  We define a generalized almost para-Hermitian structure to be a commuting
pair $(\mathcal{F},\mathcal{J})$ of a generalized almost para-complex structure
and a generalized almost complex structure with an adequate non-degeneracy
condition. If the two structures are integrable the pair is called a
generalized para-K\"ahler structure. This class of structures contains both the
classical para-K\"ahler structure and the classical K\"ahler structure. We show
that a generalized almost para-Hermitian structure is equivalent to a triple
$(\gamma,\psi,F)$, where $\gamma$ is a (pseudo) Riemannian metric, $\psi$ is a
$2$-form and $F$ is a complex $(1,1)$-tensor field such that
$F^2=Id,\gamma(FX,Y)+\gamma(X,FY)=0$. We deduce integrability conditions
similar to those of the generalized K\"ahler structures and give several
examples of generalized para-K\"ahler manifolds. We discuss submanifolds that
bear induced para-K\"ahler structures and, on the other hand, we define a
reduction process of para-K\"ahler structures.
