The invention concerns a device for the non-contact measurement of the position of the teeth (13) of a workpiece (14) with precut teeth on a gear finishing machine. The measuring probe, retractable from the measuring position into a position of rest protected against soiling, is arranged in a holder (5) for radial and axial adjustment relative to the workpiece, the said holder (5) being a kinematic member of a parallelogram linkage (A) and by means of a hydraulic, pneumatic or electromechanical swivel drive (11) is swivellable from stop to stop between measuring position and position of rest in a plane containing the workpiece axis, such that in the advancement action from the lower end position to the top end position motions of the measuring probe (1) tangential to the workpiece circumference are completely avoided. The parallelogram kinematics moreover afford adequate protection against swarf and grinding dust, and lends the device a high stiffness and reliability.