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As a general rule, in the study of transport phenomena analytical-type methods have been based on Boltzmann-like transport theories, which however have limitations when nonlinear effects become to have relevance. Thus, improved analytical methods, that is nonlinear quantum kinetic theories for studying physical phenomena in systems arbitrarily away from equilibrium, are desirable. An advantage over Monte Carlo computational methods resides in that the analytical equations may provide a better physical insight and interpretation of the results. Nonlinear quantum kinetic theories more appropriate for the purpose just stated have been derived under some type or other of intuitive techniques and ideas. One such theory based on sound physical foundations, which is compact and practical, is presently available. It is the kinetic theory derived from a powerful approach consisting of a nonequilibrium ensemble formalism. The latter is the so-called ``Nonequilibrium Statistical Operator Method". It is a powerful formalism that seems to offer an elegant and concise way for an analytical treatment in the theory of irreversible processes, adequate to deal with a large class of experimental situations. It provides a kinetic theory of large scope, kind of a far-reaching generalization of the Chapman-Enskog approach or the Mori-Langevin formalism. We resort to this approach to study some transport properties and phenomena in the case of doped polar semiconductors: GaAs, GaN, AlN and InN, and some comparison with experimental data is done. The study of transport properties of semiconductors under high level of excitation, eventually following nonlinear laws, are of great interest not only for its relevance in the functioning of electronic and optoeletronic devices, but also because of providing an excellent testing ground for theoretical ideas in the field of many-body systems in far-from-equilibrium conditions as we do here. Hence, as noticed, nonlinearities are present in both transport properties and relaxation processes, which may give origin to new and interesting phenomena. They may arise, for example, in the case of nonuniform (variation in space) and sufficiently intense (critical point) electric fields, as a result of the influence of an increasing (with the electric field strength) shear stress leading the system to an instability. It is conjectured to be of some chaotic or turbulent type and, of course, relevant to be characterized and fully analyzed because of the accompanying interest on its influence on the performance of electronic and optoelectronic devices. The author CGR acknowledges the financial support received from the FAPEG and CNPq.