A fitting head has a sleeve receptacle and a widener, the fitting head being displaceable forward/backward in the direction of the longitudinal axis of a wire. Also arranged on the fitting head are a transmitter and a receiver. The transmitter generates a curtain-like beam that is positioned between the sleeve receptacle and the widener and can be measured by the receiver. Like the sleeve receptacle and the widener, transmitter and receiver are displaceable forward/backward in the longitudinal axis of the wire, during the forward movement the wire fitting or sleeve being fitted onto the wire and during the backward movement the sleeve being positionally measured. The movement of the fitting head is measured by a stationary measuring head and a scale that moves together with the fitting head. During evaluation of the measurement results, fitting faults are detected.