Amplitude fluctuations of the signal wave of an optical parametric oscillator are evaluated for the case of nonresonant pumping by calculating the decrease of a random deviation ε of the signal amplitude from its stationary value during a round trip through the (ring) resonator. From this, a damping term governing the temporal behaviour of ε is deduced which, together with a Langevin force connected with the spontaneous decay of pump photons into both signal and idler photons, determines the amplitude fluctuations of the signal wave. In addition, it is shown that the same results may be obtained from a mode formalism for signal and idler waves taking into account the spatial variation of the pump wave following from Maxwell's equations.