  We discuss the realization of inflation and resulting cosmological
perturbations in the low-energy effective string theory. In order to obtain
nearly scale-invariant spectra of density perturbations and a suppressed
tensor-to-scalar ratio, it is generally necessary that the dilaton field $\phi$
is effectively decoupled from gravity together with the existence of a slowly
varying dilaton potential. We also study the effect of second-order corrections
to the tree-level action which are the sum of a Gauss-Bonnet term coupled to
$\phi$ and a kinetic term $(\nabla \phi)^4$. We find that it is possible to
realize observationally supported spectra of scalar and tensor perturbations
provided that the correction is dominated by the $(\nabla \phi)^4$ term even in
the absence of the dilaton potential. When the Gauss-Bonnet term is dominant,
tensor perturbations exhibit violent negative instabilities on small-scales
about a de Sitter background in spite of the fact that scale-invariant scalar
perturbations can be achieved.
