  Kinetics of the first order phase transition is investigated. In some rather
wide spread situations the property of avalanche growth of the objects of a new
phase doesn't take place. This radically complicates the theoretical
description of the nucleation kinetics and this case was completely
investigated here. The power-like dependencies with decreasing absolute value
of derivative on time were chosen as the model laws of embryos growth. All main
characteristics of the nucleation period including the spectrum of sizes of the
new phase objects were obtained. An analytical approximate description of
nucleation in different external conditions was fulfilled. The errors of such
description are found and proved to be small.
