Photoluminescence (PL) spectra of undoped single crystals of the layered semiconductor GaSe have been measured in the temperature range from 10 K to room temperature and in the wavelength range from 635 to 750 nm. Two wide bands centred at 644 and 695 nm have been observed at T = 10 K. A detailed analysis of the spectra obtained by varying the excitation intensity and temperature resulted in the identification of the levels involved. A simple model is proposed to account for the observed data.