We discuss several aspects of the cosmological evolution of moduli fields in
heterotic string/M-theory scenarios. In particular we study the equations of
motion of both the dilaton and overall modulus of these theories in the
presence of an expanding Universe and under different assumptions. First we
analyse the impact of their couplings to matter fields, which turns out to be
negligible in the string and M-theory scenarios. Then we examine in detail the
possibility of scaling in M-theory, i.e. how the moduli would evolve naturally
to their minima instead of rolling past them in the presence of a dominating
background. In this case we find interesting and positive results, and we
compare them to the analogous situation in the heterotic string.Comment: 12 pages, 4 postscript figure
