The goal of this article is to examine the validity of some properties of photochemical models, which were found numerically in recent studies: (1) the existence of periodic solutions and (2) the stability of these solutions. Even though we are interested in a more complete mesospheric model, we examine first the simple Chapman model and then we generalize the results to the complete one. We show that the 48-hours periodic solution found in earlier work is orbitally stable, thus enhancing its physical significance. On the other hand, we find two new 24-hours periodic solutions, which present ozone concentrations at much lower levels relative to the experimental data. ¿ 1999 American Geophysical Union