[en] Two types of high order effects associated with perturbations in the flux shape are considered: Spectral Fine Structure Effects (SFSE) and non-linearity between changes in performance parameters and data uncertainties. SFSE are investigated in Part I using a simple single resonance model. Results obtained for each of the resolved and for representative unresolved resonances of ²³⁸U in a ZPR-6/7 like environment indicate that SFSE can have a significant contribution to the sensitivity of group constants to resonance parameters. Methods to account for SFSE both for the propagation of uncertainties and for the adjustment of nuclear data are discussed. A Second Order Sensitivity Theory (SOST) is presented, and its accuracy relative to that of the first order sensitivity theory and of the direct substitution method is investigated in Part II. The investigation is done for the non-linear problem of the effect of changes in the 297 keV sodium minimum cross section on the transport of neutrons in a deep-penetration problem. It is found that the SOST provides a satisfactory accuracy for cross section uncertainty analysis. For the same degree of accuracy, the SOST can be significantly more efficient than the direct substitution method