  We generalize the results of Leger and Luks, Zhang R. and Zhang Y.; Chen, Ma,
Ni, Niu, Zhou and Fan; Kaygorodov and Popov about generalized derivations of
color $n$-ary algebras to the case of $n$-ary Hom-$\Omega$ color algebras.
Particularly, we prove some properties of generalized derivations of
multiplicative $n$-ary Hom-$\Omega$ color algebras. Moreover, we prove that the
quasiderivation algebra of any multiplicative $n$-ary Hom-$\Omega$ color
algebra can be embedded into the derivation algebra of a larger multiplicative
n-ary Hom-$\Omega$ color algebra.
