A labelling machine with a labelling device, which has a feeder unit for feeding a backing strip, which is provided with detachable labels, and a transfer unit for transferring the labels from the backing strip onto an object that is to be labelled. The labelling machine further has a winding device for winding a section of the backing strip from which labels have been detached, containing at least one guidance unit with a guidance element, along which the backing strip section can be guided in a direction of transport, and a winding unit, which is mounted downstream of the at least one guidance element, and includes fixing means, on which a free end section of the backing strip section can be fixed, whereby the fixing means are arranged on a winding core that can rotate about an axis of rotation, and follow a rotational movement of the winding core.