Simultaneous in situ measurements of the concentrations of OH, HO2, ClO, BrO, NO, and NO2 demonstrate the predominance of odd-hydrogen and halogen free-radical catalysis in determining the rate of removal of ozone in the lower stratosphere during May 1993. A single catalytic cycle, in which the rate-limiting step is the reaction of HO2 with ozone, accounted for nearly one-half of the total O-3 removal in this region of the atmosphere. Halogen-radical chemistry was responsible for approximately one-third of the photochemical removal of O-3; reactions involving BrO account for one-half of this loss. Catalytic destruction by NO2, which for two decades was considered to be the predominant loss process, accounted for less than 20 percent of the 0(3) removal. The measurements demonstrate quantitatively the coupling that exists between the radical families. The concentrations of HO2 and ClO are inversely correlated with those of NO and NO2. The direct determination of the relative importance of the catalytic loss processes, combined with a demonstration of the reactions linking the hydrogen, halogen, and nitrogen radical concentrations, shows that in the air sampled the rate of O-3 removal was inversely correlated with total NOx loading.