An attachment for an epilator or an epilator comprising: an axle arranged for driven movement around a centre axle axis; the axle being locked against movement in axial direction; an end plate arranged at a first end of the axle for rotation together with the axle, the end plate having at least a first functional surface and the end plate is an outer housing part of the epilator or the attachment for an epilator; wherein a clamping head is mounted on the axle and is arranged for epilating hairs at the lateral side of the attachment; a first clamping element having a functional surface; the first functional surface of the end plate being arranged face-to-face with the functional surface of the first clamping element 120A); the first clamping element being arranged for repeatedly being moved towards and away from the end plate such that repeatedly a closed position is obtained in which the two functional surfaces abut on each other, characterized in that it comprises a second clamping element having a functional surface that is face-to-face arranged with a second functional surface of the end plate, where the second functional surface of the end plate is circumferentially displaced from the first functional surface of the end plate and the second clamping element is circumferentially displaced from the first clamping element, the second clamping element being arranged for repeatedly being moved towards and away from the end plate such that repeatedly a closed position is obtained in which the two functional surfaces abut on each other, where the closed positions of the first clamping element and of the second clamping element are successively obtained. an axle arranged for driven movement around a centre axle axis; the axle being locked against movement in axial direction; an end plate arranged at a first end of the axle for rotation together with the axle, the end plate having at least a first functional surface and the end plate is an outer housing part of the epilator or the attachment for an epilator; wherein a clamping head is mounted on the axle and is arranged for epilating hairs at the lateral side of the attachment; a first clamping element having a functional surface; the first functional surface of the end plate being arranged face-to-face with the functional surface of the first clamping element 120A); the first clamping element being arranged for repeatedly being moved towards and away from the end plate such that repeatedly a closed position is obtained in which the two functional surfaces abut on each other, characterized in that it comprises a second clamping element having a functional surface that is face-to-face arranged with a second functional surface of the end plate, where the second functional surface of the end plate is circumferentially displaced from the first functional surface of the end plate and the second clamping element is circumferentially displaced from the first clamping element, the second clamping element being arranged for repeatedly being moved towards and away from the end plate such that repeatedly a closed position is obtained in which the two functional surfaces abut on each other, where the closed positions of the first clamping element and of the second clamping element are successively obtained.