  We study the perturbative stability of four settings that arise in String
Theory, when dilaton potentials accompany the breaking of Supersymmetry, in the
USp(32) and U(32) orientifold models, and also in the heterotic SO(16)xSO(16)
model. The first two settings are a family of AdS3xS7 orientifold vacua and a
family of AdS7xS3 heterotic vacua, supported by form fluxes, with small
world-sheet and string-loop corrections within wide ranges of parameters. In
both cases we find some unstable scalar perturbations, as a result of mixings
induced by fluxes, confirming for the first class of vacua a previous result.
However, in the second class they only affect the l=1 modes, so that a Z2
projection induced by an overall internal parity suffices to eliminate them,
leading to perturbative stability. Moreover, the constant dilaton profiles of
these vacua allow one to extend the analysis to generic potentials, thus
exploring the possible effects of higher-order corrections, and we exhibit wide
nearby regions of perturbative stability. The solutions in the third setting
have nine-dimensional Poincare' symmetry. They include regions with large
world-sheet or string-loop corrections, but we show that these vacua have no
perturbative instabilities. Finally, the last setting concerns cosmological
solutions in ten dimensions where the "climbing" phenomenon takes place: they
have bounded string-loop corrections but large world-sheet ones close to the
initial singularity. We find that perturbations generally decay, but
homogeneous tensor modes exhibit an interesting logarithmic growth that signals
a breakdown of isotropy. If the Universe then proceeds to lower dimensions,
milder potentials from other branes force all perturbations to remain bounded.
