A mathematical analysis of the stratospheric photochemical system (gas phase reactions only) shows the existence of potential catastrophe mechanisms which could produce a dramatic reduction in the ozone concentration near 25 km altitude. The conditions leading to such catastrophe correspond to a relatively modest (i.e., factor 2--2.5) increase in the stratospheric source of reactive nitrogen (NOx). For a tenfold increase in the source of reactive chlorine (ClOx), the ozone system exhibits a large amplitude oscillatory behavior with a period of several tens of years. Transport processes could, however, damp these dramatic changes resulting from the nonlinear nature of the stratospheric chemical system. ¿ 2001 American Geophysical Union