In order to investigate the nonlinear behaviour which leads the vehicle steady-state cornering to destabilization, a 4—D (four-dimensional) nonlinear vehicle lateral dynamic system consisting of the roll and the planar motions was founded utilizing a quadratic tire model. Considering the relation between the vehicle destabilization and the saddle-node bifurcation in critical conditions, a method for analyzing vehicle steady-state cornering stability was proposed based on the real-time tracking of the closest bifurcation point. The objective is to compute the shortest distance from the current operating point to bifurcation by iteration method in the u—δf parameter space to evaluate the steady-state cornering stability margin. Testing computation conducted in symmetrical and μ-split conditions respectively demonstrates that the closest bifurcation point can be found after a short-time iteration which satisfies the real-time computation demand and this method can provide valuable information for vehicle stability control system.