The sensitivity of the middle atmosphere circulation to ozone depletion and increase in greenhouse gases is assessed by performing multiyear simulations with a chemistry-climate model. Three simulations with fixed boundary conditions have been carried out: one simulation for the near-past (1960) and two simulations for the near-present (1990 and 2000) conditions, including changes in greenhouse gases, in total organic chlorine, and in average sea surface temperatures. Changes in ozone are simulated interactively by the coupled model. It is found that in the stratosphere, ozone decreases, and that in the Antarctic, the ozone hole develops in both the 1990 and the 2000 simulations but not in the 1960 simulation, as observed. The simulated temperature decreases in the stratosphere and mesosphere from the near past to the present, with the largest changes at the stratopause and at the South Pole in the lower stratosphere, in agreement with current knowledge of temperature trends. In the Arctic lower stratosphere, a cooling in March with respect to the 1960 simulation is found only for the 2000 simulation. Wave activity emerging from the troposphere is found to be comparable in the winters of the 1960 and 2000 simulations, suggesting that ozone depletion and greenhouse gases increase contribute to the 2000--1960 March cooling in the Arctic lower stratosphere. These results therefore provide support to the interpretation that the extreme low temperatures observed in March in the last decade can arise from radiative and chemical processes, although other factors cannot be ruled out. The comparison of the 1960 and 2000 simulations shows an increase in downwelling in the mesosphere at the time of cooling in the lower stratosphere (in March in the Arctic; in October in the Antarctic). The mesospheric increase in downwelling can be explained as the response of the gravity waves to the stronger winds associated with the cooling in the lower stratosphere. Planetary waves appear to contribute to the downward shift of the increased downwelling, with a delay of about a month. The increase in dynamical heating associated with the increased downwelling may limit the cooling and the strengthening of the lower stratospheric polar vortex from above, facilitating ozone recovery and providing a negative dynamical feedback. In both the Arctic and Antarctic the cooling from ozone depletion is found to affect the area covered with polar stratospheric clouds in spring, which is substantially increased from the 1960 to the 2000 simulations. In turn, increased amounts of polar stratospheric clouds can facilitate further ozone depletion in the 2000 simulation.