Certification Pursuant to Section 906 of the Sarbanes-Oxley Act

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, each of the undersigned officers of  Rochdale Core Alternative Strategies Fund LLC, does hereby certify, to such officer’s knowledge, that the report on Form N-CSR of the Rochdale Core Alternative Strategies Fund LLC for the year ended March 31, 2011 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as applicable, and that the information contained in the Form N-CSR fairly presents, in all material respects, the financial condition and results of operations of the Rochdale Core Alternative Strategies Fund LLC for the stated period.

/s/ Garrett R. D’Alessandro                     Garrett R. D’Alessandro President, Rochdale Core Alternative Strategies Fund LLC	/s/ Edmund Towers                               Edmund Towers Treasurer, Rochdale Core Alternative Strategies Fund LLC
Dated: June 9, 2011	Dated: June 9, 2011

This statement accompanies this report on Form N-CSR pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 and shall not be deemed as filed by Rochdale Core Alternative Strategies Fund LLC for purposes of Section 18 of the Securities Exchange Act of 1934.