The photoluminescence spectrum and transient behaviour of free and bound excitons in CdSe have been studied with both resonant and above band-gap excitation. The free- and bound-exciton lifetimes were found to be excitation-intensity dependent even at very low levels. In all cases, the free-exciton luminescence decayed more rapidly than that of the bound excitons. A comparison of the no-phonon and longitudinal-optic-phonon replicas of the free-exciton luminescence indicates that the observed doublet structure of the no-phonon spectrum arises from the two polariton branches. Resonant excitation of the donor and acceptor bound excitons revealed two-electron and two-hole replicas, respectively. We believe these to be the first reported two-hole transitions in CdSe. The initial rapid cooling of the free-exciton gas could be observed in a series of time-resolved spectra.