We discuss in detail how to consistently impose boundary conditions in
quantum string cosmology. Since a classical time parameter is absent
in quantum gravity, such conditions must be imposed with respect to in
trinsic variables. Constructing wave packets for minisuperspace models
from different tree-level string effective actions, we explain in par
ticular the meaning of a transition between ''pre-big-bang'' and ''pos
t-big-bang'' branches. This leads to a scenario different from previou
s considerations. (C) 1997 Elsevier Science B.V.