Reversible electrochemical system, having first anode and cathode ports and opposite second anode and cathode ports, intended to operate alternately: - in electrolysis cell mode in which it is suitable for receiving water to be electrolyzed at the first anode port and for supplying oxygen to the second anode port and hydrogen to the second cathode port, and - in fuel cell mode, in which it is suitable for receiving hydrogen at the second anode port and oxygen at the second cathode port and for supplying water to the first cathode port; comprising a primary electrochemical device comprising a membrane electrode assembly, comprising a primary anode and a primary cathode separated by a primary proton-exchange membrane, ∘ the primary anode, connected to the first anode port and to the second anode port, being suitable for carrying out an oxidation of the water originating from the first anode port and an oxidation of the hydrogen originating from the second anode port; ∘ the primary cathode, connected to the first cathode port and to the second cathode port, being suitable for carrying out a reduction of protons, and a reduction of oxygen originating from the second cathode port; characterized in that it comprises a secondary electrochemical device comprising a membrane electrode assembly, comprising a secondary anode and a secondary cathode separated by a secondary proton-exchange membrane, ∘ the secondary anode being connected to the primary anode and to the second anode port, and being suitable for carrying out an oxidation of hydrogen originating from the primary anode and an oxidation of hydrogen originating from the second anode port; ∘ the secondary cathode being connected to the primary cathode and to the second cathode port, and being suitable for carrying out a reduction of protons and a reduction of oxygen originating from the second cathode port. - in electrolysis cell mode in which it is suitable for receiving water to be electrolyzed at the first anode port and for supplying oxygen to the second anode port and hydrogen to the second cathode port, and - in fuel cell mode, in which it is suitable for receiving hydrogen at the second anode port and oxygen at the second cathode port and for supplying water to the first cathode port; ∘ the primary anode, connected to the first anode port and to the second anode port, being suitable for carrying out an oxidation of the water originating from the first anode port and an oxidation of the hydrogen originating from the second anode port; ∘ the primary cathode, connected to the first cathode port and to the second cathode port, being suitable for carrying out a reduction of protons, and a reduction of oxygen originating from the second cathode port; ∘ the secondary anode being connected to the primary anode and to the second anode port, and being suitable for carrying out an oxidation of hydrogen originating from the primary anode and an oxidation of hydrogen originating from the second anode port; ∘ the secondary cathode being connected to the primary cathode and to the second cathode port, and being suitable for carrying out a reduction of protons and a reduction of oxygen originating from the second cathode port.