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We report the demonstration of multilevel operation using Cu/Cu-GeTe/W nonvolatile resistive memory devices for enhanced storage density. We incorporated Cu atoms into GeTe solid-electrolyte switching layers in Cu/Cu-GeTe/W nonvolatile resistive memory devices by applying a bias to the sample holder during a radio-frequency sputtering process. By analyzing the dependence of the device current (resistance) on both the pulse input voltage magnitude and width, we achieved four distinct resistance levels that correspond to the 2-bit operation of a single memory cell. Moreover, a model was suggested and discussed to account for the observed multibit operation.