<p>The transport properties of materials based on polysulfone with addition of graphene oxide with a step of 0.1% and with a change in its concentration from 0 to 0.5% were investigated by the method of dynamic change in pressure. The permeabilities of membranes at pressures of 3–7 MPa were determined, and nonlinear changes in their transport properties were revealed. It was established that the formation of carbon structures in a hydrophobic polymer makes it permeable to water and that the permeability of such polymers depends nonlinearly on the concentration of the graphene particles introduced into them, which can be explained within the framework of the percolation approach. The results obtained allow one to answer the fundamental questions about the mechanisms of transfer of continuous media through composite materials and heterogeneous structures.</p>