  We study the stability of black holes that are solutions of the dilaton
gravity derived from string-theoretical models in two and five dimensions
against to scalar field perturbations, using the Quasinormal Modes (QNMs)
approach. In order to find the QNMs corresponding to a black hole geometry, we
consider perturbations described by a massive scalar field non-minimally
coupled to gravity. We find that the QNM's frequencies turn out to be pure
imaginary leading to purely damped modes, that is in agreement with the
literature of dilatonic black holes. Our result exhibits the unstable behavior
of the considered geometry against the scalar perturbations. We consider both
the minimal coupling case, i.e., for which the coupling parameter $\zeta$
vanishes, and the case $\zeta={1/4}$.
