EXHIBIT 32(i)

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

In connection with the Quarterly Report of Campbell Soup Company (the "Company")
on Form 10-Q for the fiscal quarter ended February 1, 2004, as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I, Douglas
R. Conant, President and Chief Executive 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.

Date:  March 16, 2004

                                                      By: /s/  Douglas R. Conant
                                                          ----------------------
                                                          Douglas R. Conant
                                                          President and Chief
                                                          Executive Officer