Continuous slowing-down theory is generalized so that inelastic scattering can be accurately taken into account. The basic idea underlying generalized theory is the assumption that the ratio, R(u), of the solution spectrum to a reference spectrum, g(u), varies linearly with the lethargy, u; that is, R(u) can be approximated by two terms of a Taylor series as long as g(u) is chosen reasonably. Such conventional theories as Geortzel-Greuling (GG) or Stacey’s improved-GG are included in this theory by taking g(u) as 1/∑s,i(u) or 1/∑t(u), respectively. The present theory is demonstrated to yield quite accurate results for the neutron spectra and coarse-group effective cross sections in many varieties of core and blanket compositions of fast reactors, using three alternative prescriptions for g(u).