We use the global Community Earth System Model to investigate the response of secondary pollutants (ozone O3, secondary organic aerosols SOA) in different parts of the world in response to modified emissions of primary pollutants during the COVID‐19 pandemic. We quantify the respective effects of the reductions in NOx and in volatile organic carbon (VOC) emissions, which, in most cases, affect oxidants in opposite ways. Using model simulations, we show that the level of NOx has been reduced by typically 40% in China during February 2020 and by similar amounts in many areas of Europe and North America in mid‐March to mid‐April 2020, in good agreement with space and surface observations. We show that, relative to a situation in which the emission reductions are ignored and despite the calculated increase in hydroxyl and peroxy radicals, the ozone concentration increased only in a few NOx‐saturated regions (northern China, northern Europe, and the US) during the winter months of the pandemic when the titration of this molecule by NOx was reduced. In other regions, where ozone is NOx‐controlled, the concentration of ozone decreased. SOA concentrations decrease in response to the concurrent reduction in the NOx and VOC emissions. The model also shows that atmospheric meteorological anomalies produced substantial variations in the concentrations of chemical species during the pandemic. In Europe, for example, a large fraction of the ozone increase in February 2020 was associated with meteorological anomalies, while in the North China Plain, enhanced ozone concentrations resulted primarily from reduced emissions of primary pollutants.