Triggering, frequency shifting, mode switching and hysteresis are commonly encountered during self-sustained oscillations in combustors. These mechanisms cannot be anticipated from classical linear stability analysis and the nonlinear flame response to incident flow perturbations is often invoked to interpret these features. However, the flame may not be solely responsible for nonlinearities. Recent studies indicate that interactions with boundaries can be influenced by the perturbation level and that this needs to be considered. The nonlinear response of acoustic boundary conditions to flow perturbations is here exemplified in two configurations which typify practical applications. The first corresponds to a perforated plate backed by a cavity conveying a bias flow and the second corresponds to a set of flames stabilized at a burner outlet. These systems are submitted to acoustic perturbations of increasing amplitudes as can be encountered during unstable operation. It shown that these terminations can be characterized by an impedance featuring an amplitude dependent response. The classical linear impedance Z(ω ) is then replaced by its nonlinear counterpart an Impedance Describing Function (IDF), which depends on the perturbation level input Z(ω , |p′ | or |u′ |). Using this concept, it is shown that the passive perforated plate optimized to damp instabilities of small amplitudes may eventually loose its properties when submitted to large sound pressure levels and that the flame response shifts when the amplitude of incoming flow perturbations is amplified. The influence of these nonlinear elements on the stability of a generic burner is then examined using a methodology which extends a previous analysis based on the Flame Describing Function (FDF) to systems with complex flow interactions at the boundaries.