System for controlling the stability of a vehicle, the system comprising means for imparting a longitudinal force to the tire and means for calculating a slip G.sup.Opt by determining the values of the coefficient of friction .mu..sub.i, for each slip G.sub.i corresponding to successive levels "i", using in parallel "n" calculation algorithms each determining a target value of the slip making it possible thus to obtain as many target values G.sup.Cn as there are algorithms used, the system selecting the best of the target values G.sup.Cn as the optimum slip value G.sup.Opt by subjecting the "n" target values G.sup.Cn to comparisons aimed at eliminating the least likely target values, the comparisons being made on the basis of a function f(.lamda.) of a descriptor of the physical functioning of the rotation of the tire on the ground making it possible to calculate characteristic values. For example, one interesting characteristic value is the variation in G with respect to time.