We show the existence of (  ϵ  )-almost contact metric structures and give examples of (  ϵ  )-Sasakian manifolds. Then we get a classification theorem for real hypersurfaces of indefinite complex space-forms with parallel structure vector field. We prove that (  ϵ  )-Sasakian real hypersurfaces of a semi-Euclidean space are either open sets of the pseudosphere S 2 S 2 n + 1 (1) or of the pseudohyperbolic space H 2 S − 1 2 n + 1 (1). Finally, we get the causal character of (  ϵ  ) cosymplectic real hypersurfaccs of indefinite complex space-forms.