[en] Generalized continuous slowing down (CSD) theory coupled with integral transport concepts has been shown to give accurate prediction of the spatial variation of exposure dependent spectra at the core-blanket interface and in the blanket region of the homogeneous design fast reactor. The spectrum and the spectrum-averaged cross sections (SAXS) exhibited a strong space dependence as one proceeded from the outer core into the blanket. However, at any given location these varied rather weakly with exposure. In the paper the authors have extended the procedure to analyse the heterogeneous LMFBR spectra with depletion. Briefly, one solves a matrix differential equation of the zonal slowing down densities; the equation being a generalization of slowing down equations of the Greuling--Goertzel type with a source term. One then uses a multiregion analogue of the usual expressions of flux in terms of slowing down densities, either of the Greuling--Goertzel or Wigner form. The formalism has been applied to an infinite array of alternating core and blanket zones in slab geometry. The properties of these zones are based on Clinch River Breeder Reactor (CRBR) parameters and calculations were performed with the 29 group FTR-300 data set