Abstract: This machine is intended for bonding stretched pieces of elastic band to a moving sheet so that these pieces extend transversely relative to the direction of movement of this sheet.The pieces are transferred from a cutting station to a stretching station by means of a transfer station.The stretching station comprises several pairs of grippers distributed around an axis about which they are driven in rotation. The grippers of one and the same pair are arranged axially opposite one another and are designed to be successively moved away from, and close to, one another so that, during their rotation, they grip the lateral ends of the pieces subsequently stretching the latter by moving axially away from one another. Once stretched, the pieces are bonded to the sheet entrained about a drum at the moment when the grippers pass opposite this sheet.The invention is used for the production of a composite sheet intended for providing diapers.