Luminaire system - having at least one luminaire unit (2, 2i) containing a light segment, which is configured to hold at least one illuminant or has at least one illuminant, and at least two connecting elements (2d-2h), which are electrically conductive at least in sections and are mechanically and electrically connected to the respective light segment at the ends thereof, - having at least one connector (1, 3, 4), which has at least one element (1c-1e) circulating around a central connector axis and at least one electrical conductor, which is mechanically connected to the circulating element (1c-1e) or formed by the circulating element (1c-1e), - wherein each of the connecting elements (2d-2h) of the luminaire unit (2, 2i) is mechanically connected to the circulating element (1c-1e) of the respective connector (1, 3, 4) and, as a result, the at least one luminaire unit (2, 2i) is mechanically and electrically connected to the connector (1, 3, 4), - wherein the luminaire unit (2, 2i), together with the connector (1, 3, 4), can be arranged in various positions around the central connector axis and is mechanically and electrically connected to the connector (1, 3, 4) in each position of the luminaire unit (2, 2i) and - wherein a plurality of luminaire units (2, 2i) are mechanically and electrically connected to a common connector (1, 3, 4), characterized in that - the luminaire unit (2, 2i), together with the connector (1, 3, 4), can be arranged in arbitrary positions around the central connector axis over a continuous angular range of at least 330° or in each case over a plurality of continuous angular ranges of together at least 330°, and in that the luminaire unit (2, 2i) can be plugged to the connector (1, 3, 4). - having at least one luminaire unit (2, 2i) containing a light segment, which is configured to hold at least one illuminant or has at least one illuminant, and at least two connecting elements (2d-2h), which are electrically conductive at least in sections and are mechanically and electrically connected to the respective light segment at the ends thereof, - having at least one connector (1, 3, 4), which has at least one element (1c-1e) circulating around a central connector axis and at least one electrical conductor, which is mechanically connected to the circulating element (1c-1e) or formed by the circulating element (1c-1e), - wherein each of the connecting elements (2d-2h) of the luminaire unit (2, 2i) is mechanically connected to the circulating element (1c-1e) of the respective connector (1, 3, 4) and, as a result, the at least one luminaire unit (2, 2i) is mechanically and electrically connected to the connector (1, 3, 4), - wherein the luminaire unit (2, 2i), together with the connector (1, 3, 4), can be arranged in various positions around the central connector axis and is mechanically and electrically connected to the connector (1, 3, 4) in each position of the luminaire unit (2, 2i) and - wherein a plurality of luminaire units (2, 2i) are mechanically and electrically connected to a common connector (1, 3, 4), - the luminaire unit (2, 2i), together with the connector (1, 3, 4), can be arranged in arbitrary positions around the central connector axis over a continuous angular range of at least 330° or in each case over a plurality of continuous angular ranges of together at least 330°, and in that the luminaire unit (2, 2i) can be plugged to the connector (1, 3, 4).