A process for the guiding of fibre web or the like, in particular for paper production, especially in paper driers, wherein the suction applied can be varied both in real time operation and along the axes of the one or more suction rolls that is/are present and which may be used in conjunction with at least one travelling screen or the like. The object is to make the start-up process for the treatment of fibre webs on suction rolls more convenient without too much equipmental and operational overhead, and to prevent shrinkage of the web by providing good location at the web in the edge regions. This is achieved by restricting the suction which acts on the inside of the roll jacket to a region of the roll jacket which comes into contact with a lead-in strip for the fibre web during start-up operation. This process is continued until a sufficient length of fibre web has passed over the suction roll for the web to have reached its full or final width on this suction roll. As the web width increases the suction spreads out to encompass the full width of the fibre web. The control of the vacuum within the compartments of the suction roll is preferably effected by means of valve discs provided on slide rods.