Higher Loop String Cosmology with Moduli and Antisymmetric Tensor Field

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.