The results of an ensemble Monte Carlo simulation of electron drift velocity response on the application field in bulk AlAs , AlGaAs and GaAs are presented. All dominant scattering mechanisms in the structure considered have been taken into account. For all materials, it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Transient velocity overshoot has also been simulated, with the sudden application of fields up to 1600 kVm-1, appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of ~105 ms-1 within 4 ps, for all crystal structures. The steady state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.