In this paper, we report an approach to design nanolayered memristive compositions based on TiO/AlO bilayer structures with analog non-volatile and volatile tuning of the resistance. The structure of the TiO layer drives the physical mechanism underlying the non-volatile resistance switching, which can be changed from electronic to ionic, enabling the synaptic behavior emulation. The presence of the anatase phase in the amorphous TiO layer induces the resistive switching mechanism due to electronic processes. In this case, the switching of the resistance within the range of seven orders of magnitude is experimentally observed. In the bilayer with amorphous titanium dioxide, the participation of ionic processes in the switching mechanism results in narrowing the tuning range down to 2-3 orders of magnitude and increasing the operating voltages. In this way, a combination of TiO/AlO bilayers with inert electrodes enables synaptic behavior emulation, while active electrodes induce the neuronal behavior caused by cation density variation in the active AlO layer of the structure. We consider that the proposed approach could help to explore the memristive capabilities of nanolayered compositions in a more functional way, enabling implementation of artificial neural network algorithms at the material level and simplifying neuromorphic layouts, while maintaining all benefits of neuromorphic architectures.