Device to dry a damp compressed gas, whereby the device (2) is provided with a dryer that is provided with a liquid desiccant and configured to bring compressed gas in contact with the aforementioned desiccant that is capable of absorbing moisture from the compressed gas, characterised in that the dryer is a membrane dryer (11); the device (2) to dry compressed gas contains a circuit (20) in which the aforementioned liquid desiccant is placed and means to allow the circulation of the desiccant in the circuit (20), consecutively through the membrane dryer (11) with a membrane (13) that forms a partition between the compressed, gas on one side and the liquid desiccant on the other side of the membrane (13), whereby the membrane (13) is impermeable or virtually impermeable to the gas in the compressed gas but selectively permeable to the moisture in the compressed gas; a heat exchanger (29} to heat up the liquid desiccant; a regenerator (22) used to remove at least partially the moisture absorbed in the liquid desiccant before this is returned through the membrane dryer (11) for a following cycle, whereby the regenerator (22) is formed by a housing (23) through which the liquid desiccant with the moisture absorbed therein is guided in moisture-transfer contact with a flushing agent that is simultaneously guided through the housing (23) and is capable of absorbing moisture from the liquid desiccant upon contact; and the circuit (20) is provided with a closable bypass (45) between a branching point in the circuit downstream from the regenerator (22) and upstream from the membrane dryer (11) and a confluence point in the circuit downstream from the membrane dryer (11) and upstream from the regenerator (22).