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The paper presents the results of a theoretical and practical study of the mechanisms of mass transfer through membranes formed from layers of quasi-two-dimensional compounds with a hydrophilic (graphene oxide, layered titanium carbides, molybdenum disulfide) and hydrophobic surface (graphene, CdTe nanosheets in an oleic acid shell). The mechanisms of transport in these systems have been studied and the possibility of implementing the processes of separation of components according to the mechanisms of configurational diffusion, transport with carriers and capillary condensation in the interlayer space has been shown. Using these classes of membranes, the possibility of effective separation in vapors of H2O/N2, H+/H2O, H2/CH4, NH3/H2, C4H10/CH4, etc. was established. During the work, record values of permeability and selectivity of thin (50-200 nm) selective layers of modified graphene oxide by water vapor (P(H2O) ~100 m3/(m2•bar•h); S(H2O/N2) > 1.0•105), and the high performance of membranes in gas drying processes was demonstrated (more than 30 m3 /(m2•h) for feed gas) and pervaporation desalination (up to 10 kg/(m2•h) at 60 °C). To establish the features of transport in nanoslits, methods of in situ and in operando monitoring of the interlayer distance using synchrotron radiation were used. It was found that the transport mechanism changes as the penetrant is sorption and the interplanar distance increases, which is associated with a change in the entropy factor and the activation barrier to diffusion. The value of the activation barrier is also significantly affected by the density of functional groups on the surface of nanosheets. It has been shown that the transport of water molecules through highly oxidized graphene oxide (C/O ≈ 1.8) is much easier than through the reduced form (C/O ≈ 2.1) and is significantly hampered by the intercalation of ions into the interlayer space. Transport activation energies were experimentally determined based on the temperature dependences of permeability and nanogap width in the processes of vapor transport and pervaporation and confirmed theoretically using semi-empirical models. It has been shown that controlled changes in the interplanar distance using spacer molecules or fixing the size of the gap between nanosheets using intercalated ions or molecules, as well as changes in the chemical composition of graphene oxide, make it possible to create membrane materials with specified transport characteristics. In addition, changing the interlayer distance using external influences (using temperature-controlled adsorption or the configuration of spacers) makes it possible to regulate the performance of such membranes directly during operation, which opens the way to the creation of new classes of “smart” membrane materials. The work was carried out with the financial support of the Russian Science Foundation, grant No. 23-13-00195.