Hybrid memory devices with polyimide and SnO2 nanocrystals on a flexible polyethersulphone substrate have shown a memristor behavior from current-voltage (I-V) measurements. The resistive-switching effects with a current bistability appeared during cycling voltage sweeping within the range of +/- 4 V. This I-V switching effect might have originated from a resistance fluctuation due to the charge trapping into the SnO2 nanocrystals as well as the oxygen vacancies of the ZnO layer and aluminum oxides that were formed between the polyimide and the interface of the Al gate electrode. In the bipolar resistance-switching behavior, the ratio of the high- and low-resistance state currents was about 3.7 x 10(4) at 1 V.