A phenomenological thermodynamic theory of ferroelectric thin films epitaxially grow on cubic substrates is developed using a new form of the thermodynamic potential. which corresponds to the ac tual mechanical boundary conditions of the problem, For single-domain BaTiO3 and PbTiO3 films, the "misfit-temperature" phase diagrams are constructed. It is found that the 2D clamping of the films, apart from a shift of the temperature of the ferroelectric transition, results in a change of its order. A change of the sequence of the phases and the appearance of phases forbidden in the bulk crystals are predicted. [S0031-9007(98)05421-0].