We consider the theory obtained by adding to the usual string frame dilaton
gravity action specially constructed higher derivative terms motivated by
the limited curvature construction of [1] and determine the spatially homog
eneous and isotropic solutions to the resulting equations of motion. All so
lutions of the resulting theory of gravity with these symmetries are nonsin
gular and all curvature invariants are bounded. For initial conditions insp
ired by the pre-big-bang scenario solutions exist which correspond to a spa
tially at Universe starting in a dilaton-dominated superinationary phase wi
th (H) over dot >0 and having a smooth transition to an expanding Friedmann
Universe with (H) over dot <0. Hence, the graceful exit problem of pre-big
-bang cosmology is solved in a natural way.