Abstract: A machine for the treatment of containers (12) provided with a neck (14), includes at least one treatment station provided with a nipple (22) having gripping elements (26) in order to seize a container (12), the gripping elements (26) including a tubular supporting cuff (50) which is provided with a series of radial drillholes (52), each intended for receiving a ball (54) movable radially between an inner gripping position and an outer release position, characterized in that the gripping elements (26) include a tubular control cuff (56) which is mounted slideably between a locked position, in which a frustoconical bearing surface (58) cooperates with the balls (54) in order to stress them toward their gripping position, and an unlocked axial position, and in that the nipple (22) includes controlled drive elements (62) capable of causing the sliding of the control cuff (56).