A theoretical analysis of the incompressible bending-torsion flutter of a two-dimensional airfoil with nonlinear structural characteristics is presented. The Method of Slowly Varying Parameters of Kryloff and Bogoliuboff is applied, and the steady-state oscillations are found. The stability of the steady-state oscillation is analyzed through the use of perturbation equations. A quasi-steady aerodynamic approximation is used, and closed-form solutions for the steady-state oscillations are found for the case of elastic torsional nonlinearities. A numerical example of a soft-hard stiffness characteristic is treated, and the steady-state and stability results given.