The nonequilibrium dynamics of hot-electron transport in a strong electric field is modeled by a Boltzmann-Vlasov equation with a relaxation-time formulation of the collision terms. Solutions of the first-order theory in a six-dimensional phase space are constructed in closed form. The associated hierarchy of hydrodynamiclike moment equations is shown to be closed exactly. The stability of the nonequilibrium solutions is governed by a field-dependent dispersion relation. Analytic solutions to this dispersion relation in the long-wavelength limit illustrate the salient features of mean-field effects, collisional damping, and medium polarization. © 1992 The American Physical Society.