To achieve a reduction of the concentration of carbon dioxide in the atmosphere in a long term contraction, it is necessary to implement new technologies like Power to Gas. The electricity, produced from renewable energy sources, is used for water electrolysis in the Power to Gas system. In the water electrolysis pure hydrogen and oxygen are produced. In the following methanation the hydrogen is used to react with carbon dioxide and generate methane and water. The produced methane can be liquefied in a liquefaction process or can be fed in a natural gas grid if present. Several technologies to provide the carbon dioxide for the methanation exist, e.g. the Oxyfuel process or the possibility to strip the carbon dioxide from seawater. Requirement for the in this work investigated, self-sufficient Power to Gas system is an off-shore wind farm in which the whole energy for the total system is created. The whole system, including all process steps except the Oxyfuel plant, should therefore be built on an off-shore platform. The necessary mass flows also should be created or processed on the platform. In this thesis the requirements for a self-sufficient Power to Gas system are analyzed by determination the state of the art of all process steps as well as creating mass- and energy balances in consideration of the state of the art.