ensured that the surface roughness on the source material contact surface 42 is achieved with threads or fibers with a maximum of 3 dtex for example it is also possible with the previously described construction in particular the fineness of the supporting layer which also provides the source material contact surface 42 to ensure an adequately high through flow capability that is to say permeability to air this can lie in a region of at least 15 cfm more preferably at least 20 cfm or at least 25 cfm whereby it is preferable that the permeability to air even lies in a region of at least 50 cfm and ideally even at least above 80 cfm so that relatively high requirements are imposed in respect of the air permeability on the one hand and the comparatively low surface roughness on the other hand which can nevertheless be realized with the construction according to the invention it can be further appreciated in fig3 that material 68 influencing the permeability of the press belt 32 is provided in some areas in the boundary region between the two support layers 58 62 that are constructed with fibrous material this can be applied for example to.