A complete inverse mass expansion is derived for the difference-differential equation describing neutron moderation in infinite homogeneous media, far energetically from the sources. We consider slowing down equations with different values of the nucleus-to-neutron mass ratio, and a common value of the capture-to-scattering cross-section ratio. The latter is assumed to be an analytic function of lethargy. A preliminary analysis suggests the functional form of the leading term of the expansion. Further treatment leads to a first-order, linear, inhomogeneous, ordinary differential equation satisfied by the expansion terms. Different terms of the expansion correspond to different free terms of the differential equation. Imposing a normalization condition, the solution of the differential equation is made unique, and a formal, practically effective solution to the general asymptotic moderation problem is obtained.