We investigate the hole perpendicular transport properties in semiconductor superlattices (SLs) by using the extended Lei–Ting balance equation theory for an arbitrary energy band including hole-impurity, hole-polar-optic-phonon, and hole-nonpolar-optic-phonon scatterings. Effects of heavy-hole–light-hole mixing are taken into account by means of the approximate dispersion relation suggested by O. E. Raichev [Phys. Rev. B50, 5382 (1994)]. Numerical calculations show that the complex hole energy spectrum causes a breakdown of the negative differential conductance for the hot-hole perpendicular transport in SLs in contrast with the results corresponding to a simplified electronlike energy spectrum. ©1997 American Institute of Physics.