  We analyze evolution of gravitational perturbations of D-dimensional
Schwarzschild, Reissner-Nordstr\"om, and Reissner-Nordstrom-de Sitter black
holes. It is known that the effective potential for the scalar type of
gravitational perturbations has negative gap near the event horizon. This gap,
for some values of the parameters Q (charge), Lambda (cosmological constant)
and D (number of space-time dimensions), cannot be removed by S-deformations.
Thereby, there is no proof of (in)stability for those cases. In the present
paper, by an extensive search of quasinormal modes, both in time and frequency
domains, we shall show that spherically symmetric static black holes with
arbitrary charge and positive (de Sitter) lambda-term are stable for D=5, 6,
>...11. In addition, we give a complete numerical data for all three types
(scalar, vector and tensor) of gravitational perturbations for
multi-dimensional black holes with charge and Lambda-term. The influence of
charge, Lambda-term and number of extra dimensions on black hole quasinormal
spectrum is discussed.
