A study of the electronic structure of about thirty transition-metal sulphides (TMS) of various stoichiometries and crystal structures is presented, supplementing recent studies of their structural and cohesive properties (P Raybaud, G Kresse, J Hafner and H Toulhoat, preceding paper). The electronic structure of the TMS is found to be determined by short-range interactions in the S 3p - TM d band complex, with the ligand-field splitting of the TM d states in the environment of the S atoms determining the structure of the d band. For the layered group VI disulphides, for and for the group VIII pyrites this leads to the formation of a gap at the Fermi surface. Semiconducting properties are predicted also for the monosulphides PtS and PdS and for and . We show that the semiconducting TMS have a higher catalytic activity for hydro-desulphurization than the metallic sulphides. We suggest a correlation between the catalytic activity and the characters of the highest occupied states (the frontier orbitals).