A theoretical study on the electron drift velocity and some nonequilibrium thermodynamic characteristics of wurtzite GaN, AlN, and InN is presented. It is based on a nonlinear quantum kinetic theory which provides a description of the dissipative phenomena developing in the system. The ultrafast time evolution of the electron drift velocity and quasitemperature is obtained, and overshoot effects are evidenced on both. The overshoot onsets are shown to occur at 20 kV/cm in GaN, 60 kV/cm in AlN, and 10 kV/cm in InN, electric field intensities which are considerably smaller than those that have been recently derived resorting to Monte Carlo simulations. (C) 2000 American Institute of Physics. [S0003-6951(00)03914-0].761418931895