Electrolysis system for electrochemical decomposition of water to afford hydrogen and oxygen comprising: - at least one electrolyzer for electrochemical decomposition of water to afford hydrogen and oxygen, wherein the electrolyzer comprises a periphery which comprises conduits (9, 11, 12, 15) and a first heat exchanger, - a first gas separation apparatus for separation of oxygen and water and a second gas separation apparatus for separation of hydrogen and water, wherein the gas separation apparatuses (20, 21) are at a height above the electrolyzer so that a natural circulation of the reactants and products in the electrolyzer is ensured solely as a result of the density differences arising in the electrolyzer, - a housing apparatus for receiving the electrolyzer, wherein the entire electrolyzer and the gas separation apparatuses (20, 21) are arranged in the housing apparatus and the housing apparatus is tightly sealed off from a first fluid surrounding the housing apparatus, wherein a first pressure inside the housing apparatus is higher than a second pressure outside the housing apparatus, - wherein the housing apparatus comprises a second heat exchanger for thermal equalization of the temperature in the housing apparatus and outside the housing apparatus, - and wherein the gas separation apparatuses (20, 21) are connected via a respective conduit (12, 15) to the first heat exchanger and via a respective conduit (9, 11) to the corresponding side of the anodic and the cathodic side of the electrolyzer, wherein the water circuits of the hydrogen and oxygen side are connected to one another via the first heat exchanger and the conduits (9, 11) respectively pass oxygen-water mixture to the first gas separation apparatus and hydrogen-water mixture to the second gas separation apparatus. - at least one electrolyzer for electrochemical decomposition of water to afford hydrogen and oxygen, wherein the electrolyzer comprises a periphery which comprises conduits (9, 11, 12, 15) and a first heat exchanger, - a first gas separation apparatus for separation of oxygen and water and a second gas separation apparatus for separation of hydrogen and water, wherein the gas separation apparatuses (20, 21) are at a height above the electrolyzer so that a natural circulation of the reactants and products in the electrolyzer is ensured solely as a result of the density differences arising in the electrolyzer, - a housing apparatus for receiving the electrolyzer, wherein the entire electrolyzer and the gas separation apparatuses (20, 21) are arranged in the housing apparatus and the housing apparatus is tightly sealed off from a first fluid surrounding the housing apparatus, wherein a first pressure inside the housing apparatus is higher than a second pressure outside the housing apparatus, - wherein the housing apparatus comprises a second heat exchanger for thermal equalization of the temperature in the housing apparatus and outside the housing apparatus, - and wherein the gas separation apparatuses (20, 21) are connected via a respective conduit (12, 15) to the first heat exchanger and via a respective conduit (9, 11) to the corresponding side of the anodic and the cathodic side of the electrolyzer, wherein the water circuits of the hydrogen and oxygen side are connected to one another via the first heat exchanger and the conduits (9, 11) respectively pass oxygen-water mixture to the first gas separation apparatus and hydrogen-water mixture to the second gas separation apparatus.