The responses of a zonally symmetric model of the global energy balance to perturbations in incident solar radiation are analyzed. The model is forced with seasonally varying insolation and incorporates in a simple way the positive feedback due to the high albedo of snow and sea ice. Meridional energy transport by oceanic currents is ignored, as are possible variations in cloudiness. Emphasis is placed on the model's sensitivity to the latitudinal and seasonal redistribution of insolation produced by variations in the obliquity, the eccentricity, and the longitude of perihelion of the earth's orbit. It is found that when albedos are allowed to vary, increased seasonal variation of insolation leads to increased temperature in the northern hemisphere. In all cases considered, the latitudinal extent of perennial snow cover in the northern hemisphere is particularly sensitive to the perturbations, a response suggestive of the large fluctuations of continental glaciers during the Pleistocene. When the model is forced with the orbital variations of the past 150,000 years, its response is qualitatively similar to the geologic record of that period.