  We describe exact cosmological solutions with rotation and expansion in the
low-energy effective string theory. These models are spatially homogeneous
(closed Bianchi type IX) and they belong to the family of shear-free metrics
which are causal (no closed timelike curves are allowed), admit no parallax
effects and do not disturb the isotropy of the background radiation. The
dilaton and the axion fields are nontrivial, in general, and we consider both
cases with and without the central charge (effective cosmological constant).
