  We analyze the horizon and geodesic structure of a class of 4D off--diagonal
metrics with deformed spherical symmetries, which are exact solutions of the
vacuum Einstein equations with anholonomic variables. The maximal analytic
extension of the ellipsoid type metrics are constructed and the Penrose
diagrams are analyzed with respect to adapted frames. We prove that for small
deformations (small eccentricities) there are such metrics that the geodesic
behaviour is similar to the Schwarzcshild one. We conclude that some vacuum
static and stationary ellipsoid configurations may describe black ellipsoid
objects.
