Exhibit 32.1

CERTIFICATION BY CHIEF EXECUTIVE OFFICER
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 Annual Report of Rockwell Collins, Inc. (the “Company”) on Form 10-K for the fiscal year ended September 30, 2007 (the “Report”) filed with the Securities and Exchange Commission, I, Clayton M. Jones, Chairman, 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 to my knowledge:

(1) The Company’s 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 15, 2007	/s/ Clayton M. Jones
	Clayton M. Jones
	Chairman, President and
	Chief Executive Officer