A hair cutting appliance comprising: - a support structure accommodating a drive system; - at least one cutting unit supported by the support structure and comprising an external cutting member having a plurality of hair entry openings, and an internal cutting member rotatable relative to the external cutting member; and - at least one drive spindle (24, 24a) rotatable about an axis of rotation and having a first spindle part arranged to be driven by the drive system and a second spindle part arranged to be coupled to the internal cutting member, the first and second spindle parts (26, 30) being displaceable relative to each other in an axial direction parallel to the axis of rotation; wherein the internal cutting member comprises a plurality of cutting elements, a first coupling element, and a carrier carrying the cutting elements and the first coupling element; wherein the second spindle part comprises a second coupling element which is coupled to the first coupling element for transmitting, during operation, a driving torque about the axis of rotation from the drive spindle (24, 24a) to the internal cutting member; and wherein one of the first and second spindle parts (26, 30) comprises an abutment element and the other of the first and second spindle parts (26, 30) comprises an abutment surface arranged to cooperate with the abutment element for transmitting, during operation, the driving torque from the first spindle part to the second spindle part; characterized in that the abutment surface is arranged at an angle α relative to a line extending parallel to the axis of rotation, wherein 0° < α < 90° such that a transmission of the driving torque from the first spindle part to the second spindle part via the abutment element and the abutment surface results in a force exerted by the first spindle part on the second spindle part having a component parallel to the axis of rotation and directed towards the internal cutting member, wherein the first and second coupling elements (56, 34) are configured to transmit said component from the second spindle part to the internal cutting member. - a support structure accommodating a drive system; - at least one cutting unit supported by the support structure and comprising an external cutting member having a plurality of hair entry openings, and an internal cutting member rotatable relative to the external cutting member; and - at least one drive spindle (24, 24a) rotatable about an axis of rotation and having a first spindle part arranged to be driven by the drive system and a second spindle part arranged to be coupled to the internal cutting member, the first and second spindle parts (26, 30) being displaceable relative to each other in an axial direction parallel to the axis of rotation; wherein the internal cutting member comprises a plurality of cutting elements, a first coupling element, and a carrier carrying the cutting elements and the first coupling element; wherein the second spindle part comprises a second coupling element which is coupled to the first coupling element for transmitting, during operation, a driving torque about the axis of rotation from the drive spindle (24, 24a) to the internal cutting member; and wherein one of the first and second spindle parts (26, 30) comprises an abutment element and the other of the first and second spindle parts (26, 30) comprises an abutment surface arranged to cooperate with the abutment element for transmitting, during operation, the driving torque from the first spindle part to the second spindle part; characterized in that the abutment surface is arranged at an angle α relative to a line extending parallel to the axis of rotation, wherein 0° < α < 90° such that a transmission of the driving torque from the first spindle part to the second spindle part via the abutment element and the abutment surface results in a force exerted by the first spindle part on the second spindle part having a component parallel to the axis of rotation and directed towards the internal cutting member, wherein the first and second coupling elements (56, 34) are configured to transmit said component from the second spindle part to the internal cutting member.