The role of high-lying minibands in superlattice vertical transport is investigated using a nonparabolic balance-equation approach extended to include multi-miniband occupation. We find that the existence of high-lying minibands results in a decrease of the electron temperature, a reduction of the peak drift velocity and a slowdown of the velocity-drop rate in the negative differential mobility (NDM) regime, in comparison with those predicted by a single miniband model. Numerical calculations of steady-state transport in typical GaAs-based superlattices at room temperature, show that these effects become significant when the strength of the electric field gets close to or falls in the NDM regime. ©1997 American Institute of Physics.