Vehicle cornering system is a complicated system, the nonlinear tire force makes cornering system present strong nonlinear. The nonlinear model of the vehicle cornering system is established and the theory of nonlinear dynamics is introduced in this paper. Through the analysis of the character of the singular point, the influence of the geometrical character of the tyre and the longitudinal acceleration to the handling stability is studied, and the longitudinal acceleration is added to the stability condition, which deepen the study of the handling stability.