A drying device for moving webs of material has at least two serial drying groups each having a plurality of heatable drying cylinders. The drying cylinders of at least one first drying group are steam-heated in a first heat circuit. The drying cylinders of at least one second drying group have supply piping for a combustible energy source and discharge piping for waste heat originating from the combustion. A first heat exchanger is provided that couples the first heat circuit for the steam-heated drying cylinders to the discharge piping for the waste heat from the drying cylinders of the second drying group.