Continuous neutron slowing down theory has proved useful in problems associated with thermal reactors. There are, however, two principal problem areas which inhibit obtaining the full benefits of continuous neutron slowing down models in fast reactor problems. One problem area is the treatment of inelastic scattering. The second problem area is the treatment of scattering and absorption resonances in a mixture of several moderating materials. In this paper, new methods are advanced for each of these problem areas. These methods are shown to lead to a continuous neutron slowing down model of reasonable accuracy for fast reactor problems. The inelastic treatment is based on matching the solution for an easily solvable reference problem (the zero absorption case). The mixture treatments (several are considered) are based on averaging procedures over a scattering interval instead of at a single energy.