Through the 21st century, global-mean stratospheric ozone abundances are projected to increase due to decreasing chlorine and bromine concentrations (as a consequence of the Montreal Protocol for Substances that Deplete the Ozone Layer), and continued CO₂-induced cooling of the stratosphere. Along with CO₂, anthropogenic emissions of the greenhouse gases N₂O and CH₄ are projected to increase, thus increasing their atmospheric concentrations. Consequently, reactive nitrogen species produced from N₂O and reactive hydrogen species produced from CH₄ are expected to play an increasingly important role in determining stratospheric ozone concentrations. Chemistry-climate model simulations were performed using the NIWA-SOCOL (National Institute of Water and Atmospheric Research - SOlar Climate Ozone Links) model, which tracks the contributions to ozone loss from a prescribed set of catalytic cycles, including the ozone-depleting nitrogen and hydrogen cycles, over latitude, longitude, pressure and time. The results provide a comprehensive picture of how stratospheric ozone may evolve through the 21st century under a range of greenhouse gas emissions scenarios, and quantitatively extend concepts that had previously been understood only qualitatively.