  Corrections to a mean number of droplets appeared in the process of
nucleation have been analyzed. The two stage model with a fixed boundary can
not lead to a write result. The multi stage generalization of this model also
can not give essential changes to the two stage model. The role of several
first droplets have been investigated and it is shown that an account of only
first droplet with further appearance in frame of the theory based on the
averaged characteristics can lead to a suitable results. Both decay of
metastable phase and smooth variations of external conditions have been
investigated.
