Nucleation from the vapor phase on a foreign substrate with a low numb
er of inhomogeneities is studied. Kinetic equations describing the 3D
nucleation on active sites are solved numerically. It is shown that th
e cluster flux (i.e., the rate of; formation of nuclei of a given size
) reaches some extremal value at certain time and then tends to zero a
s time increases; In such a sense, formation of nuclei is a fully nons
tationary process, in contrast to the standard nucleation theory. The
total number of nuclei formed bn a unit surface reaches for a sufficie
ntly long time some stationary value which is close to the number of n
ucleation active sites. (C) 1998 American Institute of Physics.