N-CSR Item 12(b) - Exhibits: Certifications

                           SECTION 906 CERTIFICATION

Pursuant to 18 U.S.C.{section} 1350, the undersigned officers of FEDERATED CORE
TRUST II, L.P. ON BEHALF OF MARKET PLUS CORE FUND (the "Registrant"), hereby
certify, to the best of our knowledge, that the Registrant's Report on Form N-
CSR for the period ended June 30, 2007 (the "Report") fully complies with the
requirements of Section 13(a) or 15(d), as applicable, of the Securities and
Exchange Act of 1934 and that the information contained in the Report fairly
presents, in all material respects, the financial condition and results of
operations of the Registrant.


Dated: August 21, 2007

/s/ J. Christopher Donahue
Name:  J. Christopher Donahue
Title: President, Principal Executive Officer

Dated: August 21, 2007

/s/ Richard A. Novak
Name:  Richard A. Novak
Title: Treasurer, Principal Financial Officer

This 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.