Substantially non-crosslinked fluorocarbon polymers containing carboxyl groups are prepared starting from non-crosslinked and in some cases new, fluorocarbon polymers in which the linear macromolecules carry side chains containing the end group --CHFX (X is F or CF.sub.3). The starting polymers are first reacted with peroxodisulfuryl difluoride FSO.sub.2 O--OSO.sub.2 F to give the corresponding fluorosulfato derivatives containing the side chain end groups. ##STR1## In the event that X is F, these derivaties are then converted into the corresponding carboalkoxy derivatives by means of an alcohol, the fluorosulfato group being split off, and these carboalkoxy derivatives are then converted by saponification into the products containing the free carboxyl groups; the fluorosulfato derivatives can also be hydrolyzed with water, if appropriate in the presence of an inert solvent and/or bases, to give, without further treatment, the products containing the free carboxyl groups.The fluorosulfato derivatives in which X is CF.sub.3 in the side chain end groups are first decomposed in the presence of catalytic amounts of alkali metal fluorides and/or aprotic nitrogen bases to give the products containing the side chain end groups ##STR2## and the latter are then hydrolyzed to give the products containing the free carboxyl group.Virtually non-crosslinked fluorocarbon polymers containing carboxyl groups are of industrial importance in the form of cation exchanger membranes in electrolytic cells, particularly in chlor-alkali electrolysis.