Fibers or one-dimensional, two-dimensional, or three-dimensional fibrous structures configured to be hydrogelling, produced from fibers made of a first fiber raw material, whereby the first fiber raw material contains water-soluble polyvinyl alcohol and/or polyvinyl alcohol copolymer, whereby the hydrogelling configuration of the fibers or fibrous structures is achieved by tempering the fiber raw material at a predetermined tempering temperature that is preferably higher than the glass transition temperature and/or lower than the melting or decomposition temperature of the first fiber raw material employed, as well as by tempering for a predetermined tempering duration, and whereby the fiber raw material is cross-linked by the tempering.