The goal of our project is to mimic fish-like movement in air, propelling an airship by undulating its hull and a caudal fin. The activation of the fish-like body in air is realized by dielectric elastomers. These actuators are quite unique for their soft light-weight membrane structure and they are therefore very appropriate to the application on inflated structures. The principles of biomimetics for the structural design and movement are discussed and the conception and design of the airship is described. Various development tests, including wind tunnel testing and flight trials, were performed and the results obtained are presented. It can be shown that an 8 m model airship can be propelled in a fish-like manner in air and that the propulsion can be drastically improved by undulating the body as well as the caudal fin contrary to propulsion with only the caudal fin.