  In multidimensional gravity with an arbitrary number of internal Ricci-flat
factor spaces, interacting with electric and magnetic $p$-branes, spherically
symmetric configurations are considered. It is shown that all single-brane
black-hole solutions are stable under spherically symmetric perturbations,
whereas similar solutions possessing naked singularities turn out to be
catastrophically unstable. The black hole stability conclusion is extended to
some classes of configurations with intersecting branes. These results do not
depend on the particular composition of the $D$-dimensional space-time, on the
number of dilatonic scalar fields $\phi^a$ and on the values of their coupling
constants. Some examples from 11-dimensional supergravity are considered.
