  We study density perturbations in several cosmological models motivated by
string theory. The evolution and the spectra of curvature perturbations ${\cal
R}$ are analyzed in the Ekpyrotic scenario and nonsingular string cosmologies.
We find that these string-inspired models generally exhibit blue spectra in
contrast to standard slow-roll inflationary scenarios. We also clarify the
parameter range where ${\cal R}$ is enhanced on superhorizon scales.
