The invention relates to an electrical braking system of a road vehicle in which at least two wheels (1) are rotatably connected to at least one rotary electrical machine (2) and each rotary electrical machine (2) co-operates with a single wheel, at least one electronic wheel control module (23) controlling the electrical machine(s) of one wheel, whereby each electronic control module can be used to impose a determined control torque selectively on the wheel in question, defined in terms of amplitude and sign, such that the wheel in question imposes a driving force or a braking force on the vehicle depending on the determined control torque. The invention is characterised in that it includes at least two sub-systems (A and B) which are connected to a central electrical line (40), each sub-system comprising: part of the above-mentioned wheels (1); the electronic control modules associated with each wheel of said part; a dissipation device controlled by an electronic dissipation module (60A, 60B); and a device which provides protection against over-currents (41A, 41B) and which can electrically insulate the sub-system from the central electrical line.