A three-dimensional (3D) radiative-dynamical-chemical model has been developed and used to study the evolution of trace gases in the Arctic lower stratosphere during winter 1989–1990. A series of 10-day model integrations were performed throughout this period. The model includes a comprehensive scheme of gas phase chemical reactions as well as a parameterization of heterogeneous reactions occurring on polar stratospheric cloud (PSC) surfaces. An important element of a 3D chemical model is the transport scheme. In this study the transport of chemical species is achieved by a non diffusive method well suited to the preservation of sharp gradients. During the winter studied temperatures were cold enough for the formation of both type I and type II polar stratospheric clouds from early December to early February. Model simulations in late December show that inside the polar vortex air is rapidly processed by polar stratospheric clouds converting HCl and ClONO2 to active chlorine. The possibility of ozone destruction depends strongly on the amount of sunlight. In early February an average ozone loss of 15 ppbv (parts per billion by volume) /day is predicted in PSC-processed air at 50 hPa, giving a column loss of just under 1 DU/day. This loss increases to 25 ppbv/day if PSCs persist until March with a column loss of around 1.5 DU/day. The relatively small magnitude of the ozone loss predicted in the model, compared to the variability of ozone induced by dynamics, highlights the problems in identifying the signature of chemical ozone loss in the Arctic. In future years significant ozone depletion could occur if PSCs persist until late March. The efficiency of the catalytic cycles responsible for the ozone loss has been analyzed as a function of latitude, altitude and time. In general, the cycle involving ClO + ClO is the dominant loss mechanism in the polar lower stratosphere. Cycles involving BrO can make a relatively large contribution early in the season and when the levels of ClO are low. The cycle initiated by ClO + O destroys ozone at altitudes above 30 hPa but the loss is compensated, to some extent, by in situ ozone production. The results for trace species are validated, where possible, by comparison with the available measurements, although the sparse nature of the observations does not effectively constrain the model.