Kinetics of nucleation on active centers in supersaturated vapors is studied by a numerical solution of kinetic equations, including depletion of active centers during the phase transition process. The basic characteristics of the nucleation process (the size distribution of nuclei, nucleation rate and the total number of nuclei) are determined at various conditions. Nuclei are formed on all active centers at a sufficiently long time in coincidence with a widely used Avrami model. An increase of the total number of nuclei with time is steeper in the Avrami model as compared with our numerical solution of kinetic equations. The nucleation rate does not reach its stationary limit and becomes negligibly small with increasing time. (C) 2003 American Institute of Physics.