Low temperature photoluminescence spectra of Be-doped layers grown on Si (111) by molecular beam epitaxy have been analyzed. Emissions at 3.466 eV and 3.384 eV, and a broad band centered at 2.4-2.5 eV are observed. Their evolution with temperature and excitation power, and time resolved PL measurements ascribe an excitonic character for the luminescence at 3.466 eV, whereas the emission at 3.384 eV is associated with a donor-acceptor pair transition. This recombination involves residual donors and Be-related acceptors, which are located around 90meV above the valence band, confirming Be as the shallowest acceptor reported in GaN. The intensity of the band at 2.4-2.5 eV increases with the Be content. This emission involves a band of deep acceptors generated by Be complex defects, as suggested by the parameter g = 2.008 ± 0.003 obtained by photoluminescence-detected electron paramagnetic resonance.