa L. Herda, President and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 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 (15 U.S.C. Section 78m or 78o(d)); 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/ Larissa L. Herda

Name: Larissa L. Herda

Date: May 10, 2004