Seasonally dependent quasi-stationary planetary wave activity in the southern hemisphere influences the distribution of ozone within and near the equatorward edge of the stratospheric polar vortex. Accurate representation of this zonal asymmetry in ozone is important in the characterisation of stratospheric circulation and climate and their associated effects at the surface. In this study, we used the Australian Community and Climate Earth System Simulator-Chemistry Climate Model to investigate the influence of greenhouse gases (GHGs) and ozone depleting substances (ODSs) on the zonal asymmetry of total column ozone (TCO) and 10 hPa zonal wind between 50 and 70°S. Sensitivity simulations were used from 1960 to 2100 with fixed ODSs and GHGs at 1960 levels and a regression model that uses equivalent effective stratospheric chlorine and carbon dioxide equivalent radiative forcing as the regressors. The model simulates the spring and summer zonal wave-1 reasonably well, albeit with a slight bias in the phase and amplitude compared to observations. An eastward shift in the TCO and 10 hPa zonal wave-1 is associated with both decreasing ozone and increasing GHGs. Amplitude increases are associated with ozone decline and amplitude decreases with GHG increases. The influence of ODSs typically outweigh those by GHGs, partly due to the GHG influence on TCO phase at 50°S likely being hampered by the Andes. Therefore, over the 21st century, influence from ozone recovery causes a westward shift and a decrease in amplitude. An exception is at 70°S during spring, where the GHG influence is larger than that of ozone recovery, causing a continued eastward trend throughout the 21st century. Also, GHGs have the largest influence on the 10 hPa zonal wave-1 phase, but still only induce a small change in the wave-1 amplitude. Different local longitudes also experience different rates of ozone recovery due to the changes in phase of the zonal wave-1. The results from this study have important implications for understanding future ozone layer distribution in the Southern Hemisphere under changing GHG and ODS concentrations. Important future work would involve conducting a similar study using a large ensemble of models to gain more statistically significant results.