We study the evolution of tensor metric fluctuations in a class of non-sing
ular models based on the string effective action, by including in the pertu
rbation equation the higher-derivative and loop corrections needed to regul
arise the background solutions. We discuss the effects of such higher-order
corrections on the final graviton spectrum, and we compare the results of
analytical and numerical computations. (C) 2001 Elsevier Science B.V. All r
ights reserved.