  We review some formal aspects of cosmological solutions in closed string
theory with duality symmetric ``matter'' following recent paper with C. Vafa
(HUTP-91/A049). We consider two models : when the matter action is the
classical action of the fields corresponding to momentum and winding modes and
when the matter action is represented by the quantum vacuum energy of the
string compactified on a torus. Assuming that the effective vacuum energy is
positive one finds that in both cases the scale factor undergoes oscillations
from maximal to minimal values with the amplitude of oscillations decreasing to
zero or increasing to infinity depending on whether the effective coupling
(dilaton field) decreases or increases with time. The contribution of the
winding modes to the classical action prevents infinite expansion. Duality is
``spontaneously broken'' on a solution with generic initial conditions.
