In the recent past, the evolution of stratospheric ozone (O3) was affected by both increasing ozone depleting substances (ODSs) and greenhouse gases (GHGs). The impact of the single forcings on O3 is well known. Interactions between the simultaneously increased GHG and ODS concentrations, however, can occur and lead to nonlinear O3 changes. In this study, we investigate if nonlinear processes have affected O3 changes between 1960 and 2000. This is done with an idealised set of time slice simulations with the chemistry-climate model EMAC. Due to nonlinearity the past ozone loss is diminished throughout the stratosphere, with a maximum reduction of 1.2 % at 3 hPa. The total ozone column loss between 1960 and 2000 that is mainly attributed to the ODS increase is mitigated in the extra-polar regions by up to 1.1 % due to nonlinear processes. A separation of the O3 changes into the contribution from chemistry and transport shows that nonlinear interactions occur in both. In the upper stratosphere a reduced efficiency of the ClOx-catalysed O3 loss chiefly causes the nonlinear O3 increase. An enhanced formation of halogen reservoir species through the reaction with methane (CH4) reduces the abundance of halogen radicals significantly. The temperature-induced deceleration of the O3 loss reaction rate in the Chapman cycle is reduced, which leads to a nonlinear O3 decrease and counteracts the increase due to ClOx. Nonlinear effects on the NOx abundance cause hemispheric asymmetric nonlinear changes of the O3 loss. Nonlinear changes in O3 transport occur in particular in the Southern Hemisphere (SH) during the months September to November. Here, the residual circulation is weakened in the lower stratosphere, which goes along with a reduced O3 transport from the tropics to high latitudes. Thus, O3 decreases in the SH polar region but increases in the SH midlatitudes. The existence of nonlinearities implies that future ozone change due to ODS decline slightly depends on the prevailing GHG concentrations. Therefore the future ozone evolution will not simply be a reversal of the past.