fleece web having a thickness variable across the laying width the nonwoven web is cyclically drawn on the way between the nonwoven producing means and the fleece laying machine at a fixedly determined location said drawing depending on the laying movements of the fleece laying machine to form a fleece web of a regular cross sectional profile between a separate drawing equipment performing the drawing process and the inlet into the fleece laying machine the nonwoven web may run through a separate variable buffer storage which adapts the speed fluctuations of the nonwoven web on the outlet side of the drawing equipment to the intake speed of the fleece laying machine the fleece laying machine can be formed without its own buffer storage since the separate buffer storage may also compensate the transport speed fluctuations of the nonwoven web required by the laying movements application_number US 21877802 A description on the left side the drawings show the swift 1 of a carding machine from which upper and lower transfer belts 2 a and 2 b extend to a drawing equipment 3 consisting of two disk rollers to which said drawing equipment 3 a first intermediate belt 10 of a nonwoven storage 4 is connected downstream which leads to the supply belt.