Time series modeling of total ozone data is considered for the detection of changes in ozone due to the possible effects of nuclear weapons testing in the early 1960's and more recent effects of the release of chlorofluromethanes (CFMs). Based on ozone data from a network of Dobson stations over the period 1958--1979, the results of this analysis are consistent with a maximum decrease in ozone in the northern hemisphere of approximately 2 to 4.5% due to nuclear testing effects in the early 1960's. In addition, our findings show little evidence of any significant trend in global total ozone occurring in the 1970's, with the global change during 1970--1979 estimated as (.488¿1.354)%.