AbstractThe Boltzmann transport equation is used to derive a set of conservation equations which is capable of describing the electron transport phenomena in a single‐valley semiconductor. These conservation equations are averaged over the different valleys of the conduction band to develop another set of equations that can be used to describe accurately the electron transport phenomena in a multi‐valley semiconductor, such as GaAs, using the equivalent single‐electron gas model whose characteristics are the average weighted characteristics of the constituent gases. The nonstationary effects are included by using energy dependent mobility and electron temperature functions. This program is used to simulate a GaAs MESFET with a 0·5 μm gate length and a 0.2 μm thick active layer. The active layer is doped at 1017cm−3. A travelling Gunn domain is observed between the gate and the drain. The domain oscillation frequency is much higher than the normal operating frequency of the MESFET. The domain formation's dependence on the gate bias and the active layer thickness are also