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

                            SECTION 906 CERTIFICATION

Pursuant to 18 U.S.C.ss. 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, 2006 (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, 2006

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



Dated: August 21, 2006

/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.ss. 1350 and
is not being filed as part of the Report or as a separate disclosure document.