A shaving apparatus provided with at least one pivotable cutting unit (3) comprising an external cutting member (4) and an internal cutting member (6) which can be driven in rotation with respect to the former (4), a drive mechanism (8) for driving the internal cutting member (6) into rotation, and a coupling member (18) comprising a coupling head (19) and a coupling body (20), which coupling head (19) can be detachably coupled to a coupling element (16) of the internal cutting member (6), said coupling body (20) being coupled to the drive mechanism (8),
- which coupling member has an axis of rotation (24), and
- which coupling head (19) is provided with curved drive surfaces (25) between which curved connecting surfaces (26) are situated,
- while, seen in a plane (P1) substantially transverse to the drive surface (25) and containing the axis of rotation (24), each drive surface (25) has a curvature with a first radius of curvature (R1) whose center (M1) lies substantially on the axis of rotation (24), and each connecting surface (26) has a curvature with a second radius of curvature (R2) whose center (M2) coincides with the center (M1) of the first radius of curvature (R1), said second radius of curvature (R2) being greater than said first radius of curvature (R1), and
- the coupling element (16) of the internal cutting member (6) is provided with a cavity (21) in which the coupling head (19) can be accommodated and which is provided with drive surfaces (28) for cooperating with the curved drive surfaces (25) of the coupling head (19), characterized in that
- both the coupling head (19) and the cavity (21) of the coupling element (16) have an approximately triangular shape which is rotationally symmetrical through 120°, seen in a direction along the axis of rotation (24).