Complete hemispheric budgets of relative angular momentum are presented for the sostice seasons. Domain is the zonal mean northern atmosphere, divided into 4¿4 equal-area/equal mass annuli (Δ sinϕ=0.25, Δp=250 mbar) plus for annuli in the southern tropical belt, making 20 annuli in total. Emphasis is on the vertical momemnum transport due to eddies on all scales. This component is determined as being residual from the budget equation. Observed transports, used as specified input, include net horizontal momentum transport across latitude circles, vertical cell transport of &OHgr; momentum and relative momentum across pressure surfaces, and vertical momentum transport across the earth's surface due to mountain torque (observed) plus stress torque (parametrized). The imbalances represent the net reliability of the input data plus the error of miscellaneous torques which are not explicitly specified (storage, mass drift, and variation of annulus area with height). Principal results are: (1) The vertical eddy momentum transport (WE) is of the order of 10 Hadley units (1 HU=1018 J). In the tropics it is upward in summer and downward in winter, presumably because of the location of the intertropical Convergence Zone and because of the Asiatic monsoon. In the extratropics it is upward in both seasons. (2) The vertical cell transport of &OHgr; momentum (PSI) is represented by the mass flux stream function. It is also of the order of, and opposite to WE. The principal momentum balance is between WE and PSI; the horizontal transports are significantly smaller (except across 30¿N in winter). (3) The hemispheric rms imbalance, averaged over all annuli and seasons, is 0.4 HU. This is well below the order of WE and is considered as the statistical error of the vertical eddy transports. (4) Possible systematic errors were investigated with a sentivity test by independently changing the scales of PSI and of the stress torque (TL). The rms imbalance reaches a minimum for 78% of the observed PSI and for 90% of th TL. This seems to indicate that both the observed meridional wind and the surface wind stress as used in this study are overestimates. When the reduced fields are used as input variables, WE is also reduced by about a quarter; however, the patterns of WE remain essentially unaltered. Thus our vertical eddy momentum transport estimates deserve credence with an error margin of 25%. (5) WE is highly variable throughout the year, mostly because of the variability of PSI. Although WE is, on the seasonal time scale, large and clearly a significant link in the momentum budget, is annual values are small and much less significant. The reason is that opposite processes work together to form WE. (6) WE combines the net effect of all eddy processes, from the molecular up to the synoptic scale. It is not possible with the present data to split WE into its components. Various mechanisms contributing to WE are speculatively discussed. They include the hot tower mechanism, which seems to be predominant in the tropics and over the monsoon areas as well as in extratropical convective zones, and baroclinic plus gravity wave processes in the extratropics.