  We study the stability under linear perturbations of a class of static
solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial
slices of the form $\Sigma_{\k}^n \times {\mathbb R}^+$, $\Sigma_{\k}^n$ an
$n-$manifold of constant curvature $\k$. Linear perturbations for this class of
space-times can be generally classified into tensor, vector and scalar types.
In a previous paper, tensor perturbations were analyzed. In this paper we study
vector and scalar perturbations. We show that vector perturbations can be
analyzed in general using an S-deformation approach and do not introduce
instabilities. On the other hand, we show by analyzing an explicit example
that, contrary to what happens in Einstein gravity, scalar perturbations may
lead to instabilities in black holes with spherical horizons when the
Gauss-Bonnet string corrections are taken into account.
