1. A labeling machine, comprising a conveyor of containers to be labeled along an advancement path and at least one labeling unit arranged along said advancement path and provided with a respective transfer drum that can move in rotation about a drum axis, with respect to a supporting base, and which is adapted to receive, in adhesion to a lateral surface thereof, from a feeder unit, labels to be applied to said containers, at a feeding station, and to transfer the labels received at said feeding station to respective containers that arrive from said conveyor at a transfer station which is angularly spaced apart from said feeding station about the drum axis, on the lateral surface of said transfer drum at least one sector being defined which extends along at least one portion of a circumferential extension of the lateral surface of said transfer drum and is adapted to accommodate, in each instance, a single label to be transferred to a single one of the containers, wherein at least one portion of said at least one sector is rotatably movable, with respect to a remaining part of said transfer drum, about an oscillation axis, which is substantially parallel to the drum axis, in order to pass from a receiving position, in which said at least one portion is arranged at a first angular distance from the drum axis, to a transfer position, in which said at least one portion is arranged, with at least one part thereof, at a second distance, greater than said first distance, from the drum axis, and vice versa;