A mathematical method based on a reduced representation of the electron–electron collision operator acting in the space of quasi-equilibrium functions is constructed. A number of kinetic phenomena such as the evolution of highly anisotropic and high-energy electron distributions, the quasi-hydrodynamic effect in electrical conduction, and a new nonlinear transport mode are described from a unified point of view. Kinetic effects which can be observed in experiments on electron beam propagation and electrical conduction of (GaAs)Al wires with a high mobility of charge carriers are predicted. ©1997 American Institute of Physics.