Gust interaction is a crucial design consideration for civil aircraft. A gust disturbance is defined as any air velocity component normal to the flight path. Gust interactions can rapidly change the aerodynamic forces acting on a wing and in turn the loads on the aircraft. Indeed, during this interaction, the structure of the aircraft may experience significant dynamic loading. It is therefore desirable to utilise gust load alleviation systems in aircraft design. This thesis investigates the influence of nonlinear structural behaviour in aeroelastic systems for gust load alleviation. In conjunction to the study of nonlinearities in structures, numerical methods for the fast prediction of stability and dynamic response for the nonlinear aeroelastic systems are required. To this end, this thesis investigates the nonlinear model order reduction framework based on eigenmode decomposition. The nonlinear model reduction approach based on eigenmode decomposition is formulated and extended to include expansion terms up to fifth order such that higher-order nonlinear behaviour of a physical system can be captured. The method is first applied to a two degree-of-freedom pitch-plunge aerofoil structural model in unsteady incompressible flow. Structural stiffness nonlinearity is introduced as a fifth-order polynomial, while the aerodynamics follow linear theory. It is demonstrated that the reduced-order model is capable of accurately capturing the nonlinear aeroelastic behaviour arising from gust excitation. Furthermore, an analysis of the computational cost associated with constructing such reduced-order model and its applicability to more complex aeroelastic problems is provided. The model reduction approach is then extended for a full-scale passenger aircraft exhibiting geometric structural nonlinearity. A structured approach to identify the dominant modes required to construct an accurate reduced-order model for such nonlinear aeroelastic system is presented. The effect of structural nonlinearities are studied through time domain gust response calculations and the reduced order model results are compared against the full-order reference solution. It is demonstrated that both the linear and nonlinear reduced-order models are capable of accurately predicting the dynamic gust response of aircraft structures while achieving significant reduction in system size.