Calculated trajectories have been compared with the 1995 Polar Vortex Balloon Experiment (POVORBEX) and 1997 and 1999 Montgolfier Infra-Red (MIR) long-duration balloon flights in the Arctic stratospheric vortex. The POVORBEX flight lasted 6 days, whereas the MIR flights lasted 13, 22, 7, and 17 days. The trajectories have been run at the pressure of the balloon (10--120 hPa), whereby the dominant contribution of the horizontal trajectory errors can be assessed. To obtain statistically significant results, new trajectories were started every 2 hours along the balloon flight track. Trajectories run at a temporal resolution of the meteorological fields of 24 hours sometimes give substantially larger errors than trajectories run at 12 hours or higher resolution owing to rapid nonlinear temporal developments. In 1995 the European Center for Medium-Range Weather Forecasts (ECMWF) trajectories generally have substantially larger errors than the U.K. Meteorological Office (UKMO) and National Centers for Environmental Prediction (NCEP) trajectories, when 24 hourly analyses are used. In 1997 and 1999, when ECMWF had introduced a variational data assimilation, their trajectory errors inside the vortex have apparently reduced considerably and are generally substantially smaller than UKMO and NCEP errors. ¿ 2001 American Geophysical Union