Adhesive labels are applied to a continuous strip by a unit fed with a first continuous strip of wrapping material advancing along a first path, and a second continuous strip of backing material presenting a succession of labels and advancing along a second path. The labels are detached singly from the second strip by a diverter blade placed along the second path and presenting a sharp edge over which the backing strip is routed through an acute angle to induce the separation of the labels. The unit comprises an aspirating first drum rotating substantially in contact with the edge of the diverter blade at an angular velocity greater than the linear velocity of the second strip, so as to increase the distance between successive transferred labels, and a second drum around which the first strip is looped in such a way that it can be offered to the first drum; the first and second drums rotate tangentially one to another and at the same angular velocity through a point of mutual tangency coinciding with the point at which the labels are transferred from the first drum to the first continuous strip.