The nonlinear response of a swirl-stabilized flame to equivalence ratio oscillations was experimentally investigated in an atmospheric-pressure, high-temperature, lean-premixed model gas turbine combustor. To generate high-amplitude equivalence ratio oscillations, fuel was modulated using a siren type modulating device. The mixture ratio oscillations at the inlet of the combustion chamber were measured by the infrared absorption technique and the flame's response, i.e., the fluctuation in the flame's rate of heat release, was estimated by CH chemiluminescence emission intensity. Phase-resolved CH chemiluminescence images were taken to characterize the dynamic response of the flame. Results show that the amplitude and frequency dependence of the flame's response to equivalence ratio oscillations is qualitatively consistent with the flame's response to inlet velocity oscillations. The underlying physics of the nonlinear response of the flame to equivalence ratio oscillations, however, is associated with the intrinsically nonlinear dependence of the heat of reaction and burning velocity on the equivalence ratio. It was found that combustion cannot be sustained under conditions of high amplitude equivalence ratio oscillations. Lean blowoff occurs when the normalized amplitude of the equivalence ratio oscillation exceeds a threshold value. The threshold value is dependent on the mean equivalence ratio and modulation frequency.