In the Department attention is granted to the process of first order phase transitions. The problem is to invent a theory describing all stage of system evolution, from the moment of metastability formation up to its disappearance. Barrier character of the new phase generation process imply the main difficulty. The particle of new phase has to overcome in a fluctuating way the state unfavourable from the energetic point of view. Parameters of this effective energy barrier are depending on the metastability degree of the initial phase so this phenomenon is essentially non-liner process. The serious problem is to describe the barrier as it is localized in the region of very small sizes of new phase particles. In order to obtain a reasonable accuracy we have to consider very delicate microeffects, such as dependence of the evaporation velocity on particles cooling due to the lost of each molecules.