In this gaper, we report the models of fast recrystallization processes in a-Si thin films. An important feature of the modeling of nucleation in a-Si films is the capability of allowing description of non-equilibrium solidification including the distribution of small crystalline clusters which can be responsible for visible photoluminescence. We integrate the results of the description of nucleation and growth on the phase interface of c-Si from a-Si or l-Si. The transient time, nucleation rate and growth rate were determined as a function of temperature and the position of local extremes of these functions were stated. The solidification velocity was calculated from the nucleation rate and growth rate with respect to the temperature distribution in a system. The suitability of the particular approximations and models is discussed.