The paper theoretically investigates high-field transport in the class of model materials of the nonparabolic, nonspherical energy-momentum dispersion relation ${\mathit{p}}_{\mathit{x}}^{2}$/2${\mathit{m}}_{\mathit{x}}$+${\mathit{p}}_{\mathit{y}}^{2}$/2${\mathit{m}}_{\mathit{y}}$+${\mathit{p}}_{\mathit{z}}^{2}$/2${\mathit{m}}_{\mathit{z}}$=\ensuremath{\gamma} (E), in which the electron-phonon interaction is of the deformation-potential type with some degree of anisotropy. The predictions of the Boltzmann and Fokker-Planck theories of transport are paralleled: the former is in momentum space and is solved numerically through Monte Carlo simulations, while the latter is in energy space and has an analytical solution. Without using adjustable parameters, excellent agreement is obtained for the expectation values (drift velocity and energy) in all cases. The Fokker-Planck approach accurately reproduces the detail of the Monte Carlo--simulated nonequilibrium energy distribution wherever the energy gained over a mean free path is larger than twice the phonon energy. The Fokker-Planck picture allows one to grasp the link between transport properties and material parameters in a straightforward manner. \textcopyright{} 1996 The American Physical Society.