Self–excited combustion oscillations arise from a coupling between unsteady combustion and acoustic waves, and can cause structural damage to many combustion systems. Active control provides a way of extending the system's stable operating range by interrupting the damaging thermoacoustic interaction. The active controller considered injects some fuel unsteadily into the burning region, thereby altering the heat–release rate, in response to an input signal detecting the oscillation. Although the feasibility of such a control configuration was demonstrated on laboratory–scale experiments over 15 years ago, the triple requirement for full–scale applications is to adapt the controller response to varying operating conditions and to guarantee that the controller will cause no harm, while relying as little as possible on a particular combustion model. As a first step towards meeting these requirements, a self–tuning regulator (STR) is proposed in this paper for a class of combustion systems that satisfy some fairly non–restrictive assumptions. An open–loop transfer function from the controller output voltage driving the actuator to the pressure signal detecting the oscillation is derived, and is shown to be the product of a time delay τtot and a transfer function that satisfies certain structural properties. Using the open–loop transfer function, it is shown that the stabilizing STR structure is that of a simple phase–lead compensator if τtot=0, and the same compensator combined with a Smith controller if τtot=0. The adaptive rule for the adjustment of the STR parameters is derived from a Lyapunov stability analysis. Promising results are obtained on a simulation based on a nonlinear premixed flame model and on an experimental set–up which consists of a laminar flame burning in a Rijke tube.