Abstract: An electro-hydraulic braking system for motor vehicles. The system includes a brake pedal and a braking device associated with at least one vehicle wheel which is brought into communication with an electronically controlled valve arrangement in order to apply hydraulic fluid under pressure to the braking device. A fluid pressure accumulator fed by the pump provides a pressurized hydraulic fluid which can be passed to the braking device by way of an electronically controlled valve arrangement in order to apply hydraulic fluid in proportion to the driver braking demand as sensed at the brake pedal in the “brake by wire” mode. A first device within the system provides a level of fluid pressure supply within the electro-hydraulic system whose highest value is less than that sufficient for the maximum possible braking demand level which may be required.