  We describe the departure from equilibrium of matter distributions
representing sources for a class of Weyl metric. It is shown that, for
extremely high gravitational fields, slight deviations from spherical symmetry
may enhance the stability of the system weakening thereby its tendency to a
catastrophic collapse. For critical values of surface gravitational potential,
in contrast with the exactly spherically symmetric case, the speed of entering
the collapse regime decreases substantially, at least for specific cases.
