The effects of changes in ozone and well-mixed greenhouse gases upon the annual-mean stratospheric temperatures are investigated using a general circulation model and compared with the observed (1979--2000) trends. In the global-mean lower stratosphere (50--100 hPa), ozone changes exert the most important influence upon the cooling trend. In the upper stratosphere, where both ozone and greenhouse gas changes influence the temperature trends, the amount of cooling is sensitive to the background ozone climatology. Taking into account the uncertainties in the observed temperature trend estimates and the dynamical variability of the model, the simulated results are in reasonable quantitative agreement with the vertical profile of the observed global-and-annual-mean stratospheric cooling, and with the observed lower stratospheric zonal-and-annual-mean cooling. This affirms the major role of these species in the temperature trend of the stratosphere over the past two decades.