<p>In this paper, a method based on an integro-differential equation approach for investigating the response of a strongly nonlinear two-degree-of-freedom system subject to sinusoidal forcing is presented and applied to a set of equations based on an aeroelastic model of an all-moving control surface with a nonlinearity in its root support in supersonic flow. The method is shown to be able to accurately determine primary and subharmonic resonances together with symmetry-breaking and period-doubling responses. Additionally, their stability has been investigated using a Harmonic Balance-based implementation of Floquet theory which is a modification of a method previously used for autonomous systems. This method was validated by comparison with time domain derived Floquet multipliers, and comparisons between the two sets of values showed very close agreement. The study also highlighted several areas for further investigation.</p>