New crosslinked polysaccharides useful as absorbents or superabsorbents alone or in a mixture are obtained by reacting polysaccharides (preferably containing carboxylates groups) with at least one crosslinker selected in the group constituted by activated polyethylene glycols such as for example halogenated (Cl, Br, I), mesylated, tosylated, or triflated activated polyethylene glycols.