The resistive switching properties of HfO₂/ZrO₂ nanolayers with the total thickness of 16 nm prepared using atomic layer deposition (ALD) were investigated. Current-voltage behavior, pulse time mode measurement, retention and endurance tests were carried out to characterize the memristive (memory-resistive) properties. Resistive switching was observed in all nanolayer stacks, and the set voltage (V_set) decreased with increasing the number of layers (i.e., increasing number of hafnia-zirconia interfaces). Grazing incidence x-ray diffraction (GI-XRD) results demonstrate that the hafnia transforms from monoclinic to orthorhombic crystal structure during the post metallization annealing. Shifts in the binding energy of the x-ray photoelectron spectra (XPS) implies the existence of hafnia and zirconia suboxide (HfO_2-δ and ZrO_2-δ). Moreover, the blocking nature of the inserted oxide/oxide interfaces serves as a barrier to oxygen ion/vacancy migration. It is shown that memristive/insulating nanostructures like HfO₂/ZrO₂ can help modulate the resistive switching of memristor-based devices.