One important road vehicle dynamics problem is the determination of the lateral stability of the vehicle. In this paper, stability results for a nonlinear model of the lateral stability problem are obtained using Liapunov's Second Method. The nonlinearities in the model are present because of the nonlinear relationships that exist between the lateral forces on the tires and the tire slip angles. Two Liapunov functions are presented which reproduce the well known stability criterion, the critical speed equation, for the classical linear model of the lateral stability problem. These two functions are then used to obtain stability conditions for the nonlinear problem. Finally, the stability results obtained with the two Liapunov functions are compared with each other and with digital computer simulations of the nonlinear equations of motion.