AbstractAn approximate theory for the slowing down of neutrons in a nonmultiplying medium with plane symmetry is described. The theory is based on an approximate form of the transfer function for elastic scattering under the hypothesis that the mass number of the moderator is larger than one. In theA−Napproximation the slowing down equation is reduced to a finite system of differential equations with respect to the lethargy variable. A detailed study has been made of the results obtained in theA−Napproximation withN= 0 andN= 1. Special attention has been paid to a comparison of theA−1approximation with age theory and asymptotic theory.