CuGaSe2 (CGS) epitaxial layers grown by MBE on GaAs substrates are characterized using photoluminescence (PL). The PL spectra of Cu-rich samples have been shown to display relatively well-resolved near-band-edge transitions. A recombination path appearing at 1.62 eV has been studied in detail using selective excitation of the photoluminescence (SPL). These measurements lead to the resolution of different transitions to excited states, following a resonant excitation of donor-acceptor pairs. The identification of these states is made using the ground state binding energy deduced from the temperature dependence of the photoluminescence and the acceptor excited states in ZnSe, the binary II-VI analogue of CuGaSe2. From the binding energies extracted the excited states are ascribed to the 2s(3/2), 2p(5/2)(Gamma 8) and 3p(3/2) states, respectively. These observations clearly establish the acceptor nature of the 107 meV center involved in the recombination observed at 1.62 eV, with an effective-mass-like behavior.