  Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar
equations, with a dilatonic-type scalar-vector coupling, in $D$-dimensional
gravity with a chain of $n$ Ricci-flat internal spaces are considered. Their
properties and special cases are discussed. A family of multidimensional
dilatonic black-hole solutions is singled out, depending on two integration
constants (related to black hole mass and charge) and three free parameters of
the theory (the coordinate sphere, internal space dimensions, and the coupling
constant). The behaviour of the solutions under small perturbations preserving
spherical symmetry, is studied. It is shown that the black-hole solutions
without a dilaton field are stable, while other solutions, possessing naked
singularities, are catastrophically unstable.
