A new method for the quantitative evaluation of global atmospheric transport and the hydroxyl radical (OH)-based oxidation in three-dimensional (3-D) atmospheric chemistry transport models (CTMs) and general circulation models (GCMs) is developed. The method is based on a cosmogenic 14CO climatology that has been previously derived from a large number of 14CO observations. Using 14CO measurements to constrain model OH distributions and the simulated stratosphere--troposphere exchange (STE) provides a challenging test for 3-D atmospheric models. Here, the evaluation method is applied to the CTMs MATCH and TM3. Whereas MATCH overestimates the STE in both hemispheres, TM3 does reproduce the STE in the Southern Hemisphere (SH) but underestimates it in the Northern Hemisphere (NH). The STE phase in MATCH is 1 month too early, whereas no significant phase shift for TM3 is revealed. These characteristic deficiencies in both models were consistently determined, i.e., with the same boundary conditions (OH distribution and 14CO source distribution). The robustness of the results is tested by various sensitivity studies, involving the 14CO source distribution and strength, the tropospheric OH distribution, the stratospheric OH abundance, and the applied numerical advection scheme. Consistency is further checked by comparison of the model simulated vertical 14CO profiles to 14CO observations from a number of aircraft campaigns. The 14CO simulations do not support an interhemispheric asymmetry in the OH abundance with an on average higher concentration in the SH.