Combustion instabilities consist in self-exited oscillations in combustion chambers and can cause structure degradations. When combustion instabilities occur, the combustion process is characterised by the coupling of various non-linear phenomena, which can lead to the formation of either a limit cycle or chaos. The intrinsic highly non-linear behaviour, especially when chaos arises, poses a major problem for the formulation of good predictions and the design of reliable control systems. Due to the relevant number of degree of freedom and to the non-linear coupling of different phenomena, the mathematical modeling of combustion instabilities is computationally heavy and may produce an unsatisfactory correspondence between simulated and experimental data. Analogous problems arise also from the uncertainty for the parameters of the process, such as the local velocity of the flame front (and, hence, the reaction rate and the exhausted temperatures), and their unpredictable variations. In fact, note that most of the chemical and thermo-physical variables both strongly depend and influence the instantaneous displacement of the flame front, which is positioned on the unstationary eddies external surface. In order to obtain a reliable model for thermo-acoustic combustion instabilities, a different approach was chosen in this paper. The black-box identification of an experimental combustion chamber was obtained by means of a generalized NARMAX model. The model was implemented by training a Multilayer Perceptron artificial neural network with input-output experimental data. The main advantages of the proposed approach consisted in the natural ability of neural networks in modeling nonlinear dynamics in a fast and simple way and in the possibility to address the process to be modeled as an input-output black box, with little or no mathematical information on the system. Satisfactory agreement between simulated and experimental data was found and results show that the model successfully predicted the temporal evolution of thermo-acoustic combustion instabilities.