A process for producing an absorbent polymer structure (Pa) by treating the outer portion of an untreated absorbent polymer structure (Pu1). The process includes the step of bringing the outer portion of the untreated absorbent polymer structure (Pu1) into contact with an aqueous solution including at least one chemical cross-linker and at least one inorganic compound in dispersed colloidal form. The process also includes the step of heating the absorbent polymer structure, of which the outer portion has been brought into contact with the aqueous solution, at a temperature within a range from about 40 to about 300° C., so that the outer portion of the absorbent polymer structure is more strongly cross-linked in comparison to the inner portion and the inorganic compound is at least partly immobilized in the outer portion of the absorbent polymer structure.