Air guide box 20 for a paper machine where the paper web 16 to be dried runs together with the backing belt 18 across drying cylinders 10 through 14. The air guide box 20 extends from a point A where the backing belt 18 departs from a cylinder 10, 12 toward a point Z where the backing belt runs on the following cylinder 11, 13. A diverging gap 23 remains between the air guide box 20 and the backing belt 18. The air guide box 20 has in the area of the departure point A a mechanical air boundary layer stripper 25. Facing toward the backing belt 18 and diverging in its running direction from the contact screen, the wall 21 of the air guide box 20 is shaped in accordance with the operationally occurring curved trajectory of the contact screen 18, is composed, preferably in polygon fashion, from flat wall elements 21.1, 21.2 and 21.3.