The transformation of the European energy system in order to reduce greenhouse gas emissions requires the development of Renewable Energy Sources (RES). In future the intermittent feed-in of wind and solar power will result in energy surpluses. Using Power-to-Gas (PtG) technology, these surpluses can be converted into methane and stored in the natural gas infrastructure afterwards. Because of its characteristics, PtG influences both, the power and natural gas systems. To analyze the effect, calculations based on a cost minimizing simulation approach are performed in this paper for an RES dominated European scenario in 2050. The results show that energy surpluses occur with high power but in relatively few hours. PtG plants can store parts of these surpluses but also integrate additional base-load power into the system. Since the influence on the natural gas system turns out rather marginal, the natural gas infrastructure can be considered suitable for long-term energy storage.