Observational studies reveal the oscillatory nature of coupled stratosphere-troposphere variability, which is characterized by a slowly downward propagating anomalous zonal-mean zonal wind during the winter. The term slowly is employed compared to the rapid variation associated with stratospheric sudden warmings. In fact, strong stratospheric warming events are embedded in this slowly propagating variability as is shown in a companion paper <Kodera et al., this issue>. In the present study, the mechanism producing such variability at all levels of the atmosphere is investigated by developing a simple model that extends from the Earth's surface to 80 km altitude. The model is a quasi-geostrophic channel model similar to that used by Holton and Mass <1976>, but it includes two meridional Fourier components and latitudinal variation in the gradient of the Coriolis parameter. By this extension, the present model can incorporate both the subtropical and polar night jet and also treat the horizontal propagation of planetary waves as well as vertical propagation. The results of the simulation reproduce qualitatively well the main observed features: Interaction between the planetary waves and zonal-mean flow produces oscillations in the winter stratosphere, and zonal wind anomalies created in the subtropics of the stratopause propagate downward into the polar region of the troposphere, which provoke changes in the meridional propagation of tropospheric planetary waves. ¿ 2000 American Geophysical Union