The balance-equation approach developed by Lei and Ting for steady-state hot-electron transport is extended here to include nonequilibrium phonon occupation under the assumption that the effect of phonon-phonon interaction can be represented by an effective phonon relaxation time Tp, which may be mode dependent. Both single heterojunctions and multiplayer quantum-well superlattices, as well as three-dimensional (3D) bulk systems, are discussed. A 3D phonon model and a quasi-2D phonon model are employed in describing the various interaction electron-phonon systems. The expressions for the frictional forces and energy transfer rates obtained in steady state are structurally similar to those without hot-phonon effects and the balance equations with finite phonon relaxation can be solved with the same computational effort as in the case of Tp=0. We have examined hot phonon effects on the energy-transfer rate, the electron temperature, and the linear and nonlinear mobilities. It is given lattice temperature. However, It significantly increases the velocities. For an n-type GaAs heterosystem the normalized electron-energy-loss rate at Tp=3.5ps is seen to be a factor of 5-10 smaller than that at Tp=0. The functional dependence of the energy-loss rate on carrier temperature shows considerable difference form the prediction of a carrier temperature-type theory, and is in reasonably good agreement with experiments.