  We show that, under the conditions known to imply the validity of the Parisi
formula, if the generic Sherrington-Kirkpatrick Hamiltonian contains a $p$-spin
term then the Ghirlanda-Guerra identities for the $p$th power of the overlap
hold in a strong sense without averaging. This implies strong version of the
extended Ghirlanda-Guerra identities for mixed $p$-spin models than contain
terms for all even $p\geq 2$ and $p=1.$
