Low-frequency dielectric response of epitaxial multilayers and superlattices of Ba 0.8 Sr 0.2 TiO 3 :Ba 0.4 Sr 0.6 TiO 3 with a period 4-500 unit cells grown by pulsed laser deposition on La 0.5 Sr 0.5 CoO 3 / MgO is experimentally studied. The response is analyzed as a function of temperature, frequency, applied field, superlattice period, and epitaxial strain. Analysis reveals diffuse phase transitions with the existence of a glasslike state similar to those in thin-film BaTiO 3 and ͑Ba, Sr͒TiO 3 . The detected evolution of relaxation time spectra with decreasing period is suggested to contribute to the corresponding increase in permittivity. The importance of system dynamics for the analysis of microstructure and polarization in epitaxial superlattices of ͑Ba, Sr͒TiO 3 is discussed.Epitaxial thin-film multilayers and superlattices of BST80/20 and BST40/60 with a La 0.5 Sr 0.5 CoO 3 ͑LSCO͒ bottom electrode layer and a Ba 0.6 Sr 0.4 TiO 3 ͑BST60/40͒ buffer layer were grown on MgO ͑001͒ substrates. 19 The number of