Abstract: Aiming at addressing the loss of stability in lateral motion of hypersonic gliding vehicle with high angle of attack, the bifurcation theory and the continuation approach were used to obtain the branches of the steady equilibria where the elevator was considered as a continuation parameter. Meanwhile, the lateral maneuver branches of equilibria were also computed where the aileron was employed as a continuation parameter for the selected characteristic points. Then, the stability and bifurcation points were analyzed in detail, and the topologies for the 5 dimension model were given. It was found that the limit points, Hopf points and branch points exist for the branches. The pitchfork branches were stretched out from the BP points where the loss of stability for auto-rotation was triggered; the branches extending out from the Hopf point were also researched in detail where the complicated limit circle motion was presented involving perioddoubling bifurcation, Neimark-Sacker bifurcation, limit point of circle bifurcation etc.; furthermore, through analyzing the branches of equilibria for lateral maneuver condition, problems of loss of stability for maneuver, multi-equilibrium points and loss of stability for lateral control dynamics exist. The results of the research could provide the important dynamic information for realizing the flight stability and designing of the controller.