An electro-hydraulic braking system for motor vehicles which comprises a brake pedal, a braking device which is associated with at least one vehicle wheel and is capable of being brought into communication with an electronically controlled valve arrangement in order to apply hydraulic fluid under pressure to the braking device, a hydraulic pump, and a fluid pressure accumulator fed by the pump, for the provision of pressurized hydraulic fluid which can be passed to the braking device via the electronically controlled valve arrangement, in order to apply hydraulic fluid under pressure, in proportion to the driver's braking demand as sensed at the brake pedal, to the braking device in a ‘brake by wire’ mode, a first means which 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 to be met in use of the vehicle, and a second means which, upon recognition of a braking demand level or of a potential braking demand level which exceeds or will exceed that which can be achieved by said highest value of fluid pressure supply available via said first means, establishes a higher level of fluid pressure supply within the system for controlling the brakes in accordance with the driver's demanded braking level, characterized in that said second means is adapted to start the pump to charge the accumulator to a higher level, either when the demanded pressure level rises to a level which is higher than that which is currently available from the accumulator, or in advance of a high demand condition, in accordance with a detected or predicted level of brake fade, or lining fade change.