Abstract: In order to study the global stability of high performance aircrafts at high angle-of-attack, we set up the nonlinear dynamical equations of an aircraft and the models of aerodynamic coefficients. The theory of stability of differential equations is used to calculate and analyse the aircraft. The relation between the stability criteria commonly used in aircraft design, such as （CnB）dyn and LCDP etc., and eigenvalues of the linearized matrices at the equilibrium points is discussed. It is believed that these criteria can be deduced from the linearized matrices of the aircraft nonlinear dynamic system at a specific flight state, therefore, they can predict the local stability of an aircraft at high angle-of-attack only. So the global stability of an aircraft must be analysed by the method presented in this paper. Finally, the relation between equilibrium point, periodic attractor etc. and some high angle-of-attack flight phenomena, such as wing rock, departure and spin etc. is pointed out and confirmed by the time history study.