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Climate model simulations show an acceleration of the Brewer-Dobson circulation (BDC) in response to climate change. While the general mechanisms for the BDC strengthening are widely understood, there are still open questions concerning the influence of the details of the wave driving. Mean age of stratospheric air (AoA) is a useful transport diagnostic for assessing changes in the BDC. Analyzing AoA from a subset of Chemistry-Climate Model Initiative part 1 climate projection simulations, we find a remarkable agreement between most of the models in simulating the largest negative AoA trends in the extratropical lower to middle stratosphere of both hemispheres (approximately between 20 and 25 geopotential kilometers (gpkm) and 20-50 degrees N and S). We show that the occurrence of AoA trend minima in those regions is directly related to the climatological AoA distribution, which is sensitive to an upward shift of the circulation in response to climate change. Also other factors like a reduction of aging by mixing (AbM) and residual circulation transit times (RCTTs) contribute to the AoA distribution changes by widening the AoA isolines. Furthermore, we analyze the time evolution of AbM and RCTT trends in the extratropics and examine the connection to possible drivers focusing on local residual circulation strength, net tropical upwelling and wave driving. However, after the correction for a vertical shift of pressure levels, we find only seasonally significant trends of residual circulation strength and zonal mean wave forcing (resolved and unresolved) without a clear relation between the trends of the analyzed quantities. This indicates that additional causative factors may influence the AoA, RCTT and AbM trends. In this study, we postulate that the shrinkage of the stratosphere has the potential to influence the RCTT and AbM trends and thereby cause additional AoA changes over time.