The growth of complex binary film from the ternary solution be the method of liquid-phase epitaxy is under consideration. The mathematical model that is one-dimensional one-phase supercooled Stefan problem for the system of diffusion equations coupled in the interface conditions is studied. In the problems of 1st type called #direct# the concentration distribution and the free boundary motion law must be determined when the temperature of the process is given. In the problems of the 2nd type called #inverse# the temperature of the process provides the desired film composition is searching. The solvability condition for the problems are found and the properties of the solutions in dependence on input data are studied. Also the conditions of existence and the algorithm of construction of the family of exact (self-similar) solutions are formulated.