Abstract: A moving-weight, dynamic balancing apparatus for a rotary machine, in particular an industrial fan, having a rotary shaft, and at least one rotor carried by the rotary shaft and provided with main rotor bearings to allow rotary movement thereof. The balancing apparatus includes at least one moving-weight balancing unit is carried by the rotary shaft, and at least one monitoring and correcting system having a drive assembly. The at least one monitoring and correcting system monitors and corrects the unbalanced state of the rotor, and acts continuously on the at least one moving-weight balancing unit when the rotor is rotating to monitor and correct for rotor unbalance. The at least one moving-weight balancing unit has at least two balancing masses mounted to be movable under drive from the drive assembly controlled by the monitoring and correction system.