The mean annual energy balance climate model of Gal-Chen and Schneider (1976) is expanded to a more general model which includes an interactive lower layer. The two-layer model is used to simulate the seasonal cycle through the use of seasonally varying insolation. Rather than greatly modifying the zonal model parameterizations, we choose to determine the extent to which the use of the present parameterizations in a completely zonally averaged model can reasonably simulate the seasonal cycle of surface air temperature and meridional heat transport. It is found that the model-derived cycle of surface air temperature lags the observations by 1-2 months, but the amplitude of the seasonal cycle can be well simulated by using reasonable annual mean values of the seasonally effective zonal thermal inertia. The seasonal variations in the meridional transport of energy by the atmosphere agree qualitatively in midlatitudes with the data of Oort (1971), but they suffer from large errors in the tropics. Seasonal simulation indicates that the diffusive atmospheric energy transport parameterization based on annual data is inappropriate in this region. Comparisons of annual and seasonal models show that there is little difference in temperature sensitivity for solar constant changes. Unlike previous low-resolution climate models the seasonally effective thermal inertia is also allowed to vary with time to simulate the seasonal variation of the oceanic mixed layer depth. This modification requires the addition of a second lower vertical layer in the model, the temperature of which is predicted explicitly. Such seasonal thermal inertia variations have little effect on the model's equilibrium response to solar constant changes. Experiments employing step function and exponential solar constant increases show the time-dependent response of global surface temperature to lag the solar constant perturbation by from a few years to a few decades, depending on the assumptions of seasonal thermal inertia variation and lower layer thickness. The uncertainty in the range of global temperature lag time implies that modeling the time-dependent temperature response to a CO2 perturbation will require refined treatment of the coupling between upper and lower oceanic heat reservoirs. The most important general conclusion from these experiments is that realistic values of seasonally effective thermal inertia (i.e. primarly the oceanic mixed layer depth) are needed for the realistic simulation of the seasonal cycle of temperature. Use of realistic seasonal thermal inertia implies that climate sensitivity experiments with seasonal models (including global circulation models) will require decades of model simulation time to approach a reasonable climatic equilibrium.