The invention relates to an apparatus (10) for drying and/or cooling gas (12), in particular air, by means of a hygroscopic solution (14), said apparatus comprising an absorption device (16) which comprises at least one gas flow duct (18) and at least one flow duct (20) carrying the hygroscopic solution, wherein the inner or gas chamber (22) of a respective gas flow duct is at least partly delimited by a vapor-permeable liquid-tight membrane wall (24) and at least one flow duct is provided, which is formed between such a gas flow duct and a further such gas flow duct adjacent to the latter or an adjacent cooling unit (26) and which carries the hygroscopic solution, so that moisture, in particular water vapor, passes from the gas into the hygroscopic solution via the membrane wall and is absorbed in said solution.