GRACEFUL EXIT IN QUANTUM STRING COSMOLOGY

We write an O(d, d)-covariant Wheeler-De Witt equation in the (d(2) 1)-dimensional minisuperspace of low-energy cosmological string backgr ounds. We discuss explicit examples of transitions between two duality -related cosmological phases, and we find a finite quantum transition probability even when the two phases are classically separated by a cu rvature singularity. This quantum approach is completely free from ope rator ordering ambiguities as a consequence of the duality symmetries of the string effective action.