The optical parametric oscillator is investigated theoretically for the general case of resonant pump, signal and idler waves. Mean photon numbers, threshold energies and conversion rates are calculated explicitly for different types of the waves (standing and running ones), where in the case of both signal and idler being standing waves the appearance of an oppositely running (“reflected”) pump wave is properly taken into account. In addition, from the equations of motion for the photon creation operators approximately valid rate equations are deduced which in certain cases predict a damped oscillating transition (analogous to the relaxation oscillations of a ruby laser) to the stationary state.