  We discuss a gauge invariant approach to the theory of cosmological
perturbations in a higher-dimensonal background. We find the normal modes which
diagonalize the perturbed action, for a scalar field minimally coupled to
gravity, in a higher-dimensional manifold M of the Bianchi-type I, under the
assumption that the translations along an isotropic spatial subsection of M are
isometries of the full, perturbed background. We show that, in the absence of
scalar field potential, the canonical variables for scalar and tensor metric
perturbations satisfy exactly the same evolution equation, and we discuss the
possible dependence of the spectrum on the number of internal dimensions.
