The invention relates to a method of clamping a tool or a workpiece, using an electric actuator (1) having a housing (2) attached to a work spindle of a machine tool and in which a threaded spindle (3) for moving jaws of a chuck is axially displaceable, and an electric servomotor (4) having a rotor connected with a drive wheel (6) that moves a nut (7) on the threaded spindle (3), a first sensor being associated with the threaded spindle (3) for detecting the axial position thereof, and a second sensor being associated with the spindle nut (7) for detecting the axial position thereof, and including the method step of determining the position of the threaded spindle (3) by the first sensor when a slight axial force occurs due to contact of the clamping jaws with the tool or the workpiece, and continued movement of the spindle nut (7) until a specified sensor difference (12) between the first sensor and the second sensor is determined by the second sensor. The invention further relates to an apparatus for carrying out the method.