Cross tropopause air mass flux plays an important role for the exchange of minor constituents between the troposphere and stratosphere. In general, one can assume net upward air mass fluxes in the tropics and net downward flow in the extratropics. Yet the detailed picture exhibits coexisting up- and downgoing meso-scale flows in the tropopause region probably occurring at all latitudes. This feature of stratosphere-troposphere exchange is particularly addressed in the paper with emphasis on the extratropics. Tropopause depressions like folds and cut-off lows are meso-scale features heavily contributing to downward transport at middle and high latitudes. Statistics derived from global analyses for the period 12/1983 to 11/1991 reveal that folding and cut-off low activity is about twice as strong in the northern hemisphere than in the southern one. A case study of a folding event overthe North Atlantic using a mesoscale meteorological model shows that downward cross-tropopause fluxes are partly compensated by upward fluxes. The ratio of up- and downgoing air mass is about 2:3 during the simulated episode. Note that the upward flux is not a mere return flow. It is expected that this air mass exchange leads to structural and chemical modifications of the lowest stratosphere.