Very simple two-component models of the earth's cryosphere-lithosphere system are analyzed. The models consist of a continental ice sheet coupled to a responding earth model. Because of relatively long response times of the bedrock, at least over shorter wavelengths, long-period (of the order of 50,000 years) internal or ''free'' oscillations in the system occurover a wide range of parameters and parameterizations. The oscillatory mechanism operates primarily in the ablation zone and in particular at the firn line. These free oscillations could play a dynamic role in the response of the climae system to eccentricity forcing. A simple analysis presented strongly suggests that for the simplest rheological models of the earth response to Pleistocence ice sheets, elastic response is confined to a layer considerably less than the thermal thickness of the lithosphere. Furthermore, because of the striking lack of geological evidence for large depressions of bedrock at the leading edge of growing continental ice sheets, predicted by viscoelastic models of the earth, more sophisticated rheological models of the earth's uppermost layer appear necessary.