A labelling machine (1; 10; 100) comprising: - a supporting frame; - a carrousel rotatably mounted on the supporting frame in such a way that the carrousel can rotate about a first axis of rotation; - a plurality of supporting elements for articles to be labelled, the supporting elements being mounted on the periphery of the carrousel, each supporting element being able to rotate relative to the carrousel about a respective second axis of rotation; - one or more motor devices (39, 49) designed to move the carrousel relative to the supporting frame and to move the supporting elements relative to the carrousel; - a feed station for feeding the articles to be labelled to the supporting elements and a pickup station for picking up the labelled articles from the supporting elements; - an operating unit (55; 550) having an operating line (50; 500), the operating unit (55; 550) being designed to perform an operation on a lateral surface of an article which is located on said operating line (50; 500), said operation being related to labelling the article, such as an operation of scanning the lateral surface to detect a reference element, thereby determining an angular position of the article and allowing a precise label application in a desired position, or such as a printing operation on the lateral surface, thereby producing a label or part of it directly on the article, the labelling machine (1; 10; 100) being characterised in that the operating unit (55; 550) is mounted on a rotary support which is mounted on the supporting frame, the rotary support being able to rotate about a third axis of rotation which is at a distance, along a radial line, from the first axis of rotation, the operating unit (55; 550) being rotatable together with the rotary support and the carrousel being movable relative to the third axis of rotation, wherein, in use, an article to be labelled is positioned on a respective supporting element, which passes near to the operating unit (55; 550) during the rotation of the carrousel about the first axis of rotation, and the rotation of the rotary support about the third axis of rotation is coordinated with the rotation of the carrousel about the first axis of rotation, so that the rotation of the rotary support about the third axis of rotation keeps the operating unit (55; 550) with the operating line (50; 500) towards said article to be labelled, so that the operating unit follows the article along a stretch of angular movement of the carrousel about the first axis of rotation during the rotation of the carrousel about the first axis of rotation. - a supporting frame; - a carrousel rotatably mounted on the supporting frame in such a way that the carrousel can rotate about a first axis of rotation; - a plurality of supporting elements for articles to be labelled, the supporting elements being mounted on the periphery of the carrousel, each supporting element being able to rotate relative to the carrousel about a respective second axis of rotation; - one or more motor devices (39, 49) designed to move the carrousel relative to the supporting frame and to move the supporting elements relative to the carrousel; - a feed station for feeding the articles to be labelled to the supporting elements and a pickup station for picking up the labelled articles from the supporting elements; - an operating unit (55; 550) having an operating line (50; 500), the operating unit (55; 550) being designed to perform an operation on a lateral surface of an article which is located on said operating line (50; 500),