The ultrafast transient transport in wide-gap polar III-nitride semiconductors in electric fields is considered. A nonlinear and time-dependent (on the evolution of the nonequilibrium-irreversible thermodynamic state of the system) Drude-like law is derived, with the conductivity related to a so-called transport time (or current characteristic time which is related to a memory-dependent momentum relaxation time). From the collision operators, present in the evolution equations for the carriers' energy and momentum, are obtained quantities playing the role of time-dependent energy and momentum relaxation times. The electron drift velocity overshoot at intermediate-intensity fields in GaN, AlN and InN is evidenced, and its onset is explained as a result of the interplay of momentum and energy relaxation times.1934