CHANGES in insolation caused by periodic changes in the Earth's orbital parameters provide the primary forcing for global ice ages1-6. But it is not clear to what extent the climates in continental interiors are controlled directly by regional variations in insolation and to what extent they are driven instead by the highly nonlinear response of the oceans and ice sheets. Here we investigate this question using the record of biogenic silica in Lake Baikal as a proxy for climate change in this high-latitude mid-continental region. We find a good correlation between this record and that of marine oxygen isotopes4. Over the past 250 kyr the Baikal record exhibits both a strongly nonlinear component (manifested in a 100-kyr periodicity) and weaker direct-insolation components (manifested in the 41-kyr (obliquity) and 23- and 19-kyr (precession) orbital cycles). These results show that even though extreme continental climates such as this are influenced directly by insolation variations, they are dominated by the nonlinear rhythm of the oceans and ice sheets.