An evasion and brake-assist system for motor vehicles, having a sensory system for sensing the traffic environment of the vehicle, an actuator system for interventions in a steering system and a brake system of the vehicle, and having an electronic control device in which an emergency evasion function is implemented that checks whether an emergency evasive maneuver is necessary based on the data supplied by the sensory system and then acts on the dynamics of the vehicle via the actuator system to assist the vehicle driver in initiating and/or executing the emergency evasive maneuver, characterized in that in the first phase of an evasive maneuver, the emergency evasion function intervenes exclusively in the transverse dynamics, and only after this phase, decides whether an intervention in the longitudinal dynamics will also take place.