The equations which determine partitioning of Clx in steady state have multiple (three solutions) under conditions which might arise in the high-latitude winter stratosphere. Two of these solutions are stable, one is unstable, to infinitesimal perturbations. The relative stability of solutions is examined by subjecting the system to finite perturbations. The more stable solution is found to eliminate the less stable when semi-infinite volumes of the two solutions are placed in contact. The high-ClO, low-NO2 solution is more stable under most conditions. Transtions from less to most stable states are slow in winter but may occur more rapidly when the seasonal variation of insolation is taken into account.