The low water vapor pressures of mixtures of water with the ionic liquids (ILs), [EMIM][EtSO4] and [BEIM][EtSO4], indicate that a process of gas dehydration by absorption in ILs might be an alternative to the classical absorption process with triethylene glycol (TEG). The activity coefficient for an infinite dilution of water in the IL (x(IL) -> 1), which should be low for efficient dehydration, is only about 0.2 for [EMIM][EtSO4] compared to 0.6 for triethylene glycol. In contrast to TEG, losses by evaporation are excluded with ILs as solvents, because they have a negligible vapor pressure. The number of separation stages needed for the absorption in the IL and for the subsequent regeneration of the water-loaded IL is small, about six and eight, respectively. IL regeneration can be achieved by distillation of water out of the IL (e. g., at 120 degrees C) and stripping with ambient air, which is not possible in the case of TEG (chemical attack by O-2).