A method is developed to quantify the quasi-horizontal, isentropic mass transport across the dynamical tropopause by small-scale filaments. This method is based on the contour advection technique and is used to calculate isentropic mass fluxes across the tropopause on the 330, 345, and 360 K surfaces from the European Center for Medium-Range Weather Forecasts analyses for the years 1997 and 1998. The annually integrated isentropic net mass flux across the extratropical tropopause is directed from the stratosphere into the troposphere. Isentropic stratosphere troposphere exchange is, however, a two-way process, and the net flux is the residual of troposphere to stratosphere and stratosphere to troposphere transport, which can be of similar magnitude. It is shown that the isentropic mass fluxes are of the same order of magnitude as the upward vertical mass fluxes across the tropical tropopause by the large-scale circulation. Further, the extratropical lowermost stratosphere consists of a well-ventilated outer zone in which tropospheric and stratospheric air are heavily mixed, enclosing a more isolated inner zone. The mixing in the outer zone is equivalent to a mass exchange of 7 times the mass of the lowermost stratosphere per year in the Northern Hemisphere and 5 times per year in the Southern Hemisphere. The mixing of tropospheric and stratospheric air is strongest on the lower isentropic surfaces, and the stratosphere and the troposphere become more isolated with increasing altitude. There is greater troposphere to stratosphere transport during the spring of 1997 compared with that of 1998. This might partly explain why stratospheric ozone concentrations were lower during the spring of 1997 than during the spring of 1998. ¿ 2000 American Geophysical Union