The authors have grown epitaxial ZnO/BaTiO3 (BTO) heterostructures by pulsed laser deposition on lattice matched Nb-doped SrTiO3 substrates. Epitaxial growth of the BTO layers has been confirmed by x-ray diffraction. The electrical properties of ZnO/BTO heterostructures have been investigated by current-voltage and capacitance-voltage measurements, showing that the BTO layers are highly insulating (leakage current density j(l)< 10(-9) A/cm(2) at 5 V). The structures were processed into field-effect transistors, and their output and transfer properties have been determined. A large memory effect of the source-drain current on the previously applied "programm" gate voltage (-7 or +20 V) has been observed. It is reproducible in repeated switching cycles, showing the suitability of the structure as a nonvolatile memory device.