Core/shell heterostructure nanowires are one of the most interesting mesoscopic systems potentially suitable for the study of quantum interference phenomena. Here, we report on experimental observations of both the Aharonov-Bohm (h/e) and the Altshuler-Aronov-Spivak (h/2e) oscillations in radial core/shell (In2O3/InOx) heterostructure nanowires. For a long channel device with a length-to-width ratio of about 33, the magnetoresistance curves at low temperatures exhibited a crossover from low-field h/2e oscillation to high-field h/ e oscillation. The relationship between the oscillation period and the core width was investigated for freestanding or substrate-supported devices and indicated that the current flows dominantly through the core/shell interface.