Wing structures often contain nonlinearities which affect their aeroelastic behavior and performance characteristics. Aerodynamic flows at transonic Mach numbers generate nonlinear aerodynamic forces on the wing affecting the aeroelastic response of the wing. Analysis techniques accounting for these structural and aerodynamic nonlinearities, and an understanding of their potential influence on the flutter mechanism of two-dimensional and three-dimensional wing-structures model are the main objective of this study. Two different categories of structural nonlinearities, i.e. (i) distributed nonlinearity and (ii) concentrated nonlinearity , are considered. The concentrated nonlinearities are mathematically modeled using Asymptotic Expansion method which based on on the Krylov-Bogoliubov-Mitropolski technique. The effective stiffness coefficient of a nonlinear element is defined as the ratio of the amplitude of the Fourier series expansion of the load and the amplitude of the displacement of that element. The effects of distributed nonlinearities on the aeroelastic characteristic of three-dimensional wing model are also investigated. The influences of this type of nonlinearity is treated in a quasi-nonlinear approach, which allows the variation of the the natural frequencies and damping factor of the structure model with respect to the amplitude of the motion. The transonic aerodynamic pressure distributions have been obtained by solving the unsteady Transonic Small Disturbance ( TSD ) flow equation using finite-difference techniques. An Alternating Direction Implicit ( ADI ) algorithm was used for two-dimensional flow model, and an Approximate Factorization ( AF ) algorithm was used for three-dimensional flow model. The finite-state generalized aerodynamic forces used in the aeroelastic analysis have been calculated by employing the Method of Harmonic Oscillation and the Pulse Transfer Function analysis. The solution of the aeroelastic equation in frequency domain is obtained by representing the equation in a finite-state form through the modal approach using Lagrange’s equation. The flutter boundary is obtained by solving this equation using the classical U-g method and root locus analysis. Flutter analysis of a two degree-of-freedom , two-dimensional typical wing sections with nonlinear torsional springs are studied. The aeroelastic responses of the system are obtained by integrating the nonlinear structural terms and aerodynamic terms simultaneously using Newmark-β and Wilson-θ methods. Flutter results obtained from both time integration and eigenvalue solutions are compared. These two results, in general, are in agreement. Flutter behavior of a simple three-dimensional swept wing model is also investigated. Comparison of the flutter boundary obtained by using the eigenvalue solution with flutter data from wind-tunnel experiments are made. / Ph. D.