An analytical approach to the solution of the neutron slowing down problem with anisotropic scattering is presented. The basic ideas are the representation of the transport equation by a set of infinitely many first-order linear partial differential equations, the application of the “central limit theorem,” and integral transform techniques. The distribution of the n-times scattered neutrons is given as a superposition of space- and angle-dependent functions with coefficients depending on the energy. In the isotropic case, these coefficients are directly related to the Placzek slowing down distributions.