true for all embodiments is that the air guide box with the illustrated cross sectional shape extends normally crosswise through the entire drying section that is from the backing belt edge on the tending side to that of the drive side and still somewhat farther beyond these edges but it is also possible to provide two relatively short air guide boxes only in the area of the two edges since it may at times be sufficient to suck only the paper web edges to the backing belt an air guide box 20 is described hereafter in more detail essentially closed on all sides the air guide box 20 has a first wall 21 which hereafter will be referred to as foil wall and which viewed in the cross section of the air guide box 20 extends along the backing belt 18 up to the inlet gore formed by it and the free cylinder surface of the lower drying cylinder 11 respectively 13 this leaves between the foil wall 21 and the backing belt 18 a gap 23 that diverges toward the inlet gore the air guide box described thus far is the object of the german patent document no 32 36 576 different from it the air guide box according to the present invention extends considerably farther in the direction toward the upper half of the cylinder surface of the respective upper drying cylinder 10 respectively 12 and the foil wall 21 is with regard to the divergence of the gap 23 of the real web curve designed accordingly this air guide box 20 will.