The dielectric response of epitaxial BaTiO3 thin films deposited on MgO was measured through surface electrodes as a function of applied bias, frequency, and temperature. The room temperature value of the dielectric constant was ∼500 with a dissipation factor, tan(δ), of 0.05 at 100 kHz. Measurements varying the bias field showed hysteresis of the dielectric response and a tunability of 30% for a maximum applied field of ∼7 MV/m. The frequency response of the dielectric constant is well described by a Curie–von Schweidler power law with an exponent ∼0.04 in the range 1 kHz–13 MHz. The films undergo a diffuse phase transition at temperatures higher than the bulk Curie temperature. The behavior of the dielectric response is attributed to the presence of residual strain in the epitaxial thin films. © 1998 American Institute of Physics.