This paper describes a new two-dimensional model of the stratosphere and the mesosphere in which dynamics, radiation and chemistry are treated interactively. The transport equations are expressed in the transformed Eulerian framework. Momentum deposition associated with Rossby wave absorption and gravity wave breaking and related eddy diffusion coefficients are parameterized as a function of the mean zonal state of the atmosphere. Diabatic heating and cooling is derived from the detailed National Center for Atmospheric Research community climate model radiative code. The distributions of chemically active species belonging to the oxygen, hydrogen, nitrogen and chlorine families are calculated for present-day conditions. By applying near the tropopause a different dynamical forcing in each hemisphere, the model produces significant hemispheric asymmetries in dynamical quantities (e.g., temperature) and trace gas densities (e.g., column ozone), in good agreement with climatological values. It is shown that the calculated distributions of source gases, such as nitrous oxide and methane, are very sensitive to the calculated (and parameterized) dynamical quantities and that species produced in the atmosphere, like carbon monoxide and odd nitrogen, can provide interesting information on the role of atmospheric transport. A major problem that remains to be elucidated is the underestimation by most models of the ozone density in the upper stratosphere. Because of the many feedback mechanisms included in its formulation, the model is well adapted to study the effects of human or natural perturbations. The response of the atmosphere to perturbations resulting from increasing emissions of CO2 and chlorofluorocarbons is considered.