A zonally averaged model using the residual circulation formalism has been built to study the possible dynamical effects of the El Chich¿n dust cloud in the middle atmosphere. A time dependent calculation of the residual mean velocities is performed, using as data the temperature field and the ozone distribution from a run of an updated version of the Massachusetts Institute of Technology--Georgia Institute of Technology stratospheric general circulation model (GCM). Eddy fluxes are parameterized using the technique described by Tung (1983); input data are the time dependent fields of stream function and vertical velocity from the same run of the stratospheric GCM. Dust effects are included through a perturbation in the diabatic advection calculated as a function of net heating rates introduced by the presence of dust. A perturbative approach is used to solve the thermodynamic, continuity, thermal wind, and momentum balance equations, along with the explicit calculation of heating rates produced by the interaction of both long-wave and solar radiation with dust. Heating rates due to absorption of scattered radiation by the aerosol cloud are also included. The numerical experiment starts about 3 months after the eruption, using lidar data by McCormick et al. (1984) as an initial condition for the aerosols, and is continued for about 1 year. Results are shown for heating rates, temperature, residual velocities, and aerosol distribution following the time evolution of the El Chich¿n dust cloud. It is shown that the perturbation in the heating rates is readily balanced by the radiative relaxation processes, so that the effects on the residual circulation are negligible. ¿American Geophysical Union 1987