The breakthrough in electronics and information technology is anticipated by the development of emerging memory and logic devices, artificial neural networks and brain-inspired systems on the basis of memristive nanomaterials represented, in a particular case, by a simple ‘metal–insulator–metal’ (MIM) thin-film structure. The present article is focused on the comparative analysis of MIM devices based on oxides with dominating ionic (ZrOx, HfOx) and covalent (SiOx, GeOx) bonding of various composition and geometry deposited by magnetron sputtering. The studied memristive devices demonstrate reproducible change in their resistance (resistive switching – RS) originated from the formation and rupture of conductive pathways (filaments) in oxide films due to the electric-field-driven migration of oxygen vacancies and / or mobile oxygen ions. It is shown that, for both ionic and covalent oxides under study, the RS behaviour depends only weakly on the oxide film composition and thickness, device geometry (down to a device size of about 20×20 μm2). The devices under study are found to be tolerant to ion irradiation that reproduces the effect of extreme fluences of high-energy protons and fast neutrons. This common behaviour of RS is explained by the localized nature of the redox processes in a nanoscale switching oxide volume. Adaptive (synaptic) change of resistive states of memristive devices is demonstrated under the action of single or repeated electrical pulses, as well as in a simple model of coupled (synchronized) neuron-like generators. It is concluded that the noise-induced phenomena cannot be neglected in the consideration of a memristive device as a nonlinear system. The dynamic response of a memristive device to periodic signals of complex waveform can be predicted and tailored from the viewpoint of stochastic resonance concept. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)