The suppression of pressure oscillations in combustion chambers through the use of active feedback control is a new technology with high potential. In this article, we present a feedback control strategy based on an Internal Model Control System for nonlinear plants that uses artificial neural networks. This control system uses two neural networks: The Internal Model which approximates the plant forward dynamic; and a controller which gives the appropriate control input. The controller's parameters are updated adaptively for that purpose. We demonstrate numerically the capabilities of the developped control system in a numerical simulation of control of combustion instabilities. Then, we demonstrate the ability of this neural networks based control system to actively damp instabilities in a Rijke-tube burner.