  The classical evolution of a homogeneous cosmological model is investigated
within the framework of low - energy effective string gravity with higher genus
corrections. Various conformal frames are considered. For the general case of
correction functions in the Lagrangian we give the cosmological solutions with
arbitrary curvature and dilaton, modulus and Kalb-Ramond fields. They
generalize previously known tree level solutions. The features of the solutions
are discussed.
