The invention relates to a superabsorbent powder consisting of polymer particles which have a core swelling in the presence of water and a superficially postcured shell, in which the powder is a screening fraction of such polymer particles which have not been crushed after the superficial postcure of their shell. This superabsorbent powder is especially suitable for the finishing of textile webs made of super-fine fibers or filaments with a diameter of less than 10 μm, in particular for the finishing of sanitary products. There is further proposed the use of a nanofiber nonwoven, finished with a superabsorbent for the absorption and retention of hydrophilic fluids, for the absorption and/or sustained release of at least one of the following fluids: body fluids, sweat of humans and animals, water, including cooling water, condensation water and water vapor, chemicals, including agrochemicals and pesticides, pharmaceuticals, biocides, germicides and fungicides, diagnostics, fire protection and fire extinguishing agents, cleaning agents, hydraulic fluids, heating and cooling fluids, sewage, including radioactively contaminated fluids, perfumes.