(110)‐ and (103)‐oriented almost stoichiometric YBa2Cu3O7−&dgr;(YBCO) films have been grown epitaxially on hot SrTiO3(110) substrates using a 90° off‐axis rf magnetron sputtering technique, for fabrication of vertical sandwich‐type YBCO/insulator/YBCO or YBCO/normal metal/YBCO Josephson junctions utilizing the high‐quality YBCO films. The YBCO epitaxial films with high transition temperaturesTcof ∼90 K have been depositedinsituonly under the conditions of substrate temperaturesTsof ∼650–∼700 °C and oxygen partial pressurePO2of ∼5×10−3–∼10×10−3Torr, which are in close proximity to the critical stability/decomposition line for YBa2Cu3O6in the ordinary Y–Ba–Cu–O phase diagram. Using a quadrupole mass spectrometer, a high density of atomic oxygen has directly been observed to be efficiently produced in the sputter glow discharge under the above optimum conditions ofPO2. This atomic oxygen has played a key role in promoting the formation of the perovskite structure and the epitaxial growth of the YBCO films. Furthermore, Shapiro steps have successfully been observed for a Nb–YBCO point‐contact junction, which is made by pressing a Nb needle on a surface‐etched YBCO epitaxial film, under 525.4 GHz submillimeter‐wave irradiation. ©1995 American Institute of Physics.