The paper presents a mathematical analysis of a nonlinear box system describing the oxygen-hydrogen photochemistry of the mesosphere. The system is represented by 14 chemical and photochemical reactions, and by two additional physical processes representing the injection of water vapor into the mesosphere and the escape of hydrogen to outer space. The distribution of the photochemical system at equilibrium is investigated in detail. The results show that, for conditions representative of the present atmosphere, the system is characterized by a single solution. For certain ranges of the parameters describing the external forcing to the system, multiple equilibria exist and constitute a ''cusp'' catastrophe manifold; i.e., under certain conditions, catastrophic transitions between stable equilibria may occur. It is shown that the whole structures of the equilibria and their distribution in the parameter space are stable. ¿ American Geophysical Union 1994