EXHIBIT 32(b)

CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350

In connection with the Annual Report of Campbell Soup Company (the “Company”) on Form 10-K for the fiscal year ended August 3, 2008 (the “Report”), I, Anthony P. DiSilvestro, Vice President — Controller (Principal Financial Officer and Principal Accounting Officer) of the Company, hereby 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 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.

By:  /s/  Anthony P. DiSilvestro

Name:     Anthony P. DiSilvestro

Title:  Vice President — Controller

(Principal Financial Officer and

Principal Accounting Officer)

Date: October 1, 2008