Exhibit 32.1

CERTIFICATE PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, Peter H. Pfeiffer, president and chief executive officer of AptarGroup, Inc., certify that (i) the Quarterly Report on Form 10-Q of AptarGroup, Inc. for the quarter ended September 30, 2008 (the “Form 10-Q”) fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934 and (ii) the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of AptarGroup, Inc.

/s/ Peter H. Pfeiffer   

Peter H. Pfeiffer

President and Chief Executive Officer

November 4, 2008