Blackstone (BX) 10-Q 2010 Q3 Quarterly report

Exhibit 32.1

Certification of the Chief Executive Officer

Pursuant to 18 U.S.C. Section 1350,

As Adopted Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Quarterly Report of The Blackstone Group L.P. (the “Partnership”) on Form 10-Q for the quarter ended September 30, 2010 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Stephen A. Schwarzman, Chief Executive Officer of Blackstone Group Management L.L.C., the general partner of the Partnership, certify, pursuant to 18 U.S.C. § 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 Partnership.

Date: November 5, 2010

/s/ Stephen A. Schwarzman

Stephen A. Schwarzman

Chief Executive Officer

of Blackstone Group Management L.L.C.

* The foregoing certification is being furnished solely pursuant to 18 U.S.C. Section 1350 and is not being filed as part of the Report or as a separate disclosure document.