  We study the perturbations of two classes of static black ellipsoid solutions
of four dimensional vacuum Einstein equations. Such solutions are described by
generic off--diagonal metrics which are generated by anholonomic transforms of
diagonal metrics. The analysis is performed in the approximation of small
eccentricity deformations of the Schwarzschild solution. We conclude that such
anisotropic black hole objects may be stable with respect to the perturbations
parametrized by the Schrodinger equations in the framework of the
one--dimensional inverse scattering theory.
