The electrical and electroluminescent properties of MOVPE GaN p-n homojunctions have been analyzed as a function of temperature and bias. Electroluminescence is observed for V>3 V under dc and ac conditions. The main emission at low T is a donor-acceptor transition involving shallow acceptors, though it disappears at higher T due to the ionization of the acceptors and compensation by ionized donors. Room temperature dc and ac electroluminescence spectra evolve under increasing bias from a blue-shifting visible band involving deep states at the p-type side of the p-n junction, to a band-to-band UV recombination at high bias. In agreement, the superlinear dependence of light-current characteristics at low current injection becomes linear when the defects are saturated. Time analysis of the spectra vs pulse duration and duty cycle allows the determination of the visible radiative recombination and relaxation times associated to the Mg-related deep states, which are found to behave as acceptors lying 0.55 eV above the valence band. A simple 3-level model is able to explain the visible emission, which involves the conduction band (or shallow donor) and those deep acceptors in the p-layer. Optimum UV/visible ratio emission requires intense and relatively long pulses, with a high duty cycle to impede visible recombination.