The heterogeneity due to lumping the fuel in coated particles affects the thermal-neutron spectrum. A calculational model is discussed which, apart from some simplifying assumptions about the statistical distribution, allows a rigorous computation of effective cross sections for all nuclides of the heterogeneous medium. It is based on an exact computation of the neutron-penetration probability through coating and kernel. The model is incorporated in a THERMOS code providing a double heterogeneous cell calculation that can be repeated automatically at different time steps in the depletion code system MAFIA-V.S.O.P. A discussion of the effects of the coated-particle structure is given by a comparison of calculations for heterogeneous and homogeneous fuel zones in pebble bed reactor elements. This is performed for enriched UO2 fuel and for a ThO2-PuO2 mixture in the grains. Depending on the energy-dependent total sigmas in the kernels, the changes of the cross sections range from 0.1 up to 45%. The influence on the spectrum-averaged sigmas of the nuclides in the fresh UO2 fuel is lower than 1%. For the emerging 240Pu it increases up to 3.3% during irradiation. For the ThO2-PuO2 fuel, the averaged sigmas of the isotopes vary from 0.5 to 5.7% depending on the state of irradiation. Correspondingly, there is an influence on the plutonium isotopic composition, on breeding ratios, and on the tilt of keff during burnup which will be discussed in detail.