The electronic structures of the rare-earth monosulphides are calculated wi
th the self-interaction corrected local-spin-density approximation. This sc
heme allows part of the rare-earth f shell to be localized. Both trivalent
and divalent configurations of the rare earths are considered, and the syst
ematics in lattice constants and electronic densities of states are investi
gated. The scheme is found to be accurate in describing the properties of t
hese systems and reveals that two kinds of f electrons in fact are present
in the rare-earth monosulphides, namely both localized atomic-like f electr
ons and itinerant band f electrons, which hybridize with the normal conduct
ion bands. The stability of the divalent configuration directly correlates
with the number of band f electrons.