  We classify pseudo-Riemannian submersions with connected totally geodesic
fibres from a real pseudo-hyperbolic space onto a pseudo-Riemannian manifold.
Also, we obtain the classification of the pseudo-Riemannian submersions with
(para-)complex connected totally geodesic fibres from a (para-)complex
pseudo-hyperbolic space onto a pseudo-Riemannian manifold.
