Composite membranes are formed based on ultrathin 20 nm-thick selective layers of graphene oxide nanoflakes deposited on porous anodic alumina substrates. The long-term dynamics of permanent gases transport and water vapor permeability across the composite membranes is measured during 240 days (8 months). It is revealed that the permeability towards permanent gases remains nearly constant during a prolonged period of time. Contrary, water vapor flux decreases rapidly within the first 30 days from the membrane preparation moment and reaches about 80% of permeability loss during 8 months. The rapid decrease of membrane permeability during the first month could be attributed to a gradual packing of graphene oxide nanoflakes, particularly, locating in the surface sublayers, into more tight microstructure due to the evaporation of remaining solvent (membrane drying) under ambient conditions. Further decrease in permeability during more prolonged time could be caused additionally by deoxygenation of surface GO nanoflakes preventing water vapors diffusion into the GO film. This phenomenon, the so called “ageing” accompanies graphene oxide thin films similarly to some types of highly-permeable polymers. Holding the aged membrane under saturated water vapors, and even liquid water, didn’t allow one to revitalize completely its permeability. The obtained results should be taken into account when designing membranes and other devices based on graphene oxide and its derivatives.