The effects of a freeplay structural nonlinearity on an aeroelastic system are studied experimentally. Particular attention is paid to the stability of a periodic nonlinear aeroelastic response, known as limit–cycle oscillations (LCOs). The major thrust of this research lies in the application of relatively recently developed techniques from nonlinear dynamics and signal processing to the realm of experimental aeroelasticity. Innovations from the field of nonlinear dynamics include time–delay embedded coordinates to reconstruct system dynamics, a Poincaré section to assess the periodic nature of a response and to prescribe an operating point about which a linear description of the dynamics can be approximated, stochastic perturbations to assess the stability and robustness of responses, and a basin of attraction measure to assess initial condition dependence. A novel system–identification approach is used to generate a linear approximation of the experimental system dynamics about the LCO. This technique makes use of a rotating slotted cylinder gust generator and incorporates a least–squares fit of the resulting transient dynamics. An extension to this method is then developed based on the outcome of relatively large disturbances to the flow and hence airfoil, to obtain global stability.