The influence of electron-phonon scattering on intersubband tunnelling in t
wo-band semiconductor superlattices is treated on the basis of the density-
matrix approach. Intracollisional field effects are accounted for. Three di
fferent types of current resonance are identified: (i) electrophonon resona
nces, which are expected to appear when a multiple of the Bloch frequency O
mega matches the frequency of polar-optical phonons omega (0), (ii) intersu
bband tunnelling resonances, and (iii) Zener-phonon resonances, which depen
d non-analytically on the electric field strength. The latter resonances ar
e most pronounced when the widths of the upper and lower miniband differ ap
preciably.