  The study of perturbations around black hole backgrounds in general
relativity and Einstein-Maxwell theory has a long history, going back to the
work of Regge and Wheeler in the 1950s. As part of a broader investigation of
perturbations around black holes in supergravity, we describe here our results
for the perturbations around the Gibbons-Maeda static charged black holes in a
class of Einstein-Maxwell-Dilaton theories. Our analysis follows the general
strategy developed by Chandrasekhar and Xanthopoulos for the perturbations of
the Reissner-Nordstr\"om black hole. Here, the analysis is considerably more
involved, because of the presence of the dilaton field, which couples to the
other polar modes. We nonetheless find that the problem is completely solvable,
in the sense that one can separate variables and eventually describe all the
perturbations in terms of diagonalised second-order radial equations. We are
able to prove the mode stability of all the Gibbons-Maeda black hole solutions.
