The ensemble Monte Carlo particle simulation technique is used to determine the upper operational frequency limit of the transferred electron mechanism in bulk GaAs and GaN empirically. This mechanism manifests as a decrease in the average velocity of the electrons in the bulk material with an increase in the electric field bias, which yields the characteristic negative slope in the velocity–field curves of these materials. A novel approach is proposed whereby the hysteresis in the simulated dynamic, high-frequency velocity–field curves is exploited. The upper operational frequency limit supported by the material is defined as that frequency, where the average gradient of the dynamic characteristic curve over a radio frequency cycle approaches zero. Effects of temperature and doping level on the operational frequency limit are reported. The frequency limit thus obtained is also useful to predict the highest fundamental frequency of operation of transferred electron devices, such as Gunn diodes, which are based on materials that support the transferred electron mechanism. Based on the method presented here, the upper operational frequency limits of the transferred electron mechanism in bulk GaAs and GaN are 80 and 255 GHz, respectively, at typical doping levels and operating temperatures of Gunn diodes.