We examine the effect of perturbative string loops on the cosmological pre-big-bang evolution. We study loop corrections derived from heterotic string theory compactified on a $Z_N$ orbifold and we consider the effect of the all-order loop corrections to the Kahler potential and of the corrections to gravitational couplings, including both threshold corrections and corrections due to the mixed Kahler-gravitational anomaly. We find that string loops can drive the evolution into the region of the parameter space where a graceful exit is in principle possible, and we find solutions that, in the string frame, connect smoothly the superinflationary pre-big-bang evolution to a phase where the curvature and the derivative of the dilaton are decreasing. We also find that at a critical coupling the loop corrections to the Kahler potential induce a ghost-like instability, i.e. the kinetic term of the dilaton vanishes. This is similar to what happens in Seiberg-Witten theory and signals the transition to a new regime where the light modes in the effective action are different and are related to the original ones by S-duality. In a string context, this means that we enter a D-brane dominated phase.