Water-soluble or water-swellable polymer having repeating structural units comprising 90-99.99 mole.% of one or more independent amino-sulfur trioxide group containing repeating structural units (I), and 0.01-10 mole.% of one or more independent repeating crosslinking structural units (II), is new. Water-soluble or water-swellable polymer having repeating structural units comprising 90-99.99 mole.% of one or more independent amino-sulfur trioxide group containing repeating structural units of formula (-[CH 2-C(R)-(C(=O)-NH-A-SO 2-O ->;Q +>;)]-) (I), and 0.01-10 mole.% of one or more independent repeating crosslinking structural units of formula (II), is new. R, R2a-R2c : H, CH 3or ethyl; A : linear or branched 1-12C alkylene; Q +>; : H +>;, NH 4 +>;or organic ammonium ion ([HNR5R6R7] +>;); R5-R7 : H, linear or branched 1-22C-alkyl, a linear or branched, mono- or polyunsaturated 2-22C alkenyl, 6-22C-alkylamidopropyl, linear 2-10C monohydroxyalkyl or linear or branched 3-10C dihydroxyalkyl, where at least one of R5-R7 is not H, alkali metal +>;, 1/2 alkaline earth metal 2>; +>;, 1/2 Zn 2>; +>;and/or 1/3 Al 3>; +>;; R1 : H, CH 3, ethyl, methylol or ethylol; X : a chemical bond, methylene, ethylene or linear or branched 3C alkylene; Y1-Y3 : a chemical bond, O, CH 2, C(O)O, OC(O), C(O)NR3 or NR3C(O); R3 : H or linear or branched 1-50C alkyl; D1, E, F1 : methyleneoxy, ethyleneoxy, propyleneoxy, linear or branched 1-6C alkylene, linear or branched, one or more times unsaturated 2-6C alkenylene, linear or branched 2-6C monohydroxyalkylene or linear or branched 3-6C dihydroxyalkylene; and o, p, q : 0-50, where o+p+q is >;= 3. An independent claim is included for a cosmetic, dermatological or pharmaceutical composition comprising 0.01-10 wt.% of the polymers. [Image].