The balance-equation approach for hot-electron transport previously developed is extended to systems com posed of two groups of carriers, each of different effective mass. This is the simplest model for a real band structure of a multivalley semiconductor. The separation of the center-of-mass (c.m.) motion from the relative motion of the electrons is incomplete due to the possibility of exchange of particle number between the two systems and thus is taken into account in the Liouville equation for the density matrix. General expressions for the rates of change of the c.m. momenta, electron system energies, and partcle numbers are obtained. These equations in their classical forms are used for a model calculation for the high-field steady-state transport in GaAs and the calculated results show reasonably good agreement with experiments.