An electrical multi-conductor cable with contact apparatus for a plug-in connector, for use as a charging cable for electric vehicles, including: a central cable core, a number of conductors (12; 12) which are arranged concentrically relative to each other in an annular shape around the cable core and comprising individual wires, and a respective insulation between the conductors, wherein - the contact apparatus comprises a plug-in connector, namely a plug or a socket; - the contact apparatus includes two clamping shell portions (21A, 21B), which are implemented as formed parts made of plastics and at their inside have a plurality of receiving means (22-1, 22-2, 22-3) which are stepped radially from each other, - in a first region the clamping shell portions (21A, 21B) have the receiving means (22-1, 22-2, 22-3) and in an opposite second region form housing portions of the plug-in connector, namely of a plug or a coupling; - arranged in the receiving means (22-1, 22-2, 22-3) of at least one clamping shell portion is a respective contact body (23-1, 23-2, 23-3) associated with one of the concentric conductors (12; 13) for contacting purposes, wherein each contact body in a first region has a channel shape with a longitudinal extent and of a curved cross-sectional configuration around a peripheral portion of the associated conductor (12; 13); - there is provided a closure (27, 28) for connecting the clamping shell portions (21A, 21B), which fixes the clamping shell portions to each other in a closed position; - the clamping shell portions (21A, 21B) in the closed position hold the contact bodies in coaxial relationship with each other and press each contact body for contacting purposes against the respectively associated concentric conductor; and - the contact bodies (23-1, 23-2, 23-3) in a second region, which lies opposite the first region with the channel shape, include contact pins or contact sockets of the plug-in connector; wherein the contact bodies (23-1, 23-2, 23-3) are respectively produced in one piece. - the contact apparatus comprises a plug-in connector, namely a plug or a socket; - the contact apparatus includes two clamping shell portions (21A, 21B), which are implemented as formed parts made of plastics and at their inside have a plurality of receiving means (22-1, 22-2, 22-3) which are stepped radially from each other, - in a first region the clamping shell portions (21A, 21B) have the receiving means (22-1, 22-2, 22-3) and in an opposite second region form housing portions of the plug-in connector, namely of a plug or a coupling; - arranged in the receiving means (22-1, 22-2, 22-3) of at least one clamping shell portion is a respective contact body (23-1, 23-2, 23-3) associated with one of the concentric conductors (12; 13) for contacting purposes, wherein each contact body in a first region has a channel shape with a longitudinal extent and of a curved cross-sectional configuration around a peripheral portion of the associated conductor (12; 13); - there is provided a closure (27, 28) for connecting the clamping shell portions (21A, 21B), which fixes the clamping shell portions to each other in a closed position; - the clamping shell portions (21A, 21B) in the closed position hold the contact bodies in coaxial relationship with each other and press each contact body for contacting purposes against the respectively associated concentric conductor; and - the contact bodies (23-1, 23-2, 23-3) in a second region, which lies opposite the first region with the channel shape, include contact pins or contact sockets of the plug-in connector;