The GISS Global Climate Middle Atmosphere Model is used to investigate how the stratosphere would have changed during two paleotime periods: the cold Last Glacial Maximum (~21,000 years ago) and the warm Paleocene (58 million years ago). Uncertainties in sea surface temperatures and mountain wave drag over the ice sheets are investigated in sensitivity experiments. In many respects the climate and dynamical forcing of the stratosphere was opposite in these time periods, with reduced CO2, increased topography, and increased latitudinal temperature gradients during the ice age, and increased CO2, reduced topography and latitudinal temperature gradients during the Paleocene, representative of much of the Tertiary. The results show that the stratospheric response was often of an opposite nature as well, with the ice ages featuring a warmer stratosphere, increased residual circulation in the lower stratosphere (and decreased above), and weakened polar vortices, while the Paleocene simulation had a colder stratosphere, decreased residual circulation in the lower stratosphere (and increased above), with strengthened polar vortices. Analysis shows that the stratospheric response is very individualistic to the particular climate regime, and the opposite effects are not necessarily produced by inversely related mechanisms. Of particular importance in both climates is the reduced latitudinal gradient at high latitudes, which weakens high-latitude zonal winds and limits wave energy vertical propagation. Increased planetary wave forcing in the lower stratosphere accelerates the circulation during the ice ages. A strong increase in zonal winds during the Paleocene is the result of both decreased planetary wave forcing, associated with the reduced topography, and decreased mountain wave drag. The sensitivity experiments show that if tropical sea surface temperatures were warmer, the stratospheric residual circulation was enhanced, while stratospheric warmings are sensitive to the precise sea surface temperature specifications and mountain wave drag. ¿ 2001 American Geophysical Union