In the first part of the talk I will introduce the Becker-Doring
nucleation equation and describe its singular perturbation solution under
time-dependent conditions of a nucleation pulse. In the second part, I
will discuss a supersaturated lattice gas on a square lattice, where
steady-state and time-dependent nucleation can be described from first
principles. Comparison confirms qualitative (not quantitative) validity of
the Becker-Doring model at not too small temperatures T , but also reveals
its limitations due to neglect of "magic numbers", which become prominent
as T -> 0 .