  Kinetics of the first order phase transition has been investigated. The case
when the droplets sizes have a limit value is considered. An analytical theory
for such process has been constructed and all main characteristics of the
process have been determined by rather simple approximate analytical formulas.
The limit for a droplets size violates the avalanche consumption of the mother
phase which is the basic feature of the first order phase transition and have
been actively used in previous publications. Now one can not state that the
main quantity of the already condensated substance is contained in the droplets
formed under conditions unperturbed by nucleation process. This requires to
introduce some new methods of solutions for kinetic equation which are given in
the present paper.
