A technique aimed at neutralizing the presence of free-play effects in a control surface actuation chain is presented. It is based on an adaptive inversion of a function approximating such a nonlinearity. A simple, yet robust, on-line adaptive algorithm is proposed to identify the free-play parameters, i.e. free-play width, the equivalent control stiffness and friction. The procedure is then coupled to an immersion and invariance control law to drastically reduce possible residual closed-loop limit cycle oscillations due to the free-play nonlinearity. Within such a framework, the so chosen compensation technique can be interpreted as a control augmentation, easily extendable to multiple control surfaces. The methodology is then verified on a four-degree-of-freedom airfoil in a transonic regime, characterized by highly nonlinear unsteady aerodynamic loads, producing significant shock motions and large limit cycles, at a relatively high frequency. The presence of both aerodynamic and structural nonlinearities makes such a system bistable, leading to complex responses dependent on the initial conditions and the input used to excite the system. The effective suppression of these auto-induced vibrations becomes even more challenging because the limit cycle oscillations generated by different sources are characterized by differing amplitudes and frequencies.