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 Form 10-Q for the fiscal quarter ended April 30, 2005 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 Form 10-Q for the fiscal quarter ended April 30, 2005 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: June 3, 2005