A braking system for an aircraft with electric brakes comprising plural electromechanical actuators (2). The system comprises a braking control unit (20) delivering a normal braking setpoint (21) for one or more controllers (10) of the actuators, and selection logic (15) for causing the braking system to operate in a plurality of modes. The system includes: a normal braking mode where the control unit generates a normal braking setpoint (21) for the controller(s); an ultimate braking mode, having priority over the normal braking mode, being responsive to a parking control member, and controlling actuators to respond to the actuation of the parking control member; and a parking braking mode, applied in response to the parking control member and only if the aircraft is stationary, in which the actuators are controlled to apply a force in response to the parking control member being actuated and are then blocked in position.