A comparison of tropospheric and stratospheric height fields from ECMWF and NCEP/NCAR reanalyses during 1958--2001 indicates a trend towards a strengthening Antarctic polar vortex. The reanalyses agree well on a daily basis over the Southern Hemisphere, after the advent of satellite observations in 1979. Linear trends in 500 hPa and 50 hPa geopotential height are in close spatial agreement in the period 1980--2001 (correlations >0.8), showing falling heights over Antarctica and strengthening zonal winds above the southern oceans during summer and autumn. Prior to 1980, stratospheric trends agree well (spatial correlations ≥0.7), suggesting a rise in heights over Antarctica and a weakening polar vortex since the late 1950s. Tropospheric trends are not as consistent prior to 1980, but show similar qualitative features. The strong trends observed in the past 20 years dominate the full record, but there are suggestions of cyclical components on the decadal time scale.