The multiple elastic scattering of polarized particles is governed by a generalized BOLTZMANN equation. The properties of the collision brackets connected with this equation - definiteness and invariances-are studied. Then the state near equilibrium, i. e. nearly isotropic distribution of velocities and spins, is considered (diffusion theory). To describe an ensemble of spin ½-particles one needs in the most simple non-equilibrium approximation two scalars (one pseudo) and four vectors (two pseudo). The scalars are: density of number and helicity. The vectors are: particle stream, density of velocity-spin vector (ʋ × s), stream of helicity and density of transverse spin. These scalars and vectors are connected by linear differential equations (diffusion-relaxation-equations). The entropy and the ONSAGER-CASIMIR relations are discussed. The theory, supplemented by boundary conditions, is applied on the multiple scattering of spin ½-particles by a thick foil.