The effective diffusion of aircraft emissions in the free stably stratified atmosphere is investigated by means of large-eddy simulation in a domain of size 4.3¿1.1¿1.1 km3. On that scale, the atmosphere is represented by a weakly turbulent flow under uniformly stratified and shearless conditions. It is assumed that aircraft induced turbulence has ceased. The exhaust plumes of aircraft are represented by line sources with Gaussian cross-sections. The stratification has been varied between 0.006 s-1 and 0.03 s-1. The computed effective horizontal diffusion coefficient lies between 11¿2 m2 s-1 and 21¿4 m2 s-1, depending on the level of stratification. Likewise the vertical diffusivity ranges from 2.3¿0.6 m2 s-1 to 0.37¿0.04 m2 s-1 in the beginning of the diffusion process, and amounts almost independently of the stratification to about 0.15¿0.01 m2 s-1 later on. The plume cross-sections increase with time and stratification. The scattering of the results for a given stratification reflects the action of decaying, anisotropic, and homogeneous turbulence. The results confirm very well data from recent in situ flight measurements in the North-Atlantic flight corridor in the tropopause region. ¿ American Geophysical Union 1995