The flutter of an airfoil is a typical self-excited vibration phenomenon caused by the interaction of aerodynamic,structural,and inertial forces. Hopf bifurcations of a two dimensional airfoil with structural nonlinear stiffness restoring force are studied in this paper. Firstly,the existence of non-degenerate co-dimension one Hopf bifurcation in the two dimensional airfoil is studied by an explicit criterion of Hopf bifurcation of continuoustime dynamical systems. The first Lyapunov coefficient is derived to analyze the stability of the created limit circle after bifurcation. Secondly,the existence conditions of degenerate co-dimension two Hopf bifurcations are analyzed to obtain a twoparameter bifurcation region. Then,the second Lyapunov coefficient is derived to analyze the stability of codimension two Hopf bifurcations and local unfolding near co-dimension two bifurcation points with the centre manifold theory and automorphism transformation. Finally,the third Lyapunov coefficient is derived to analyze the stability of codimension three Hopf bifurcations by using numerical simulation method.