Trends in the position of the DJF Austral jet have been analyzed for multimodel ensemble simulations of a subset of high- and low-top models for the periods 1960–2000, 2000–2050, and 2050–2098 under the CMIP5 historical, RCP4.5, and RCP8.5 scenarios. Comparison with ERA-Interim, CFSR and the NCEP/NCAR reanalysis shows that the DJF and annual mean jet positions in CMIP5 models are equatorward of reanalyses for the 1979–2006 mean. Under the RCP8.5 scenario, the mean jet position in the high-top models moves 3 degrees poleward of its 1860–1900 position by 2098, compared to just over 2 degrees for the low-top models. Changes in jet position are linked to changes in the meridional temperature gradient. Compared to low-top models, the high-top models predict greater warming in the tropical upper troposphere due to increased greenhouse gases for all periods considered: up to 0.28 K/decade more in the period 2050–2098 under the RCP8.5 scenario. Larger polar lower-stratospheric cooling is seen in high-top models: −1.64 K/decade compared to −1.40 K/decade in the period 1960–2000, mainly in response to ozone depletion, and −0.41 K/decade compared to −0.12 K/decade in the period 2050–2098, mainly in response to increases in greenhouse gases. Analysis suggests that there may be a linear relationship between the trend in jet position and meridional temperature gradient, even under strong forcing. There were no clear indications of an approach to a geometric limit on the absolute magnitude of the poleward shift by 2100.