[en] Owing to their ability to allow with relatively limited effort to account for and analyze the more or less complex processes which are involved when an alteration is induced into a given system, perturbation methods in general and generalized perturbation methods in particular have been encountering an increasing interest among reactor physicists. Most applications of these methods have been so far characterized by linear approaches. In the present paper, the scope and limits of these linear approaches are discussed and second or higher order ones are proposed in some significant cases. For what concerns the multiplying systems at critical conditions for which ratios of functionals linear with the flux are generally considered, explicit methods adopting higher mode eigenfunctions are illustrated, whereas higher order generalized perturbation techniques are proposed for time-dependent and source problems