  We discuss various superstring effective actions and, in particular, their
common sector which leads to the so-called pre-big-bang cosmology (cosmology in
a weak coupling limit of heterotic superstring). Then, we review the main ideas
of the Horava-Witten theory which is a strong coupling limit of heterotic
superstring theory. Using the conformal relationship between these two theories
we present Kasner asymptotic solutions of Bianchi type IX geometries within
these theories and make predictions about possible emergence of chaos. Finally,
we present a possible method of generating Horava-Witten cosmological solutions
out of the well-known general relativistic pre-big-bang solutions.
