A process for removing acid gases from a water vapor-containing fluid stream comprises a) providing an absorption liquid which is incompletely miscible with water; b) treating the fluid stream in an absorption zone with the absorption liquid to obtain an acid gas-depleted treated fluid stream and an acid gas-loaded absorption liquid; c) directing the treated fluid stream to a rehydration zone and treating the fluid stream with an aqueous liquid to volatilize at least part of the aqueous liquid; d) regenerating the loaded absorption liquid to expel the acid gases at least in part and obtain a regenerated absorption liquid, and directing the regenerated absorption liquid to step b); and e) separating, from the absorption liquid, an aqueous liquid that has condensed in the absorption zone, and directing the aqueous liquid to step c). The process allows for an efficient removal of water accumulated in the absorption liquid system.