The effect of anisotropic (CM) elastic scattering upon neutron moderation has been investigated. Relations between the Legendre moments of the angular scattering data (CM) and the moderating parameters of the Greuling-Goertzel (GG) and improved (IGG) theories are given, and it is shown theoretically and numerically that only the first few Legendre moments contribute significantly to the moderating parameters of the P0 (lab) theory. In general, anisotropic scattering is shown to reduce dramatically the moderating effectiveness of a material, and to produce oscillations (in energy) in the neutron flux. Numerical examples for isotopes and mixtures representative of postulated fast breeder reactors are given to illustrate quantitatively the effect of anisotropic scattering.