Electro-hydraulically boosted hydraulic braking system having a master cylinder (100) including a thrust chamber (105) and on command receives pressurized brake fluid from an accumulator (300) via an electrically operated valve (200) controlled by a computer (400) on the basis of the signal supplied by the brake pedal (411) sensor (410), and an electrical power source (450) powering at least the electrically operated valve (200), the computer (400) and the sensor (410). An auxiliary generator (470) is connected in a manner that is controlled (472) by the computer (400) to the circuit (L0, L1, L2, L3) powering the computer (400), the sensor (410) and the electrically operated valve (200) if failure of the main source (450) is detected so as to allow emergency operation of the electrically operated valve (200) and allow the brake circuit (C1, C2) to be powered for a limited number of braking actions.