Abstract Transient current–voltage (I–V) characteristics of organic light-emitting diodes made from both conjugated polymers and low molecular-weight materials show hysteresis effects in the reverse bias regime depending on the direction and speed of the bias sweep. This behaviour is quantitatively investigated here for the example of devices based on N,N′-diphenyl-N,N′-bis(1-naphtyl)-1,1′-biphenyl-4,4′-diamine with Ca and indium–tin oxide as electrodes. To clarify the origin of this peculiarity numerical simulations have been carried out supposing the existence of deep acceptor-like trap states. Typical trends are shown by systematically varying parameters such as measuring conditions, trap characteristics, basic doping level, mobility and injection conditions. Based on the simulated potential and concentration profiles it is shown that the hysteresis of the I–V characteristics is caused by recharging of deep traps for holes. It occurs only if the reverse steady-state current is lower than the trap recharging current and if both currents have different bias dependencies. The origin for the large time needed for the traps to relax into the equilibrium state is clarified. In accordance with the high barrier for the holes at the cathode the calculated reverse current is much smaller than the measured one. Using a new analytical expression for the Schottky diode I–V characteristics for a low-doped thin film device, it is shown qualitatively that in real devices a leakage current should dominate for reverse bias.