  We address the problem of classifying of irreducible Gelfand-Tsetlin modules
for gl(m|n) and show that it reduces to the classification of Gelfand-Tsetlin
modules for the even part. We also give an explicit tableaux construction and
the irreducibility criterion for the class of quasi typical and quasi covariant
Gelfand-Tsetlin modules which includes all essentially typical and covariant
tensor finite dimensional modules. In the quasi typical case new irreducible
representations are infinite dimensional gl(m|n)-modules which are isomorphic
to the parabolically induced (Kac) modules.
