Three three-dimensional trajectory models (LAGRANTO, TRAJKS and FLEXTRA), all driven with analysis wind fields from the European Centre for Medium-Range Weather Forecasts, are intercompared. The comparison has three parts: first, a case study of strong ascent in a warm conveyor belt is performed; second, a large set of back trajectories from the tropopause region over Europe and the mid-latitude Atlantic Ocean is investigated; third, a set of low-level trajectories is compared. The intercomparison shows that all three models have been implemented correctly. The degree of model accordance depends on the interpolation methods used. Deviations between the results from a single model using different interpolation schemes are of the same magnitude as the deviations of different models. If all models use linear spatial interpolation, their respective trajectories closely agree with each other, with deviations of 2% or less for the average distance between the starting and the ending positions in the free atmosphere after 48 h. Close to the surface, where the differences in the model formulations are largest, average horizontal position deviations may be up to 10%. Compared with other sources of errors, such as inaccuracies in the wind fields or insufficient temporal and spatial resolution of the data set, these differences are much smaller. Non-linear spatial interpolation leads to stronger vertical motions than linear interpolation and, in the case study, enhanced the quality of the results.