The influence of convection, anisotropy and inhomogeneity of a medium on structural phase transitions during crystallization was studied. The flow of the liquid in the channels of the two-phase region using the Darsy equation for a porous medium was described. The variation in permeability with the depth of the two-phase layer is associated with the presence of the temperature gradient. The processes of heat and mass transfer in the two-phase region using the convective equations of thermal conductivity and diffusion and the equation of the liquidus were also studied. Since the two-phase region appears as the result of the concentration supercooling and development of morphological instability of the plane front only the dynamic instability consisting of oscillations of the two phase region as a whole with a zero wave number is possible in the absence of convection.