Abstract: The invention relates to a rotary sector device turning at a variable angular speed for automatic labelling machines. Said device carries out the withdrawal of labels (6) from a container (5) acting as a magazine and the transferring of the same to an operating area where they are applied to the products for which they are meant (bottles, boxes, etc.).Said device includes a plate (1) turning at a constant angular speed to which a plurality of rotary sectors (4) are mounted, each of said sectors turning about a corresponding vertical axis (A) at an angular speed varying according to a predetermined law of motion. This law of motion is accomplished by means of a toothed belt (27) kinematically connected to a circular pulley (36) coaxial to a corresponding rotary sector (4) and to a fixed asymmetric pulley (26), disposed in a central position with respect to the rotary plate (1).