We have heteroepitaxially deposited compositionally graded (Ba1-xSrx)TiO3 (BST) thin films with increasing x from 0.0 to 0.25 on (100)-oriented MgO substrates using pulsed-laser deposition. The compositional gradients along the depth in the graded films were characterized by Rutherford backscattering spectroscopy. By using surface interdigital electrodes, the planar dielectric response of epitaxial graded BST films was measured as a function of frequency, temperature, and dc applied voltage. At room temperature, the dielectric constant of the graded BST film was about 450 with a dielectric loss, tan δ of 0.007 at 100 kHz. Measurements varying the dc bias voltage showed hysteresis of the dielectric response and a tunability of 25% at an applied electric field of 80 kV/cm. The graded BST films undergo a diffuse phase transition with a broad and flat profile of the capacitance versus temperature. Such behavior of the dielectric response in graded BST films is attributed to the presence of the compositional and/or residual strain gradients in the epitaxial graded films. With such a graded structure, it is possible to a build a dielectric thin-film capacitor with a low-temperature dependence of the capacitor over a broad temperature regime. © 2002 American Institute of Physics.