We give a comprehensive analysis of how scalar and tensor perturbation
s evolve in cosmologies with a smooth transition from power-law-like a
nd de Sitter-like inflation to a radiation era. Analytic forms for the
superhorizon and subhorizon perturbations in the inflationary and rad
iation dominated eras are found. (C) 1998 American Institute of Physic
s. [S0022-2488(98)01110-4].