We present a statistical trend analysis of stratospheric ozone profile data in the five highest Umkehr layers (layers 5--9), which cover approximately the 24 to 48 km region of the stratosphere, from the ground-based Umkehr measurements and from the Nimbus-4 BUV satellite experiment. Time series modeling of monthly Umkehr profile ozone data in Umkehr layers 5--9 from a collection of 13 ground-based Dobson stations over the period 1958--1980 is considered for the detection of trends that may be associated with the release of CFMs. Using a random effects model to account for various sources of variation among individual station trend estimates in each Umkehr layer, our findings show little evidence of any significant trend in ozone in any of the Umkehr layers over the period 1970--1980. These trend results depend to some extent, of course, on the particular choice of explanatory factors employed in the time series models to describe variations in the Umkehr data. A possibly important source of variation on the Umkehr data, especially in the uppermost two or three layers, which has not been explicitly accounted for in these models is the presence of stratospheric aerosols, caused primarily by volcanic activity. The possible impact of such aerosol effects on long-term trend estimates obtained from Umkehr data is currently under investigation, and results of such an analysis will be presented in a future report. We also analyze BUV ozone profile data from the Nimbus-4 satellite over the period April 1970 to April 1977. These BUV profile data have first been interpolated to yield ozone amounts corresponding to the Umkehr layers 5--9. The globe has then been made into a grid with blocks of 10¿ latitude by 20¿ longitude, and monthly averages of ozone have been computed for the layers 5--9 for each block. Linear regression models that contain a linear trend term are estimated from the monthly BUV time series data for each of the five Umkehr layers in each block over the 7 year period April 1970 to April 1977. The results show a large negative overall trend on the order of 1.5 to 2.0% per year in the BUV data at Umkehr layers 8 and 9, with little or no trend indicated in layers 5 and 6. However, a comparison of monthly BUV satellite data with the corresponding Umkehr ground profile ozone data is also performed, which indicates a substantial downward drift in the BUV data at layers 8 and 9, relative to the collection of Umkehr stations, of about the same magnitude as the estimated trend in BUV data in those layers.