In future years, the chlorine abundances in the earth's stratosphere are expected to increase as a result of man's activities. Currently accepted photochemistry suggests that this perturbation to the natural stratosphere will modify stratospheric ozone due to photochemical interactions. Quanitative estimates of the effect of this anthropogenic perturbation on the stratospheric ozone column abundance have largely been performed with one-dimensional models. Current (1985) one-dimensional models predict a rather small steady state ozone column reduction of about 4--6%. These small values result from a balance between large depletions in the upper stratosphere that are compensated to a substantial degree by increases in the lower stratosphere (the chemical ''self-healing'' effect) so that the total column change is a small difference between the two. It is, however, well established that lower stratospheric ozone is dynamically (not chemically) dominated, particularly at middle and high latitudes in the winter season, so that one-dimensional models may not be the most appropriate tool for evaluation of these effects at those latitudes and seasons. In particular, the lower stratospheric chemical self-healing effect is likely to be signicantly less important at high latitudes than one-dimensional model projections indicate, resulting in greater total ozone column changes there. In this paper, we preset a numerical model study of the ozone response to projected chlorofluorocarbon increases using a two-dimensional residual Eulerian circulation model. In agreement with some previous studies using classical Eulerian models (in particular Pyle (1980) and Haigh and Pyle (1982)), we find that the predicted ozone reductions during winter and spring at high latitudes are larger than the values predicted by one-dimensional models. This occurs because ozone is largely dynamically controlled at these latitudes and seasons, and because the net transport is directed downward from the region where substantial depletions occur. Some uncertainties in the projected depletions are explored.