  In this paper, we construct the multi-microlocalization functor $\mu
hom_{{\chi}}$ of homomorphisms, which is a counterpart of the functor $\mu hom$
studied by M.Kashiwara and P.Schapira. Furthermore, using the new functor, we
also introduce several sheaves of multi-microlocal operators which act on
multi-microlocalized objects such as a multi-microfunction.
