Time evolution of a Bose system passing through the critical point

Kinetics of Bose condensation of an ideal Bose gas and of the classical Bose gas of hard spheres is considered. Deviations from the equilibrium state are not assumed to be small. An analytic solution for the problem of an ideal Bose gas is found and the role of collisions between the Bose particles themselves is discussed qualitatively. It is shown that Bose condensation is a slowing down process which can be completed at $t\to \infty$ while the formation of the high-energy tail of the distribution function is relatively fast. The transition time is finite if the nuclei of new phase are present in the beginning of the cooling process.