  The notion of a $\Gamma $-symmetric space is a generalization of the
classical notion of a symmetric space, where a general finite abelian group
$\Gamma $ replaces the group $Z_2$. The case $\Gamma =\Z_k$ has also been
studied, from the algebraic point of view by V.Kac \cite{VK} and from the point
of view of the differential geometry by Ledger, Obata, Kowalski or Wolf - Gray
in terms of $k$-symmetric spaces. In this case, a $k$-manifold is an
homogeneous reductive space and the classification of these varieties is given
by the corresponding classification of graded Lie algebras. The general notion
of a $\Gamma $-symmetric space was introduced by R.Lutz. We approach the
classification of such spaces in the case $\Gamma=Z_2^2$ using recent results
on the classification of complex $Z_2^2$-graded simple Lie algebras.
