EXHIBIT 32.1


                            CERTIFICATION PURSUANT TO
            SECTION 1350, CHAPTER 63 OF TITLE 18, UNITED STATES CODE,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


Pursuant to Section 1350, Chapter 63 of Title 18, United States Code, as adopted
pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, as
President and Chief Executive Officer of The TJX Companies, Inc. (the
"Company"), does hereby certify that to my knowledge:

1.       the Company's Annual Report on Form 10-K for the fiscal year ended
         January 31, 2004 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 Company's Annual Report on Form 10-K
         for the fiscal year ended January 31, 2004 fairly presents, in all
         material respects, the financial condition and results of operations of
         the Company.


                                    /s/ Edmond J. English
                                    --------------------------------------------
                                    Name:  Edmond J. English
                                    Title: President and Chief Executive Officer


Dated: March 31, 2004