  The study of real hypersurfaces in pseudo-Riemannian complex space forms and
para-complex space forms, which are the pseudo-Riemannian generalizations of
the complex space forms, is addressed. It is proved that there are no umbilic
hypersurfaces, nor real hypersurfaces with parallel shape operator in such
spaces. Denoting by $J$ be the complex or para-complex structure of a
pseudo-complex or para-complex space form respectively, a non-degenerate
hypersurface of such space with unit normal vector field $N$ is said to be \em
Hopf \em if the tangent vector field $JN$ is a principal direction. It is
proved that if a hypersurface is Hopf, then the corresponding principal
curvature (the \em Hopf \em curvature) is constant. It is also observed that in
some cases a Hopf hypersurface must be, locally, a tube over a complex (or
para-complex) submanifold, thus generalizing previous results of Cecil, Ryan
and Montiel.
