We explore the possibility accelerating the convergence to statistical equilibrium of seasonal climate models whose ocean is a simple mixed layer. The procedure developed involves reducing the thermal inertia of the ocean and increasing the frequency of the solar forcing cycle during an acceleration period. Determining the appropriate duration and ending time for the acceleration is important, especially for avoiding problems posed by the annual temperature cycle. We present a method for calculating the ending time that requires no knowledge beforehand about details of the model's behavior other than an estimate of the temperature cycle's lag behind the solar forcing cycle. Uncertainties about the coupling between a model's atmosphere and ocean limit the degree of allowable acceleration. Model noise can also limit successful application if high accuracy is demanded. Using a numerical climate model, we obtain savings of over 50% in the amount of time necessary to reach convergence. Our success occurs in part because the accelerated integration's time average temperature field is nearly the same as that of the nonaccelerated integration. The procedure will be less effective in a model whose time average temperature is instead a strong function of the degree of acceleration. The procedure developed is simple to apply and can allow more extensive use of these models to study climate change. ¿ American Geophysical Union 1988