Abstract: A balancing arrangement for a rotating member, especially for a hollow shaft made from light-weight metal, in which a counterweight of predetermined size and weight is affixed onto the external surfaces of the rotating member in predetermined position by the use of a clamping band made from a material normally devoid of any significant elastic stretchability. Elastic stretchability is imparted to the clamping band by specially configured sections which may be formed by openings or non-rectilinear lateral band portions which become less non-rectilinear in the presence of tensional forces in the band and which elastically return to a more non-linear shape when the tensional forces disappear. The internal surfaces of the counterweight and/or of the clamping band are provided with anchoring means to assure position retention thereof on the external surfaces of the rotating member.