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1. The complex, nonlinear response of dryland systems to grazing and climatic variations is a challenge to management of these lands. Predicted climatic changes will impact the desertification of drylands under domestic livestock production. Consequently, there is an urgent need to understand the response of drylands to grazing under climate change. 2. We enhanced and parameterized an ecohydrological savanna model to assess the impacts of a range of climate change scenarios on the response of a semi-arid African savanna to grazing. We focused on the effects of temperature and CO2 level increase in combination with changes in inter- and intra-annual precipitation patterns on the long-term dynamics of three major plant functional types. 3. We found that the capacity of the savanna to sustain livestock grazing was strongly influenced by climate change. Increased mean annual precipitation and changes in intra-annual precipitation pattern have the potential to slightly increase carrying capacities of the system. In contrast, decreased precipitation, higher interannual variation and temperature increase are leading to a severe decline of carrying capacities owing to losses of the perennial grass biomass. 4. Semi-arid rangelands will be at lower risk of shrub encroachment and encroachment will be less intense under future climatic conditions. This finding holds in spite of elevated levels of atmospheric CO2 and irrespective of changes in precipitation pattern, because of the drought sensitivity of germination and establishment of encroaching species. 5. Synthesis and applications. Changes in livestock carrying capacities, both positive and negative, mainly depend on the highly uncertain future rainfall conditions. However, independent of the specific changes, shrub encroachment becomes less likely and in many cases less severe. Thus, managers of semi-arid rangelands should shift their focus from woody vegetation towards perennial grass species as indicators for rangeland degradation. Furthermore, the resulting reduced competition from woody vegetation has the potential to facilitate ecosystem restoration measures such as re-introduction of desirable plant species that are only little promising or infeasible under current climatic conditions. On a global scale, the reductions in standing biomass resulting from altered degradation dynamics of semi-arid rangelands can have negative impacts on carbon sequestration. [ABSTRACT FROM AUTHOR]