A method for handling of an offshore wind turbine component includes using a vessel having a hull on which a motion compensating crane is mounted. The crane includes a main boom; a main boom luffing assembly; a mobile hoist cable suspension member; and a hoist winch and a hoist cable driven by the hoist winch. An object suspension device is suspended from the hoist cable. The mobile hoist cable suspension member is supported by a motion compensating support device that is fitted to the tip end of the main boom, the motion compensating support device including one or more motor powered motion displacement actuator assemblies and a motion compensating support device controller. The method includes connecting the offshore wind turbine component to the object suspension device; and operating the motion compensating support device to provide motion compensation in at least one direction of the object suspension device and the connected offshore wind turbine component. The crane is provided with one or more nacelle position detectors that are configured and operated to sense at least one of actual position and actual motion of the nacelle or of one or more components in or on the nacelle, and the one or more nacelle position detectors are linked to the motion compensating support device controller.