An electricity supply system having double power-storage devices which is suitable for implementation in an electric or hybrid motor vehicle. The supply system is intended for being connected to a power network of the vehicle. The supply system is of the type that includes a first power-storage device, having a first specific energy, a first specific power and a first operating voltage (Ue), and a second power-storage device, having a second specific energy that is lower than the first specific energy, a second specific power that is higher than the first specific power and a second operating voltage (Up) that is higher than the first operating voltage (Ue). The first and second power-storage devices are electrically coupled by a bidirectional DC-DC converter controlled in accordance with the operating states of the vehicle. The DC-DC converter includes a floating capacitor connected in series between the first and second power-storage devices.