  Classical string cosmology consists of two branches related to each other by
scale-factor duality: a super-inflation branch and a Friedmann-Robertson-Walker
(FRW) branch. Curvature and string coupling singularity separates the two
branches, hence posing `graceful exit problem' to super-inflationary string
cosmology. In an exactly soluble two-dimensional compactification model it is
shown that quantum back reaction retards curvature and string coupling growth
and connects the super-inflation branch to the FRW branch without encountering
a singularity. This may offer an attractive solution to the `graceful exit
problem' in string inflationary cosmology.
