We evaluate transport characteristics of two- and three-dimensional chemical transport models of the stratosphere by comparing their simulations of the mean age of stratospheric air and the propagation of annually periodic oscillations in tracer mixing ratio at the tropical tropopause into the stratosphere to inferences from in situ and satellite observations of CO2, SF6, and water vapor. The models, participants in the recent NASA Models and Measurements II study, display a wide range of performance. Most models propagate annual oscillations too rapidly in the vertical and overattenuate the signal. Most models also significantly underestimate mean age throughout the stratosphere, and most have at least one of several unrealistic features in their mean age contour shapes. In the lower stratosphere, model-to-model variation in N2O, NOy, and Cly is well correlated with variation in mean age, and the magnitude of NOy and Cly variation is large. We conclude that model transport inaccuracies significantly affect simulations of important long-lived chemical species in the lower stratosphere. ¿ 1999 American Geophysical Union