  String cosmology solutions are examined in a generalized phase-space
including sources representing arbitrary corrections to lowest order
string-dilaton-gravity effective action. We find a set of necessary conditions
for a graceful exit transition from a dilaton-driven inflationary phase to a
radiation dominated era. We show that sources allowing such a transition have
to violate energy conditions similar to those appearing in singularity theorems
of general relativity. Since familiar classical sources, excepting spatial
curvature, obey these energy conditions we conclude that a generic graceful
exit in string cosmology requires a new effective phase of matter. Our results
clarify and generalize previous analyses and enable us to critically reexamine
proposed non-singular cosmologies.
