  Isotropic string cosmology solutions can be classified into two duality
related branches: one can be connected smoothly to an expanding
Friedman-Robertson-Walker Universe, the other describes accelerated inflation
or contraction. We show that, if the dilaton potential has certain generic
properties, the two branches can evolve smoothly into each other. We find,
however, that just the effects of a potential do not allow for a graceful exit
from accelerated inflation in the weak curvature regime. We explain how
conformal field theory techniques could be used to give a decisive answer on
whether graceful exit from accelerated inflation is possible at all.
