We investigate the qualitative nonlinear dynamic properties of the high-latitude stratospheric (HLS) photochemical system (PCS). For the investigation we use the model of HLS PCS, which includes all the most significant processes of chemical nature, taking place in the high-latitude (both Arctic and Antarctic) lower stratosphere in winter-spring period, and adequately simulates the evolution of the Antarctic ozone hole. We analyze the photochemistry in the stratospheric region at 17--18 km altitude and 70--80 degrees latitude and reveal that HLS PCS may possess simultaneously several equilibrium states (multistability) under conditions, which differ from the conditions of the actual present-day atmosphere only by smaller total mixing ratio of inorganic chlorine species. The required conditions were typical for the atmosphere in recent past and are expected in future. Through a graphical-analytical consideration we reveal the origin of multistability of HLS PCS and in doing so we insure that multistability is not a consequence of any approximation used in the model but is a property inherent in nature of HLS PCS. We demonstrate that when the multistability of HLS PCS is present, it may considerably influence the spring evolution of the Antarctic photochemistry. ¿ 1999 American Geophysical Union