  We discuss the structure of the equation of motion that governs nucleation
processes at first order phase transitions. From the underlying microscopic
dynamics of a nucleating system, we derive by means of a non-equilibrium
projection operator formalism the equation of motion for the size distribution
of the nuclei. The equation is exact, i.e. the derivation does not contain
approximations. To assess the impact of memory, we express the equation of
motion in a form that allows for direct comparison to the Markovian limit. As a
numerical test, we have simulated crystal nucleation from a supersaturated melt
of particles interacting via a Lennard-Jones potential. The simulation data
show effects of non-Markovian dynamics.
