To describe the motion of the film flowing downward the vertical wall in the mode of condensation or evaporation into the surrounding space, the model proposed in  is used. It is reduced to one equation for the film thickness. The model comprises two governing parameters. The first one is proportional to the difference in the wall temperature, assumed to be constant, and the saturation temperature, and the second is proportional to the surface tension coefficient. In a series of publications [1–4] the authors studied solutions of thementioned equation at zero surface tension. Their characteristic feature is the presence of strong and weak discontinuities of layer thickness. In this paper we studied the regularizing effect of surface tension on the film flow structure with phase transitions. Numerical and asymptotic analysis of the resulting structures is carried out. Also, the case where the wall temperature is an arbitrary function of time is considered.