Instability analysis of swirling flames is of importance in the design of advanced combustor concepts for aircraft propulsion and powerplant for electricity production. Thermoacoustic instabilities are analyzed here by making use of a nonlinear representation of flame dynamics based on a describing function. In this framework, the flame response is determined as a function of frequency and amplitude of perturbations impinging on the combustion region. This model is adapted to the case of confined swirling flames comprising an upstream manifold, an injection unit equipped with a swirler and a cylindrical flame tube. The flame describing function is experimentally determined and is combined with an acoustic transfer matrix representation of the system to provide growth rates and oscillation frequencies as a function of perturbation amplitude. These data can be used to determine regions of instability, frequency shifts with respect to the acoustic eigenfrequencies and they also yield amplitude levels when self-sustained oscillations of the system have reached a limit cycle. This equilibrium is obtained when the amplitude dependent growth rate equals the damping rate in the system. This requires an independent determination of this last quantity which is here based on measurements of the combustor resonance response curve, together with numerical estimates of the flame contribution to the system response. The geometrical parameters of the upstream manifold and flame tube are varied and the corresponding operating regimes are compared with those predicted with the FDF framework. The present demonstration of the FDF framework in a generic configuration indicates that this can be used in more general situations of technological interest. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.