This paper presents one of the first extensive intercomparisons of models and methods used for estimating stratosphere-troposphere exchange (STE). The study is part of the European Union project Influence of Stratosphere Troposphere Exchange in a Changing Climate on Atmospheric Transport and Oxidation Capacity (STACCATO). Nine different models and methods, including three trajectory methods, one Eulerian method, two Lagrangian and one Eulerian transport model, and two general circulation models applied the same initialization. Stratospheric and tropospheric tracers have been simulated, and the tracer mass fluxes have been calculated through the tropopause and the 700 hPa surface. For a 12-day case study over Europe and the northeast Atlantic the simulated tracer mass fluxes have been intercompared. For this case the STE simulations show the same temporal evolution and the same geographical pattern of STE for most models and methods, but with generally different amplitudes (up to a factor of 4). On the other hand, for some simulations also the amplitudes are very similar.