A method and an apparatus for balancing an elongate structure (1) rotating about an axis, like a spindle (3) carrying two grinding wheels (5, 6), wherein two vibration-detecting sensors (7, 8) and associated balancing devices (9, 10) with movable masses (11-14) are arranged at two checking sections (S1, S2) spaced out along the axis of rotation. Processing and control means (20) control the balancing devices on the basis of one or more signals (VC; VC1, VC2) achieved as combination(s) of the vibrations, in module, detected by both the sensors.