It is described a kinetic theory providing bases for an analytical treatmen
t of nonlinear quantum transport. It is founded on a nonequilibrium statist
ical ensemble formalism, which constitutes a soundly approach for the study
of dissipative many-body systems driven arbitrarily away from equilibrium.
This theory is applied to the study of transport of charge in n- and p- ty
pe doped polar semiconductors. Evolution of the carriers' quasitemperature
and mobility as well as of the relaxation times for energy and momentum are
derived. Some comparison with experimental data is done.