Dielectric LaAlO3 and SrTiO3 thin films and LaAlO3/SrTiO3 multilayers were grown epitaxially by pulsed laser deposition on (001) oriented (LaAlO3)0.3(Sr2AlTaO6)0.7 substrates. Their structural characterization was carried out by x-ray diffraction and cross section transmission electron microscopy, which allowed us to determine the degree of strain in the dielectric material. For a film thickness of 200 nm we observed significant structural relaxation of the LaAlO3 and SrTiO3 single layers toward their single crystal lattice parameters in contrast to LaAlO3/SrTiO3 multilayer structures, where the dielectric material remained coherently strained. The influence of strain on the dielectric properties was studied by impedance spectroscopy in the frequency range of 40 Hz–10 MHz at room temperature. The measurements were performed on parallel plate capacitors, using epitaxial La0.4Sr0.6CoO3 films as bottom and top electrodes. The dielectric constant ε of partially relaxed and coherently strained material was nearly the same. However, the dielectric tunability, i.e., the influence of a direct current bias voltage on ε, was found to be significantly larger for coherently strained dielectrics. For [LaAlO3(30 Å)/SrTiO3(60 Å)]20 multilayers we observed a tunability of nearly 20% at room temperature for a bias voltage of only 1 V, corresponding to an electric field strength of 50 kV/cm. The total dielectric loss of the multilayer capacitors is below 1% for frequencies above 1 MHz and depends only slightly on the bias voltage.