An ensemble Monte Carlo simulation is used to compare high field electron transport in bulk InN, AlN and GaN. For all materials, we find that electron velocity overshoot only occurs when the electric field in increased to a value above a certain critical field .This critical field is strongly dependent on the material parameters. Transient velocity overshoot has also been simulated, with the sudden application of fields up to1000 kV/m , appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of 105 m/s within 3 ps, for all crystal structures. The steady state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.