  We briefly review the status of the ``graceful exit'' problem in superstring
cosmology and present a possible resolution. It is shown that there exists a
solution to this problem in two-dimensional dilaton gravity provided quantum
corrections are incorporated. This is similar to the recently proposed solution
of Rey. However, unlike in his case, in our one-loop corrected model the
graceful exit problem is solved for any finite number of massless scalar matter
fields present in the theory.
