A method of controlling travel behavior of a vehicle provides assistance to the driver of the vehicle before the occurrence of travel conditions which are difficult to control. A vehicle taking a curve tends not to follow the travel curve indicated by steering, often resulting in understeering as the travel speed increases. At very high speeds in a curve, such behavior can lead to conditions that are difficult for the driver to control. Rather than intervening when an unstable travel state is already present and control of the vehicle rendered difficult, as practiced in conventional systems and processes for the regulation of travel dynamics, the wheel brake of a rear wheel of the vehicle on the inside of the curve is already subjected to a weak braking force when a relatively minor tendency to understeer occurs, so that the understeering tendency is reduced or eliminated.