Trace stratospheric species (parts per billion or less) have negligible effects on ozone (parts per million) unless they interact in catalytic cycles that regenerate the trace species. It is appropriate to regard catalytic cycles, null cycles, and consumptive sequences, rather than the elementary chemical reactions, as the components of ozone photochemistry. A general differential equation for ozone is transformed to an equivalent equation that directly identifies the catalytic cycles and sequences. The novel aspect of this article is the completeness with which this transformation is carried out and used. This method of treating stratospheric photochemistry properly partitions ozone destruction rates among Ox, NOx, HO•, and CIX families of reactions. The features of the methane-smog chemistry are clearly brought out. From the midvalues of published measurements of NO2 and CIO, it appears that NO2, CIO, and O8 are sufficient to destroy ozone as fast as it is formed in the range 23-35 km, and NO• reactions and CIX reactions appear to be roughly equal in importance. There is no need to invoke any new or unknown sink for ozone in this region if the midvalues of measured NO2 and CIO are rep?esentative of the global average. It is improbable that the high values observed for NO2 or for CIO are representative of global average values. The magnitude of the contribution of HO• reactions to ozone photochemistry cannot be found by this method because of lack of observations of HOO in the stratosphere. These conclusions depend on the accuracy of the stratospheric observations and certain rate constants. Additional measurements are needed, especially for HOO, NO2, CIO, and HO. CONTENTS