The nonlinear dynamical behavior of a laterally compressed, flat, composite panel subjected to a high supersonic flow is analyzed. The structural model considers a higher-order shear deformation theory which also includes the effect of the transverse normal stress and satisfies the traction-free condition on both faces of the panel. The possibility of small initial imperfections and in-plane edge restraints are also considered. Aerodynamic loads based on the third-order piston theory are used and the panel flutter equations are derived via Galerkin’s method. Periodic solutions and their bifurcations are obtained by using a predictor-corrector type of numerical integration method, i.e., the Shooting Method, in conjunction with the Arclength Continuation Method for the static solution. For the perfect panel, the amplitudes and frequency of flutter obtained by the Shooting Method are shown to compare well with results from the Method of Multiple Scales when linear aerodynamics is considered and compressive loads are absent. It is seen that the presence of aerodynamic nonlinearities could result in the hard flutter phenomenon, i.e., a violent transition from the undisturbed equilibrium state to that of finite motions which may occur for pre-critical speeds also. Results show that linear aerodynamics correctly predicts the immediate post-flutter behavior of thin panels only. When compressive edge loads or edge restraints are applied, in certain cases multiple periodic solutions are found to coexist with the stable static solution, or multiple buckled states are possible. Thus it is seen that the panel may remain buckled beyond the flutter boundary, or it may flutter within the region where buck-led states exist. Furthermore, the presence of edge restraints normal to the flow tends to stabilize the panel by decreasing the flutter amplitudes and the possibility of hard flutter. Nonperiodic motions (i.e., quasiperiodic and chaotic) of the buckled panel are found to exist, and their associated Lyapunov exponents are calculated. The effects of transverse shear flexibility, aerodynamic nonlinearities, initial imperfections, and in-plane edge restraints on the stability boundaries are also studied. It is observed that the classical plate theory over-predicts the instability loads, and only the shear deformation theory correctly models the panel which is flexible in transverse shear. When aerodynamic nonlinearities are considered, multiple flutter speeds may exist. / Ph. D.