Perturbation theory is applied to the description of the kinetics of a first-order phase transition illustrated by thin film growth. A small parameter was chosen as the quantity l/i(c), where i(c) is the number of particles in a critical nucleus under maximum supersaturation in the course of the phase transition. Uniform convergence of the expansions obtained is reached through time renormalization. The cases of single-and multi-component condensation have been studied. (C) 1997 American Institute of Physics.