Numerical time integrations of a 9-layer quasigeostrophic highly truncated spectral model of the atmosphere are used to study tropospheric-stratospheric interaction with particular regard to sudden stratospheric warmings. The model is global and extends to 0.05 mb (71 km) with roughly 10 km resolution in the stratosphere, and includes an annual heating cycle. A linear baroclinic analysis of a similar model shows that the inclusion of spherical geometry allows significant growth rates in the long wave region of instability. Preliminary integrations without eddies reveal the seasonal variation of a thermally driven circulation.Model integrations simulating the months of December and January were made (i) without nonzonal forcing, and (ii) with nonzonal heating and orography included, to represent southern and northern hemisphere winters. The overall features of the atmosphere were very well simulated. With the inclusion of the annual heating cycle, the model successfully reproduced a more intense circulation in January than existed in December. This caused a maximum tropospheric meridional temperature gradient in the winter hemisphere to occur some weeks prior to the maximum in the external heating field.The presence of nonzonal heating in the winter hemisphere brought about an increase in circulation intensity and produced a stationary perturbation with a strong westward slope with height extending high into the stratosphere.These are features somewhat similar to those of the Aleutian system. Associated with this were considerably warmer temperatures in the polar night stratosphere and a weaker stratospheric westerly jet.The winter mesosphere of the model was driven in the manner of the lower stratosphere and a temperature maximum was produced in mid latitudes.Sudden stratospheric warmings occurred as a result of large , increases in the intensity of planetary scale waves in the troposphere, which in turn produced surges of upwards propagating energy. The energetics of the warming occurred in two phases. A change from a baroclinically direct to a driven circulation occurred as the stratospheric temperature gradient reversed. This coincided with a change from enhancement to absorption of the vertical flux of energy. The mechanism of the warming was much as described by Matsuno (1971).Nonlinear interactions between the progressive long wave and the nonzonal heating were primarily responsible for the tropospheric events that produced the upward flux of energy, which in turn caused the stratospheric warmings. A seasonal index cycle in the very long waves was also of significance in producing transient upward energy propagation. Interactions with other waves, and orographic forcing were of secondary importance in the long wave energetics of the sudden warmings.