The invention relates to a fastening device (1) for releaseable fastening onto textile or textile-like material surfaces, comprising a self-adhesive, pressure sensitive layer (2) with a first surface intended to be firmly fixed against a substrate, as well as a second surface intended to serve as a fastening surface onto the textile or textile-like material surface. What primarily distinguishes the invention is that an essentially incompressible, non-adhesive covering layer (3), with a thickness which does not exceed 0.5 mm and which has a plurality of penetrating openings or pores (4) arranged essentially perpendicularly to the plane of the covering layer (3), is arranged on and fastened to the fastening surface of the adhesive layer (2), wherein the relative distance between two adjacent openings or pores (4) in the covering layer (3) does not exceed 3 mm, whereby the fastening means is suitable for co-operating with a textile or textile-like receiving surface (5).The invention also includes absorbent products such as diapers, sanitary napkins, panty-liners, incontinence pads, bed protectors, seat protectors or the like, comprising such a fastening means.