The theory of coherent phase diagrams is expanded to phase transformations in films. Coherent phase transformations in a free standing film or a thin plate are considered. It is suggested that the misfit between the phases dictates their layer arrangement with an interface parallel to film surfaces. Then, the transformational self-strain leads to the film bending. The elastic energy of the coherent phases depends on the interface position and, consequently, on the phase fractions. The phase equilibrium analysis shows that the polymorphic tranformation in a single compoennt system proceeds with the thermodynamic hysteresis. However, the reversible change of the two-phase equilibrium with temperature is possible if the phase fractions are maintained within a range (1/2, 2/3). The character of polymorphic phase transformations in a binary system depends on the concentration of a second component. The quasi-single component transformation takes place at small concentrations. The reversible coherent phase transformation should be observed at the concentration larger than the critical one. The irreversible transformations take place at intermediate concentrations. The irreversible transformations begin with the formation of a finite fraction of the second phase. Then, the two-phase system evaluates with temperature to the final two-phase state that transfers discontinuously to a single-phase state. The concentration diagram does not coincide with the phase diagram. The concentrations in the transforming phases change non-monotonously with temperature.