  We study the effect of higher-curvature terms in the string low-energy
effective actions on the cosmological solutions of the theory, up to
corrections quartic in the curvatures, for the bosonic and heterotic strings as
well as the type II superstring. We find that cosmological solutions exist for
all string types but they always disappear when the dilaton field is included,
a conclusion that can be avoided if string-loop effects are taken into account.
