  We investigate FRW cosmological solutions in the theory of modulus field
coupled to gravity through a Gauss-Bonnet term. The explicit analytical forms
of nonsingular asymptotics are presented for power-law and exponentially steep
modulus coupling functions. We study the influence of modulus field potential
on these asymptotical regimes and find some forms of the potential which do not
destroy the nonsingular behavior. In particular, we obtain that exponentially
steep coupling functions arising from the string theory do not allow
nonsingular past asymptotic unless modulus field potential tends to zero for
modulus field $\psi \to \pm \infty$. Finally, the modification of the chaotic
dynamics in the closed FRW universe due to presence of the Gauss-Bonnet term is
discussed.
