A microscopical model is proposed, describing the origin and properties of three closely spaced zero-phonon lines observed in the green Cu band in ZnO:Cu crystals labelled alpha, beta and gamma. These excitations are known to be formed by a charge-transfer reaction with hole bound states. These lines are shown to originate from an intermediately bound exciton of acceptor type, (Cu(+)((9)g + e), h). This sort of exciton, in which both carriers are captured at intermediate-radius orbitals, results from the wurzite-type symmetry of the ZnO:Cu system. The electronic structure obtained for these three intermediately bound excitons enables us to explain their magneto-optic behaviour and to calculate their g-values. Additionally, we determined the quantum efficiency of both intracentre and exciton transitions by using time-resolved and calorimetric absorption spectroscopy. While no (Cu(+), h)-Cu(2+)((2)T2) luminescence is observed in ZnS, the exciton states in ZnO are purely radiative only to the ground state, Cu(2+)(T-2(2)). The picture of an intermediately bound exciton explains the recombination channels and also makes clear the difference between copper states in the ZnS and ZnO systems.