The epitactic nature of the growth of YBa 2 Cu 3 O 6+ x (YBCO) superconducting thin films on ceramic substrates has been studied using high-resolution electron microscopy (HREM) and selected-area diffraction (SAD) of cross-sectional specimens. The films were grown in situ on (001)-oriented MgO and (001)-oriented Y 2 O 3 -stabilized cubic ZrO 2 (YSZ) single-crystal substrates by electron beam evaporation. Both of these materials have large lattice misfits with respect to YBCO. Different orientation relationships were observed for films grown on the two types of substrates. These orientation relationships are shown to provide the best matching of the oxygen sublattices across the substrate-film interfaces. A crystalline intermediate layer, 6 nm thick, between the YBCO film and YSZ substrate was observed by HREM and shown by EDS to be a Ba-enriched phase, possibly barium zirconate formed by a reaction. In contrast, the YBCO–MgO interface was found to be sharp and free of any intermediate layers.