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In this study a new approach for investigating the flutter speed of nonlinear aeroelastic systems is proposed. In this approach, the compatibility of nonlinear random vibration analysis based on the statistical properties of response is used and extended to the nonlinear aeroelastic systems to analyze the instability of these systems with using neither time domain analysis nor limit cycle oscillations. To this aim a 2-degree nonlinear airfoil with cubic torsional spring under quasi steady flow is considered as an aeroelastic system. At first, one random Gaussian white noise is added to the aerodynamic lift force then the statistical linearization and the random vibration analysis of the nonlinear systems are used to obtain a nonlinear map of response-variance with flow velocity as the control parameter. This nonlinear map leads to a nonlinear algebraic equation which consists of two parameters as the flow velocity and variance of the response. By solving this nonlinear equation for various flow velocities, the flutter speed is considered as the maximum of response-variance. Finally the jump phenomenon is also investigated where tangent bifurcation occurs.