  In this paper we achieve a description of the connected components of
Teichm\"uller space corresponding to Generalized Hyperelliptic Manifolds $X$.
These are the quotients $ X = T/G$ of a complex torus $T$ by the free action of
a finite group $G$, and they are also the K\"ahler classifying spaces for a
certain class of Euclidean cristallographic groups $\Gamma$, the ones which are
torsion free and even.
