Cross-flow filtration is a filtration process for separation of a disperse phase from liquids. Suspension flows tangentially to a membrane and the filtrate is drawn off perpendicular to the direction of flow. Formation of a filter cake on the membrane is thus prevented, reduced, or its composition modified. The principle of the separation is based on two opposing effects: on the one hand, the particles are transported by the filtration flux to the membrane where they cause an increase in concentration; on the other hand, concentration differences are again reduced by the turbulence of the cross-flow and by Brownian motion of the particles. The two mechanisms compete with each other and depend upon particle size in different ways. An energetic comparison of the two effects yields the separation law of cross-flow filtration asa steady state solution of the Fokker-Planck equation. The separation law has an exponential form and assigns each particle size a separation probability with which it reaches the membrane. Once on the membrane the particles may form a filter cake, flow through the pores or return to the bulk flow. If the particles remain on the membrane the ranges of layer-free and cake-forming filtration can be calculated from the hydrodynamic and geometric conditions of the cross-flow filter. Conventional cake filtration is regarded as limiting case. In continuous cross-flow filtration processes a low separation probability through the filtration pressure on selection of the filter medium resistance.