A device for processing at least two webs of material made of paper or plastic film is provided with at least two rolls of material, each of which can be rotated in an unwind unit and from each of which a predrawing unit, comprising predrawing rollers or rolls, takes off the web and pulls it into the device. To guarantee the proper infeeding of the web into the device, even if after a sudden operating stoppage the rolls of material coast longer than the predrawing units, there is between each unwind unit and each predrawing unit one brake each, which decelerates the web and which is activated when the predrawing units are abruptly stopped or they significantly delay the infeed.