Excitonic recombination processes in high quality CuInSe2 single crystals have been studied by photoluminescence (PL) and reflectance spectroscopy as a function of excitation powers and temperature. Excitation power dependent measurements confirm the identification of well-resolved A and B free excitons in the PL spectra and analysis of the temperature quenching of these lines provides values for activation energies. These are found to vary from sample to sample, with values of 12.5 and 18.4meV for the A and B excitons, respectively, in the one showing the highest quality spectra. Analysis of the temperature and power dependent PL spectra from the bound excitonic lines, labelled M1, M2, and M3 appearing in multiplets points to a likely assignment of the hole involved in each case. The M1 excitons appear to involve a conduction band electron and a hole from the B valence band hole. In contrast, an A valence band hole appears to be involved for the M2 and M3 excitons. In addition, the M1 exciton multiplet seems to be due to the radiative recombination of excitons bound to shallow hydrogenic defects, whereas the excitons involved in M2 and M3 are bound to more complex defects. In contrast to the M1 exciton multiplet, the excitonic lines of M2 and M3 saturate at high excitation powers suggesting that the concentration of the defects involved is low. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4709448