Abstract: The filler fleece material of the invention consists of a laminate of two layers of fleece containing bonding fibers. The thinner layer, which serves as a covering fleece, consists to at least 60% of thermoplastic bonding fibers which melt at the same or a lower temperature than those of the central fleece. This combination makes it possible, after the depositing of the fiber layers and the thermal consolidation of the central fleece, to perform a process for smoothing the cover layer, in which the laminate is exposed in a roller gap to a temperature that is above the fiber melting point of the cover fleece. The filler fleece material of the invention, on account of its smooth yet still sufficiently air-permeable cover layer, is no longer subject to fiber protrusion. Furthermore, the clinging of projecting fibers during application to textile surface materials is reliably prevented.