A wind turbine system is described comprising a plurality of wind turbine modules, each including a rotor, mounted to a support structure including a tower. In use, each rotor has an associated rotating unbalance that defines an unbalance vector. The wind turbine system includes control means configured to coordinate the rotational speeds of the plurality of rotors to attenuate oscillations of the support structure caused by the rotating unbalance of the rotors. Also described is a method of controlling such a wind turbine system. The method comprises coordinating the rotational speeds of the plurality of rotors to attenuate oscillations of the support structure caused by the rotating unbalance of the rotors.