The nonlinear behavior of emulsions in hydrodynamics is mostly pronounced when such emulsions flow in microchannels in experiments involving a permanent pressure gradient at the channel. It has been discovered that, despite the permanent pressure gradient, the flow of the water-in-oil emulsion almost completely ceases with time. This effect is known as dynamic blocking. It becomes pronounced when the emulsions flow through a cylindrical microchannel, in the case of a plane flow in the elements of a fracture, and when the emulsion flows through a 3D capillary structure, such as a core. 'The sizes of the water microdrops in the emulsion are an Order of magnitude Smaller than-the cross-section sizes of the microchannels. However, the structure that is formed of such microdrops blacks not only individual microchannels but also the entire microchannel system, including cores. The physical nature of the dynamic blocking of emulsions is connected to the deformations of the emulsion microdrops as the pressure gradient increases and to the friction among these microdrops. The friction between emulsion microdrops brings about non-equilibrium and nonlinear effects in the filtration flow. On the basis Of these ideas, this work describes a mathematical model of two-phase filtration through a porous medium. The results of the mathematical model satisfactorily agree with the experimental data.