A thermodynamic theory is used to calculate the dielectric properties of epitaxial thin films grown on cubic substrates imposing biaxial tension on the film prototypic cubic state. For such "tensile" substrates, the theory shows that, in a conventional plate-capacitor setup, the films should display only a monotonic variation or a broad maximum in the temperature dependence of the permittivity and an apparent absence of the hysteretic polarization behavior. Changes of the Curie-Weiss temperature and constant caused by the mechanical film/substrate interaction are also predicted. Theoretical results agree with the observed properties of columnar-structured BaTiO3 and SrTiO3 thin films grown on Si. (C) 1999 American Institute of Physics. [S0021-8979(99)01603-5].