System for realizing a luminaire elongated in a longitudinal direction, the system comprising several support rails elongated in the longitudinal direction, several current conducting rails (21, 22) elongated in the longitudinal direction and several conducting wires (31, 32) extending in the longitudinal direction, wherein the support rails each have a cross-section perpendicular to the longitudinal direction that is open at a vertical end along a vertical direction and that is limited along a transverse direction by two support rail side walls that are connected with one another by a support rail base extending along the transverse direction and that extend vertically away from the rail support base, wherein the current conducting rails (21, 22) each have a multitude of ducts extending along the longitudinal direction, arranged side by side along a transverse direction and being open at an access side configured along the vertical direction, wherein respectively one group of conducting wires (31, 32) is associated to each of the current conducting rails (21, 22), conducting wires of which each is arranged in respectively one of the ducts of the current conducting wires (21, 22), wherein in an operating position a first current conducting rail, in the ducts of which a first group of conducting wires is arranged, is fixed to a first support rail by forming a first lighting element, and a second current conducting rail, in the ducts of which a second group of conducting wires is arranged, is fixed to a second support rail by forming a second lighting element, wherein the lighting elements in the operating position are arranged side by side in the longitudinal direction and the support rails are mechanically connected to one another, and the conducting wires (31, 32) of the first and of the second group are electroconductively connected to one another, wherein the system comprises at least one mounting body elongated in the longitudinal direction, on the one side of which a contact device is arranged relative to the vertical direction, wherein the system comprises an electrical connector elongated in the longitudinal direction that comprises a first and a second group of connecting devices (101, 102), wherein the first group of connecting devices is spaced from the second group of connecting devices in the longitudinal direction and wherein each connecting device of the first group is electroconductively connected to exactly one connecting device of the second group by respectively one coupling device, wherein in the operating position each of the first group of conducting wires is connected to respectively one of the first group of connecting devices and each of the second group of conducting wires is connected to respectively one of the second group of connecting devices, wherein in the operating position the coupling devices are guided in ducts formed by the electrical connector and are accessible from the access side between the connecting devices connected by them, characterized in that the mounting body is movable with a movement along the vertical direction towards one of the support rails on which one of the current conducting rails (21, 22) is fixed that is connected to the electrical connector until it abuts at the open vertical end of the support rail so that the mounting body forms together with the support rail an inner space that is circumferentially enclosed by the support rail and the mounting body perpendicularly to the longitudinal direction and that can be fixed to the support rail by a fixing means, wherein the contact device is configured so as to be brought into electrical contact with the conducting wires of the current conducting rail (21, 22) in any longitudinal position within the longitudinal extension of the support rail along the current conducting rail (21, 22) during said movement.