Abstract Nonlinear features of flame dynamics are characterized by measuring the flame transfer functions for different input levels. This provides a family of gain and phase curves, which constitute the Flame Describing Functions (FDF) and can be used to analyze self-sustained combustion oscillations. Experiments correspond to four different flame geometries established for the same injection conditions: a single conical flame (CF), a “V”-flame, an “M”-flame and a collection of small conical flames (CSCF) stabilized on a perforated plate. It is shown that the gain and phase evolve with the level of modulation and that the response notably depends on the steady-state configuration. In the conical flame case, the gain weakly depends on the level of modulation while the phase changes linearly with frequency at low amplitudes. At higher amplitudes the phase first evolves linearly and then saturates. In the “V” and “M”-flame cases the gain exceeds unity in an intermediate range of frequencies. In that range the gain decreases monotonically as the amplitude increases. The phase evolves in a quasi-linear fashion with frequency and is essentially independent of the amplitude. In the CSCF case the gain also exceeds unity in a narrow range of frequencies and drops first slowly and then more rapidly with the amplitude of input perturbations. The phase is also quasi-linear with frequency but its slope rises as the amplitude increases indicating that the time lag associated to heat release perturbations measured with respect to the incoming disturbances is augmented when the amplitude level becomes large. All these features strongly influence the nonlinear response of the flame, its dynamics under sustained oscillations and the steady-state level reached at the limit cycle.