This paper is devoted to the fabrication of ReRAM elements based on TiN/ZnO/TiN/Al₂O₃ structures using scratching probe nanolithography of the atomic force microscope, as well as to the investigation of the resistive switching of the memristive nanostructures. The regimes of scratching probe nanolithography on the photoresist film were investigated. The memristive nanostructures were shown to exhibit a bipolar resistive switching with the ratio of HRS/LRS ratio up to 78.8 at reading voltage 0.5 V and maintaining a resistive state up to 10⁵ s. The results can be useful for micro- and nanoelectronics elements manufacturing, as well as neuromorphic applications using probe nanotechnologies and nanocrystalline ZnO-based ReRAM elements prototyping.