Abstract: A device for balancing rotating bodies including a sensing arrangement for sensing the out of balance of the rotating body and for abrasion tool at a frequency corresponding to the speed of the rotating member so as to remove material from the rotating member in phase with the working vibration in the same region of the rotating member for effecting a balancing of the rotating member. The apparatus also includes an adjusting arrangement enabling adjustment of the phase relationship of the vibration of the abrasion tool with respect to the phase relationship of the out-of-balance signal so as to effect shifting by any number of steps of 360.degree./n, n being a whole number>3, irrespective of the speed of the rotating member.