To estimate analytically the effects of discrete model and evaporation model inelastic scattering on the fast neutron spectrum, the original Greuling-Goertzel (GG) approximation was developed with the help of the generalized function theory. In place of the collision density function ψ(u), the two-term Taylor's expansion of a test function of a functional ψ was proposed to obtain analytic expressions of lethargy moments of inelastic scattering kernels. By using these moments, the author derived the standard GG approximation including all inelastic events. By introducing an approximate separable kernel of the evaporation model inelastic scattering, another conventional treatment of inelastic scatterings was proposed, i.e., the external source approximation of inelastic scattering. In this approximate method, elastic scattering was treated by the ordinary GG approximation. The present standard GG theory was useful for the preliminary description of fast neutron spectrum in a mixture in which a large amount of fuel elements is not included, while the external source approximation was shown to estimate reasonably the effects of inelastic scattering on fast neutron spectrum in any medium.