Results are presented from two 60-yr integrations of the troposphere–stratosphere configuration of the U.K. Met. Office’s Unified Model. The integrations were set up identically, apart from different initial conditions, which, nonetheless, were both representative of the early 1990s. Radiative heating rates were calculated using the IS92A projected concentrations of the well-mixed greenhouse gases (GHGs) given by the Intergovernmental Panel on Climate Change, but changes in stratospheric ozone and water vapor were not included. Sea surface conditions were taken from a separate coupled ocean–atmosphere experiment. Both integrations reproduced the familiar pattern of tropospheric warming and a stratospheric cooling increasing with height to about −1.4 K per decade at 1 mb. There was good agreement in the trends apart from in the polar upper stratosphere and, to a greater extent, the polar lower-to-middle stratosphere, where there is significant interannual variability during the winter months. Even after decadal smoothing, the trends in the northern winter were still overshadowed by the variability resulting from the planetary wave forcing from the troposphere. In general, the decadal variability of the Northern Hemisphere stratosphere was not a manifestation of a uniform change throughout each winter but, as with other models, there was a change in the frequency of occurrence of sudden stratospheric warmings. Unlike previous studies, the different results from the two simulations confirm the change in frequency of warmings was due to internal atmospheric variability and not the prescribed changes in GHG concentrations or sea surface conditions. In the southern winter stratosphere the flux of wave activity from the troposphere increased, but any additional dynamical heating was more than offset by the extra radiative cooling from the growing total GHG concentration. Consequently the polar vortex became more stable, with the spring breakdown delayed by 1–2 weeks by the 2050s. Polar stratospheric cloud (PSC) amounts inferred from the predicted temperatures increased in both hemispheres, especially in the early winter. In the Southern Hemisphere, the region of PSC formation expanded both upward and equatorward in response to the temperature trend.