Thin graphene oxide (GO) membranes supported on porous anodic aluminum oxide (AAO) substrates prepared by spin-coating and pressure-assisted filtration are tested in gas dehumidification experiments. Graphene oxides with different specific nanosheet sizes ranged from 10 x 140 to 3300 nm synthesized by modified Hummer's method were used for membrane preparation. We have shown that 25-60 nm-thick GO membranes exhibit barrier properties towards most of the gases (CH4, N-2, O-2, C4H10), while revealing high permeance for water and water soluble vapors (CO2). The influence of the GO nanosheet size and the membrane preparation technique on the gas transport characteristics of the composite membranes are investigated. The best membrane performance has been achieved for membranes prepared from medium-flake-sized GO nanosheets providing high enough defect density at the surface to allow water entrance to the interlayer space and large enough nanosheet size to cover AAO nanochannels and create continuous barrier coating towards permanent gases on the surface. Water permeance and H2O/N-2 selectivity measured in the relative humidity range of 10-80% shows strong humidity dependence due to the sorption of water vapors in the interlayer space of GO. Maximum H2O/N-2 selectivity of 13,000 at water permeance of GO membranes of similar to 1.4 m(3)/(m(2) h) has been achieved at standard conditions (298 K, 1 bar) and relative humidity of 80%. Water permeance of GO membranes strongly depends on the transmembrane pressure, diminishing an order of magnitude from equi-pressure conditions to 0.1 MPa pressure difference. The effect has been ascribed to a pressure-driven ousting of water molecules from the interlayer spacing of GO. Permeability of the GO membranes towards CO2 in humid mixed gas experiments has been shown to be enhanced strongly due to gas solubility in liquefied water enabling sweetening and dehumidification of natural and technological gases in a single stage.