Three- and two-dimensional model results have been averaged to investigate conceptual errors in two- and one-dimensional models. Average dynamical quantities show inter-hemispheric asymmetries in both mean and eddy vertical motions, with anomalous behaviour of tracers near effective source and sink regions. Zonal, hemispheric and global means of the rates of gas reactions show large deviations between terms like k : [A] [B] and k : [A] [B], causing significant errors in two- and one-dimensional model calculations. These errors are often associated with dynamical features such as jet streams or the tropopause, and affect the entire model atmospheres except in the summer mid-stratosphere. It is concluded that correlated measurements of atmospheric molecular number densities are urgently required to understand the deficiencies in models, which have been widely used to make perturbation calculations of the effects of aircraft and chloro-fluoromethanes on stratospheric ozone. The sources of error described in this work arise from inadequacies in the formulation of one- and two-dimensional models, rather than from uncertainties in the input data, and have not been included in published error analyses.