The nonlinear coupling of atmospheric trace constituents can, at least in principle, cause concentrations to oscillate with time. This is demonstrated for a simplified scheme encompassing only the tropospheric gas phase chemistry of CO, O3, HOx, and NOx. Oscillating concentrations with a common period of about 33 days were found for all chemical compounds under the forcing by time independent sources for CO and NO. Linear stability analysis shows that the periodic solution is locally stable. The periodicity is found for a large domain of NO and CO source strengths. The presence of methane destroys the oscillation. This finding limits the applicability for problems of the real atmosphere. The source strengths of NO and CO necessary to produce undamped oscillations in the model are much larger than the corresponding globally averaged source strengths. In the polluted boundary layer, however, the source strengths of NO and CO could very well be encountered. Evaluation of the Lyapunov exponents and of the dependence on the initial conditions indicates that the periodic solution is attained independent of the initial conditions, usually within a few days. Thus even if the meteorological and source strength conditions do not persist for the time of a whole period, parts of it may still be observable. ¿ American Geophysical Union 1996