An apparatus for the maintenance of wheels of vehicles, like a balancer or a device for mounting/dismounting tires, comprises a support adapted to support a rim of a wheel of a vehicle. A device for detecting the eccentricity of a tire of the wheel is mounted on the support. Such device comprises an optical system configured to capture a light beam reflected by a tread of the tire and focus it on a point of an optical sensor. The optical sensor emits a signal indicative of an average value of a radial distance of the linear portion from the main axis. A control unit processes a plurality of average values corresponding to different linear portions of the tread and obtained during the rotation of the tire, and detects the eccentricity of said tire.