  We investigate stability of the D-dimensional
Reissner-Nordstrom-anti-de-Sitter metrics as solutions of the Einstein-Maxwell
equations. We have shown that asymptotically anti-de Sitter black holes are
dynamically stable for all values of charge and anti-de Sitter radius in
$D=5,6...11$ dimensional space-times. This does not contradict to dynamical
instability of RN-AdS black holes found by Gubser in $\mathcal{N}=8$ gauged
supergravity, because the latter instability comes from the tachyon mode of the
scalar field, coupled to the system. Asymptotically AdS black holes are known
to be thermodynamically unstable for some region of parameters, yet, as we have
shown here, they are stable against gravitational perturbations.
