As an aid to the interpretation of radiation damage phenomena, calculations have been made of the energy spectrum of the fast neutrons in graphite-moderated reactor systems. A detailed study of the effect of scattering symmetry on the slowing down of neutrons from monoenergetic sources in homogeneous systems shows the importance of including a reasonably accurate representation of the scattering symmetry in estimates of fast neutron spectra. The neutron collision density and the flux density are computed for fission neutrons slowing down in an infinite, homogeneous graphite reactor. The effects of source heterogeneity are examined by applying age theoretical methods to the ORNL Graphite Reactor. The results of the calculations are in good agreement with the limited amount of experimental data available.