  We derive the formulae for the time variation of the gravitational "constant"
G and of the fine structure "constant" \alpha in various models with extra
dimensions and analyze their consistency with the available observational data
for distant supernovae. We find that the reported variation of \alpha
translates into a small variation of G that makes distant supernovae to appear
brighter, in contradiction with recent observations of high z supernovae. The
significance of these results within the framework of some cosmological
scenarios is also discussed. We find, however, that the magnitude of the effect
is not large enough to safely discard the models with extra dimensions studied
here.
