A method for removing dissolved gases comprising oxygen and nitrogen from water in a degassing device comprising - a first and a second closed degassing container (5, 6) which each have first and second container installations to bring a liquid phase and a gaseous phase in contact and - a negative-pressure generating device which is adapted to generate variously high negative pressures in relation to the ambient pressure in the first and second degassing container (5, 6) wherein a suction side of the negative-pressure generating device below the second container installations in the second degassing container but above the water level collecting at the bottom of the second degassing container is connected in a fluid-conducting manner to the interior of the degassing container, comprising the steps: - continuously introducing water into the first degassing container at a water temperature T1 and a vapour pressure P1 given at the water temperature T1, - passing the water through the first degassing container, - generating a negative pressure in the first degassing container above the given vapour pressure P1 in such a manner that at least the predominant portion of the dissolved oxygen is removed from the water, - continuously removing the partially degassed water from the first degassing container, - continuously introducing the removed and partially degassed water into the second degassing container at a water temperature T2 and at a vapour pressure P2 given at the water temperature T2, - passing the partially degassed water through the second degassing container, - generating a negative pressure in the second degassing container at the given vapour pressure P2 in such a manner that the water partially evaporates, - passing the steam in direct flow with the water through the second degassing container, - extracting the steam from the second degassing container with the negative-pressure generating device, - removing the degassed water from the second degassing container. - a first and a second closed degassing container (5, 6) which each have first and second container installations to bring a liquid phase and a gaseous phase in contact and - a negative-pressure generating device which is adapted to generate variously high negative pressures in relation to the ambient pressure in the first and second degassing container (5, 6) wherein a suction side of the negative-pressure generating device below the second container installations in the second degassing container but above the water level collecting at the bottom of the second degassing container is connected in a fluid-conducting manner to the interior of the degassing container, - continuously introducing water into the first degassing container at a water temperature T1 and a vapour pressure P1 given at the water temperature T1, - passing the water through the first degassing container, - generating a negative pressure in the first degassing container above the given vapour pressure P1 in such a manner that at least the predominant portion of the dissolved oxygen is removed from the water, - continuously removing the partially degassed water from the first degassing container, - continuously introducing the removed and partially degassed water into the second degassing container at a water temperature T2 and at a vapour pressure P2 given at the water temperature T2, - passing the partially degassed water through the second degassing container, - generating a negative pressure in the second degassing container at the given vapour pressure P2 in such a manner that the water partially evaporates, - passing the steam in direct flow with the water through the second degassing container, - extracting the steam from the second degassing container with the negative-pressure generating device, - removing the degassed water from the second degassing container.