Abstract: Aircraft global dynamic stability in maneuver is studied by using the main theorems of bifurcation and catastrophe theory, and qualitative theory of differential equation. An analytical formula for determining the critical steady-state value of roll rate is generated in the state-control space, and the phillips criteria is merely a special case. Nonlinear jump and periodic oscillation phenomena are discussed in detail, and the main factors of causing these phenomena are found. And finally, the effect of the negative feedback on control parameters from state parameters on stable regions in control variables space is studied.