  We study whether orbifold models are equivalently rewritten into torus models
in the case of fermionic string theories. It is pointed out that symmetric
orbifold models cannot be rewritten into torus models in the case of fermionic
string theories because of the absence of twist-untwist intertwining currents
on the orbifold models. We present a list of current algebras on asymmetric
$Z_N$-orbifold models of type II superstring theories with inner automorphisms
of Lie algebra lattices of the $A_n$ series. It turns out that whether an
asymmetric orbifold model is rewritten into a torus model depends on the
specific choice of a momentum lattice and an inner automorphism of the lattice.
