The boreal summer tropical upper-tropospheric momentum budget involves a balance between eddy and mean meridional fluxes. In winter, however, the eddy flux itself acts to accelerate and decelerate the zonal flow in the Asian and East Pacific regions, respectively. In a zonal mean sense, the residual of these two is then balanced by the mean meridional flux. These features are qualitatively captured by the CMIP6 suite of models in their control runs. With warming, the CMIP6 ensemble shows that the flux budget changes in a quantitative manner, in both the summer and winter seasons. Apart from the mean meridional flux which is affected by the projected weakening of the Hadley Cells, there are significant changes in eddy fluxes too. Notably, stationary wave fluxes are affected in the Asian and East Pacific regions during the summer and winter seasons, respectively. In the wintertime, extratropical wave activity penetrating into the East Pacific almost shuts off due to a weakening of the prevalent westerlies in the warming simulations. Whereas, in summer, eddy fluxes in the Asian region are displaced upward and changes are observed in the upper troposphere and lower stratosphere. Specifically, rotational flow around the Asian summer anticyclone weakens in the upper troposphere while strengthening in the lower stratosphere. Concomitantly, eddy flux convergence over the equatorial Indian Ocean decreases in the former and increases (by a larger amount) in the latter. In fact, strengthening of summertime tropical and subtropical stationary waves in the lower stratosphere with warming is not restricted to the Asian sector but is observed over all longitudes. Effectively, the magnitude of all terms in the upper tropospheric momentum flux budget decreases with warming, and an ensemble mean continues to yield a marginally westward annual and zonal mean equatorial zonal flow.