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In this letter, the unique reproducible nonpolar resistive switching behavior is reported in the Cu-doped ZrO2 memory devices. The devices are with the sandwiched structure of Cu/ZrO2:Cu/Pt. The switching between high resistance state (OFF-state) and low resistance state (ON-state) does not depend on the polarity of the applied voltage bias and can be achieved under both voltage sweeping and voltage pulse. The ratio between the high and low resistance is on the order of 106. Set and Reset operation in voltage pulse mode can be as fast as 50 and 100 ns, respectively. No data loss is found upon continuous readout for more than 104 s. Multilevel storage is considered feasible due to the dependence of ON-state resistance on Set compliance current. The switching mechanism is believed to be related with the formation and rupture of conducting filamentary paths.