  The Green-Schwarz covariant N=2 superstring action can be consistently
deduced as the action of the Wess-Zumino-Witten (WZW) sigma model defined on
the direct product of two N=1, D=10 Poincar\'e supertranslation groups.
Generalizing this result, we construct new WZW sigma models on the supergroups
with a nonabelian even part and interpret them as models of superstrings moving
on the supergroup manifolds. We show that these models are completely
integrable and in some special cases possess fermionic kappa-symmetry.
