In a class of nonsingular cosmologies derived from higher-order corrections
to the low-energy bosonic string action, we derive evolution equations for
the most general cosmological scalar, vector, and tensor perturbations. In
the large scale limit, the evolutions of both scalar and tensor perturbati
ons are characterized by conserved quantities, the usual curvature perturba
tion in the uniform-field gauge, and the tensor-type perturbed metric. The
vector perturbation is not affected, being described by the conservation of
the angular momentum of the fluid component in the absence of any addition
al dissipative process. For the scalar- and tensor-type perturbations, we s
how how, given a background evolution during kinetic driven inflation of th
e dilaton field, we can obtain the final power spectra generated from the v
acuum quantum fluctuations of the metric and the dilaton field during the i
nflation.