This disclosure relates to a labelling machine (1), comprising a carousel (3) rotatably mounted a supporting frame (2) in such a way that it can rotate about a first axis of rotation (30) and a plurality of supporting elements (4) for articles to be labelled (9). The supporting elements (4) are mounted on the periphery of the carousel (3) and are able to rotate about respective second axes of rotation (40). The machine (1) is characterised in that it comprises an operating unit (55) which is mounted on a rotary support (6) mounted on the supporting frame (2). The support (6) is able to rotate about a third axis of rotation (60) which is at a distance, along a radial line, from the first axis of rotation (30). The carousel (3) is movable relative to the third axis of rotation (60) and the operating unit (55), which is rotatable together with the rotary support (6), is designed to perform an operation on a lateral surface of an article (9) which is on its operating line when the article (9), positioned on a respective supporting element (4), passes near to the operating unit (55) during the rotation of the carousel (3). The rotation of the rotary support (6) about the third axis of rotation (60) is coordinated with the rotation of the carousel (3) about the first axis of rotation (30), whereby, in use, the rotation of the rotary support (6) about the third axis of rotation (60) keeps the operating unit (55) with the operating line towards the article to be labelled (9) along a stretch of angular movement of the carousel (3) about the first axis of rotation (30).