Numerous ultra- and microfiltration dead-end plants with inside-out capillary membranes are already in operation, but some important phenomena are still unexplained. Therefore, the fundamental processes taking place inside a capillary membrane were investigated. As a basis, the flow field depending on axial and radial position inside the capillary was determined. Then, transport and deposition of non-brownian particles were studied theoretically by determination of particle trajectories considering influences of particle concentration and wall-effects on hydrodynamics, DLVO-forces, buoyancy, gravitation, shear induced diffusion, and interparticulate forces. According to these calculations, incoming particles with a diameter smaller than a so-called "limiting diameter", which depends on operating and geometrical boundary conditions, should deposit in a widely even way. Larger particles should not deposit until they have reached a certain distance from the capillary inlet. The larger the particle size, the longer this distance. If the particle is larger than a so-called "plugforming diameter" then the particles are transported to the dead-end of the capillary which may cause clogging of the capillary. This "plugforming diameter" also depends on operating and geometrical boundary conditions. These theoretical predictions could be confirmed by experimental results. In these experiments the behaviour of spherical latex and non-spherical walnut-shell particles was studied. To avoid clogging of capillaries, the deposition of the particles should be as evenly distributed as possible, which means that the "plugforming diameter" should be as large as possible. This could be achieved using relatively short or/and wide capillaries. However, a small permeate flux, a high membrane permeability or/and a small membrane surface potential (if repulsive) have positive effects as well. Another very proper way could be to operate the capillaries with a very small cross flow.