  We introduce the notion of Poisson quasi-Nijenhuis manifolds generalizing the
Poisson-Nijenhuis manifolds of Magri-Morosi. We also investigate the
integration problem of Poisson quasi-Nijenhuis manifolds. In particular, we
prove that, under some topological assumption, Poisson (quasi)-Nijenhuis
manifolds are in one-one correspondence with symplectic (quasi)-Nijenhuis
groupoids. As an application, we study generalized complex structures in terms
of Poisson quasi-Nijenhuis manifolds. We prove that a generalized complex
manifold corresponds to a special class of Poisson quasi-Nijenhuis structures.
As a consequence, we show that a generalized complex structure integrates to a
symplectic quasi-Nijenhuis groupoid recovering a theorem of Crainic.
