We present a climatology of cross-tropopause air mass exchange on isentropic surfaces in the middle world based on a Lagrangian framework. One-month isentropic trajectories are computed for 8 years from 1992 to 1999 using the United Kingdom Meteorological Office assimilated data set. This study provides seasonal and interannual variations of isentropic mass transport between the lowermost stratosphere and the troposphere. The spatial distribution of the exchange is investigated to infer the primary mechanism for the exchange. The climatology of the stratosphere-troposphere exchange exhibits a prominent annual cycle of two-way exchange. The largest downward flux of stratospheric air to the troposphere occurs in late spring to summer in both hemispheres. The smallest downward flux of stratospheric air into the troposphere occurs during the fall season in both hemispheres. For the upward flux of tropospheric air to the stratosphere, the greatest transport appears in fall and winter, and the smallest appears in summer, in both hemispheres. The preferred routes for downward transport in both hemispheres correspond to the regions with the highest frequency of Rossby wave-breaking events and with the storm tracks along the jets, implying that tropopause folding and baroclinic eddy activity are responsible for the gross horizontal distribution. A notable interannual variation is the existence of much stronger flux of stratosphere-to-troposphere transport in the northern winter during the period 1996--1999 than during the period 1992--1995. Increased medium-scale wave activity is the likely explanation for this interannual variability. An observed increase in the northern midlatitude total column ozone in 1998 winter/spring may arise partly from the decreased upward transport of ozone-poor tropospheric air. ¿ 2001 American Geophysical Union