High‐field transport properties of ZnO and ZnO/ZnMgO heterostructures were investigated. Three types of structures, a 500‐nm‐thick ZnO and ZnO/ZnMgO single‐hetero‐ (SH) and single‐quantum‐well (SQW) structures containing a thin (10‐20 nm) ZnO channel layer, were grown on a‐plane sapphire substrates by plasma‐assisted molecular beam epitaxy. The dc and pulsed I ‐V characteristics were measured at room temperature by using two‐terminal devices with the source‐to‐drain spacing of 2‐8 μm. By using the pulsed I ‐V measurements, the velocity‐field (v ‐E) characteristics were observed for electric field up to about 100 kV/cm. The v‐E characteris‐ tics revealed that no velocity saturation was observed until the velocity reached at a value of 7.6 × 106 cm/s for the thick ZnO structure while a rapid reduction of the mobility thus a saturation of the velocity at a relatively low electric field was observed for the SH structure. The reduction of the mobility was even pronounced for SQW structure. The velocity saturation might be due to the interplay between the inhomogeneities and polarization in the heterostructures. To our knowledge, this is the first experimental report on the high‐field characteristics in ZnO and ZnO/ZnMgO heterostructures. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)