A theoretical study on the nonlinear transport of holes and of the nonequilibrium thermodynamic characteristics of p-doped wurtzite gallium nitride (GaN), aluminium nitride (AlN), and indium nitride (InN), under the influence of moderate to high electric fields, 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 hole drift velocity and of the quasitemperatures of holes and longitudinal optical phonons are obtained. The steady state is analyzed by determining the dependence on the electric field of the nonequilibrium thermodynamic state and of the non-Ohmic mobility. A velocity overshoot is evidenced. (C) 2007 American Institute of Physics.1027