In a future power supply system mainly based on renewable sources, long-term energy storage systems are crucial to replace the depleting fossil fuel reserves gradually and to balance seasonal fluctuations of energy generated by wind and sunlight. The strategy of choice comprises chemical energy carriers of high energy density, which can be generated within the “power-to-chemicals” concept using renewable H₂ from water electrolysis and the greenhouse gas CO₂. Such reactions and processes are well studied during steady state operation. However, for the utilization of power from fluctuating renewable sources, the processes and especially the catalyst systems must tolerate the dynamic supply of energy and, thus, H₂. Therefore, new challenges in process control and catalyst design arise keeping in mind that the catalyst itself is also a dynamic system. In this thesis, the methanation of CO₂ was studied as an exemplary reaction to produce a chemical energy carrier with a fluctuating H₂ supply to gain first insights into the dynamics of the process and its impact on the catalyst structure and performance.