Machine for balancing vehicle wheels includes: a base frame supporting elements for gripping and rotating a wheel around a balancing axis; first sensor elements associated with the gripping and rotation elements for detecting the unbalance of the wheel; an electronic processing and control unit associated with the first sensor elements for calculating a balancing weight to apply onto the wheel; and an auxiliary detection appliance associated with the base frame and having: a rolling device for pressing onto the wheel, and in turn including: a support structure for two rollers revolving around axes parallel to each other; and a flexible member closed on itself in a loop, wrapped around the rollers and having a substantially flat active section, and a return section substantially opposite the active section; and second sensor elements associated with the rolling device for detecting the behaviour of the wheel when pressed by the rolling device.