Abstract: In a method for disposing of used embossing foil webs during the operation of an embossing apparatus, in which at least one embossing foil web is moved with the aid of a foil feed device with varying web speeds through an embossing gap and is subsequently supplied to a disposal device, the embossing foil web is removed from a final control device of the foil feed device by means of a tension conveying device downstream of the foil feed device and which produces a tension acting on the embossing foil web independently of the direction and amount of the embossing foil web speed in the same tension direction, as well as a cutting through of the embossing foil web in predeterminable time sections downstream of the tension conveying device outside an engagement area of the tension conveying device for producing cut off embossing foil web portions. The latter can then be disposed of. An embossing apparatus equipped with a corresponding disposal device is described.