A Lagrangian methodology is applied to operational European Centre for Medium-Range Weather Forecasts analyses to study upward cross-tropopause exchange (troposphere to stratosphere exchange (TSE)) and downward cross-tropopause exchange (stratosphere to troposphere exchange (STE)) in the extratropical Northern Hemisphere for the period from May 1995 to April 1996. A residence time criterion serves to distinguish between short- (<1--2 days) and long-lasting exchange events. The adopted approach enables identification of a range of novel aspects of extratropical cross-tropopause transport which are of primary importance when assessing its chemical impact. For the considered year the annual cycle of the hemispherically integrated net cross-tropopause mass flux compares well with estimates from previous studies. The part of STE and TSE which occurs with equal amplitude in both directions (referred to as symmetric two-way exchange) has only a weak annual cycle and, for short residence times, a larger amplitude than the net exchange. The meridional distribution of the net flux reveals an upward branch in the subtropics, pronounced downward exchange in the midlatitudes and weak upward fluxes in the Arctic region. Detailed geographical distributions show significant zonal asymmetries with maximum exchange in the Atlantic and Pacific storm track regions. It is further shown that STE (TSE) events occur typically below (slightly above) the climatological tropopause position. Deep exchange (that is, rapid vertical transport between the stratosphere and the lower troposphere) is strongest during winter and confined to the midlatitude regions of baroclinic wave activity. The localized source regions for deep TSE indicate that pollutants emitted in eastern North America and Asia have an enhanced potential for being rapidly transported into the lowermost stratosphere.