In this thesis, the coupling effects of structural nonlinearities and a gust input on the aeroelastic behaviour of an airfoil are studied, and an adaptive controller which is effective for suppressing limit-cycle oscillations (LCOs) is designed. The dynamics of the airfoil are approximated via two- (pitch and plunge) and three-degree-of-freedom (pitch, plunge and flap) models. Different types of structural nonlinearities, such as free-play and hysteresis are considered in the modelling. The nonlinear dynamics is analyzed based on time history, power spectral density (PSD), phase-plane, and Poincar\'{e} section plots, along with the estimation of the dominant Lyapunov exponent for the chaotic-like motion. It is found that free-play and hysteresis nonlinearities may considerably reduce the critical flow velocity compared to the linear system. The dynamic responses of the nonlinear system to sharp-edged and 1-cosine gust profiles are obtained at different flow velocities and compared to those of the system with no gust input. In addition, basin of attraction is plotted to show the stability boundary of the system subjected to a sharp-edged gust with various amplitudes. It is discussed that as the gust becomes stronger, the likelihood of the occurrence of LCO increases. Based on the nonlinear model with a control surface, the suppression of LCO is studied. Without uncertainties, a PD controller together with a partial feedback linearized controller can effectively alleviate oscillations due to gusts and structural nonlinearities. Considering some uncertain structural parameters, an adaptive controller with estimation parameter update law is further designed to stabilize the system. A Lyapunov function is constructed and utilized to prove the stability of the system.