Because of the large number of heavy nuclide resonances, a detailed neutron flux calculation in the epithermal range cannot be made by standard nuclear reactor codes: It would need several tens of thousands of energy points. However, by using precalculated effective reaction rates, only a few tens of groups are sufficient for accurate spectrum and reaction rate calculations, if a consistent formalism is used. Such a formalism was elaborated in the 1970s by M. Livolant, F. Jeanpierre for the “one resonant nuclide-one resonant zone” problem, and was implemented in the APOLLO code. In practical cases there are several resonant nuclides and often resonant zones of different characteristics, e.g., a lattice constituted with different kinds of pins, a lattice with irregular “water holes,” a fuel element with temperature (therefore Doppler effect) gradients, and so on. Since these problems cannot be correctly treated by APOLLO, a generalization of the formalism was derived. The basic principles were retained, and an algorithm was constructed that would not require too expensive calculations. The Livolant-Jeanpierre theory is briefly summarized, equations for the most general case are presented, some approximations for practical calculations are proposed, and numerical tests on significant examples are discussed.