Provided is a balancing device for a rotating body defining an axis of rotation, including a plurality of balancing heads aligned along the axis of rotation, each balancing head including: balancing masses configured to be moved at least along a circumference of movement so as to cancel the unbalance of the rotating body; at least one motor configured to move the balancing masses independently, the balancing masses part of different balancing heads being mutually spaced along the axis of rotation; unbalance detecting means including a plurality of vibration detectors configured to measure the vibrations caused by the unbalance of the rotating body.