  We classify the semi-Riemannian submersions from a pseudo-hyperbolic space
onto a Riemannian manifold under the assumption that the fibres are connected
and totally geodesic. Also we obtain the classification of the semi-Riemannian
submersions from a complex pseudo-hyperbolic space onto a Riemannian manifold
under the assumption that the fibres are complex, connected and totally
geodesic submanifolds.
