The invention relates to polymers obtained by S-alkylation of sulfinated polymers with alkylation agents, and AB-crosslinked polymers obtained by reacting polymers containing alkylation groups with low-molecular sulfinates, under S-alkylation, or AB-crosslinked polymers obtained by S-alkylation of sulfinated polymers with polymers containing alkylation groups, whereby sulfinated polymers are reacted with alkylation agents (I) wherein R represents alkyl, aryl, or any organic radicals; M represents alkali ions or alkaline-earth ions or any monovalent or bivalent metal cation or ammonium cation;ALK represents any alkylation group or polymer; Poly represents any polymer main chain; Hal represents F, Cl, Br, or 1; x represents a number between 2 and 20; x represents electron-attracting groups; and n represents the number of repeat units (WE) of the base polymer; and whereby polymers containing alkylation groups are reacted with sulfinated compounds. The invention also relates to the polymers obtained by reacting sulfinated polymers with mixtures of various monofunctional alkylation agents. Furthermore, the invention relates to polymers obtained by reacting sulfinated polymers with mixtures of monofunctional and difunctional or oligofunctional alkylation agents (cross-linking agents), in addition to membranes and other moulded bodies. Disclosed are also the polymers obtained by reacting polymers containing alkylation groups with low-molecular or high-molecular sulfinates, whereby mixtures of various sulfinates can also be used. Finally, the invention relates to methods for producing said sulfinate-alkylated polymers, and for producing membranes and other moulded bodies from said sulfinate-alkylated polymers.