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In the present study, nonlinear flutter and post-flutter behavior of a variable stiffness composite wing-like plate is investigated. The variable stiffness is obtained by varying fiber angles continuously according to a selected curvilinear fiber path function in the composite laminates. Flutter speed, limit cycle oscillations and bifurcation diagrams of the composite plate are explored for three different fiber path functions using the nonlinear structural model obtained based on the virtual work principle. The paper aims to exploit the ideal fiber paths with enhanced aeroelastic flutter and post-flutter properties for a composite plate in supersonic flow speed. First-order linear piston theory is applied to model the aerodynamics, and generalized differential quadrature is employed to solve the governing equations. Von Karman nonlinear strain theory is used to account for the geometric nonlinearities, and first-order shear deformation theory is employed to consider the transverse shear effects in the structural model. Time integration of the equation of motion is carried out using the Newmark average acceleration method. Different curvilinear fiber paths are introduced to enhance flutter instabilities and post-flutter behavior of the composite plate. Results demonstrate that the fiber orientation has a significant effect on the dynamic behavior of the plate and the asymmetric properties as well as the behavior of the limit cycle oscillation.