This work investigates titanium dioxide nanotube arrays (TiO2-NTA) grown by anodic oxidation as an active material for memristive applications. In particular, metal-insulator-metal structures made of vertically oriented amorphous TiO2-NTA grown on titanium foil were exploited in Ti/TiO2-NTA/Pt devices. The deposition of a polymeric thin film between NTA and top electrodes significantly improved the stability of the devices and increased by more than double the off/on resistance ratio. The resistive switching of TiO2-NTA samples crystallised by thermal annealing was also studied. Such devices displayed nonlinear I-V curves characterised by a smooth rectifying behaviour, without any evident resistive switching (RS). Also in this case, the interposition of the polymeric layer enhanced the RS behaviour of TiO2-NTA samples, remarkably increasing the devices' off/on ratio and endurance. The rise of high resistance states can be simply related to the addition of the polymer as resistance in series, while the variation of the low resistance states is here attributed to the occurrence of surface chemical reactions between polymer functional groups and the metal oxide, which increase the charge carriers available for conduction.