  We construct some examples of analytic solutions of the low energy (i.e.
tree-level) string cosmological effective action. We work with the ``minimal''
field content (i.e. graviton and dilaton) in the absence of any dilaton
potential. Provided the metric is sufficiently inhomogeneous we find solutions
whose curvature invariants are bounded and everywhere defined in time and
space. The dilaton coupling and its associated energy density are regular and
homogeneous. A phase of growing (and non-singular) dilaton coupling compatible
with the regularity of the curvature invariants without the addition of higher
curvature (or higher genus) corrections to the tree-level effective action. We
discuss the symmetries of the obtained solutions.
