The budget of ozone and its evolution associated with anthropogenic activities are simulated with the Model for Ozone and Related Chemical Tracers (MOZART) (version 1). We present the changes in tropospheric ozone and its precursors (CH4, NMHCs, CO, NOx) since the preindustrial period. The ozone change at the surface exhibits a maximum increase at midlatitudes in the northern hemisphere reaching more than a factor of 3 over Europe, North America, and Southeast Asia during summer. The calculated preindustrial ozone levels are particularly sensitive to assumptions about natural and biomass burning emissions of precursors. The possible future evolution of ozone to the year 2050 is also simulated, using the Intergovernmental Panel on Climate Change IS92a scenario to estimate the global and geographical changes in surface emissions. The future evolution of ozone stresses the important role played by the tropics and the subtropics. In this case a maximum ozone increase is calculated in the northern subtropical region and is associated with increased emissions in Southeast Asia and Central America. The ozone future evolution also affects the more remote regions of the troposphere, and an increase of 10--20% in background ozone levels is calculated over marine regions in the southern hemisphere. Our best estimate of the global and annual mean radiative forcing associated with tropospheric ozone increase since the preindustrial era is 0.43 W m-2. This value represents about 20% of the forcing associated with well-mixed greenhouse gases. The normalized tropospheric ozone radiative forcing is 0.048 W m-2 DU-1. An upper estimate on our forcing of 0.77 W m-2 is calculated when a stratospheric tracer is used to approximate background ozone levels. In 2050 an additional ozone forcing of 0.26 W m-2 is calculated, providing a forcing from preindustrial to 2050 of 0.69 W m-2. ¿ 2001 American Geophysical Union