Shaving unit for an electric shaver, comprising a supporting member and at least two hair-cutting units supported by the supporting member, wherein each hair-cutting unit comprises: - a housing having a central axis (A c); - an external cutting member supported by the housing and comprising an annular shaving area having a plurality of hair-entry openings, the external cutting member being rotatable about the central axis (A c) relative to the housing; and - an internal cutting member which is covered by the external cutting member and rotatable about the central axis (A c) relative to the external cutting member and has a coupling member; wherein the shaving unit comprises, for each hair-cutting unit, an individual drive shaft which is releasably coupled to the coupling member of the internal cutting member for rotating the internal cutting member about the central axis (A c) relative to the external cutting member; wherein each hair-cutting unit comprises a transmission unit by means of which the external cutting member is rotatable about the central axis (A c) relative to the housing, the transmission unit being accommodated in the housing of the hair-cutting unit and comprising: - a first transmission member mounted to the internal cutting member to be rotatable together with the internal cutting member about the central axis (A c); - a second transmission member mounted to the external cutting member to be rotatable together with the external cutting member about the central axis (A c); and - at least one intermediate transmission member (63, 64, 65) via which the first transmission member is coupled to the second transmission member to convert a rotation of the internal cutting member about the central axis (A c) into a rotation of the external cutting member about the central axis (A c). - a housing having a central axis (A c); - an external cutting member supported by the housing and comprising an annular shaving area having a plurality of hair-entry openings, the external cutting member being rotatable about the central axis (A c) relative to the housing; and - an internal cutting member which is covered by the external cutting member and rotatable about the central axis (A c) relative to the external cutting member and has a coupling member; wherein the shaving unit comprises, for each hair-cutting unit, an individual drive shaft which is releasably coupled to the coupling member of the internal cutting member for rotating the internal cutting member about the central axis (A c) relative to the external cutting member; wherein each hair-cutting unit comprises a transmission unit by means of which the external cutting member is rotatable about the central axis (A c) relative to the housing, the transmission unit being accommodated in the housing of the hair-cutting unit and comprising: - a first transmission member mounted to the internal cutting member to be rotatable together with the internal cutting member about the central axis (A c); - a second transmission member mounted to the external cutting member to be rotatable together with the external cutting member about the central axis (A c); and - at least one intermediate transmission member (63, 64, 65) via which the first transmission member is coupled to the second transmission member to convert a rotation of the internal cutting member about the central axis (A c) into a rotation of the external cutting member about the central axis (A c). - a first transmission member mounted to the internal cutting member to be rotatable together with the internal cutting member about the central axis (A c); - a second transmission member mounted to the external cutting member to be rotatable together with the external cutting member about the central axis (A c); and - at least one intermediate transmission member (63, 64, 65) via which the first transmission member is coupled to the second transmission member to convert a rotation of the internal cutting member about the central axis (A c) into a rotation of the external cutting member about the central axis (A c).