Some important advantages of composite materials such as their high weight to strength ratio, was the cause of their prevalent use in many industrial cases in past decades. Bi-stable structures are special kinds of composite structures that their ability to maintain in their stable configurations without any source of energy has made them suitable for morphing structures. The principal application of this type of composite structures is in the morphing airfoils where they are subjected to the aerodynamic loading in various flow regimes. Since many researches on the static and dynamic behavior of such interesting structures were reported in the literature, having a comprehensive insight into their aeroelastic behavior is of crucial importance. Considerable amounts of researche were done that focused on the thermal, static and dynamic behavior of these special composite panels; subsequently, the main goal of the present study is to determine time response into arerodynamic loading and stability analysis of cross-ply and angle-ply bi-stable composite panels. Therefore, a specially-written MATLAB code based on the Rayleigh-Ritz technique is provided to compute statically stable states of [0/90] cross-plies. In this investigation the mechanical properties of the composite material was considered as functions of temperature. Moreover, the effects of large out-of-plane displacemnets were modeled considering nonlinear von-K?rm?n strain terms in estimation of in-plane strain fields. Afterwards, using the Rayleigh-Ritz model in conjunction with Hamilton principle and considering first order quasi-steady aerodynamic theory (linearized piston theory) as a simple and suitable model for aerodynamic loading in supersonic flow regime, time responses of the panel, FFT of them and their phase diagrams of were obtained. Then an aeroelastic Finite Element model were provided in ABAQUS (an FEM package) to evaluate the validity of the results obtained by Rayleigh-Ritz approach and calculate the aeroelastic time response and stability of angle-ply bi-stable laminated composite planels. In this FE model the panel was modeled as a shear deformable composite shell considering the effect of large out-of-plane displacements due to its nonlinear geometry. Considering the fact that ABAQUS dose not have the capability to apply a kind of loading that is dependent to time and spatial derivatives of out-of-plane translational DoF (linearized piston theory) as a typical loading, a DLOAD FORTRAN subroutine were provided to model the aerodynamic loading. The time response and stability analysis results have shown that depending on the dynamic pressure and the cured temperature of the panel, four major types of motion could happen. So, the motion could be dynamically stable at its thermally buckled configuration, aerodynamically buckled and dynamically stable, simple harmonic or non-harmonic but periodic limit cycle oscillations and chaotic motion. A comparison between Rayleigh-Ritz approach and FEM results for [0/90] cross-plies were made and acceptable agreement were demonstrated between them. Furthermore, the effects of aerodynamic damping parameter and fiber orientation on LCO’s maximum amplitude of some angle-pleis were evaluated. Keywords : Bi-stable laminated composite structures, Finite element method, Limit cycle oscillations, Linerized piston theory, Morphing airfoils, Rayleigh-Ritz technique, Supersonic flow regime