An original circuit-level model of two-terminal vanadium dioxide electron devices exhibiting electronic hysteresis is presented. Such devices allow realisation of very compact relaxation nano-oscillators that potentially can be used in bio-inspired neurocomputing. The proposed model is exploited to determine the parameters, values that ensure stable periodic oscillations.Introduction: Vanadium dioxide (VO 2 ) is a correlated electron material that exhibits abrupt insulator-to-metal (IMT) and metal-to-insulator (MIT) phase transitions under the application of a critical electric field (transitions may also be triggered by other stimuli, such as strain and thermal excitation) [1]. These phase transitions correspond to a large and abrupt change in electrical conductivity. Recently, it has been shown that connecting a VO 2 device with a resistor and a capacitor, of proper resistance and capacitance values, it is possible to fabricate very compact relaxation nano-oscillators [2]. The simple fabrication flow, the easy scalability with the possibility to achieve high packaging density, make VO 2 nano-oscillators promising candidates to integrate a large array of coupled oscillators for bio-inspired neurocomputing [2,3].However, electrical measurements reveal that the switching-like behaviour of a two-terminal VO 2 comes at the expense of a hysteresis with the IMT and the MIT transition being driven by two different critical electric field values. In this Letter, we provide, for the first time, a circuit-level model of the hysteresis mechanism which is a key to predicting and controlling the dynamics of relaxation oscillators built on VO 2 devices. We show how the proposed model, after being tuned with experimental data, allows us to predict the parameter values for which relaxation oscillation occurs.