Can String Theory Avoid Cosmological Singularities?

We consider the effective action for strings and describe in detail the evolution of a four dimensional homogeneous isotropic universe with matter included. We find that the evolution, which is singular in general, becomes singularity free if during certain Phase of the evolution, when the scale factor increases and the effective string coupling becomes strong, the universe is dominated by solitonic p-branes, p = 0 and/or - 1, or by `matter' for which $(pressure) \le - \frac{1}{\sqrt{3}} (density)$. The mechanism in the case of branes is reminiscent of the recently discovered field theory mechanism where heavy states become light and resolve the moduli space singularities.