This study examines which part of the observed stratospheric thermal and dynamical changes since 1979 can be attributed to the observed stratospheric ozone (O3) losses and CO2 increases. Further, the processes are studied that lead to temperature and circulation changes when stratospheric O3 and CO2 are modified. We compared results from simulations of the Freie Universit¿t Berlin Climate Middle Atmosphere Model (FUB CMAM) using observed O3 and CO2 changes with observed trends of stratospheric temperature and circulation for the period 1979--2000 from FUB data and National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalyses. The observed O3 decrease leads in the FUB CMAM to a global mean stratospheric cooling, which is enhanced in the upper stratosphere by the imposed CO2 increase. While the model is able to reproduce the observed stratospheric cooling in the upper stratosphere, it underestimates the observed trends in the lower stratosphere, particularly in middle latitudes and during Northern Hemisphere (NH) spring. The observed intensification and increased lifetimes of the polar vortices in spring are captured by the model but with smaller magnitude than observed. It is suggested that the observed upper stratospheric temperature trends during the past two decades in low to middle latitudes are caused by radiative effects due to the O3 and CO2 changes, while the cooling of the polar stratosphere in winter is enhanced by changes in dynamical heating. However, in northern midlatitudes and in Arctic spring, other effects than O3 and CO2 changes must be considered to fully explain the observed changes in the lower stratosphere.