A method is provided for obtaining crosslinked polymers, particularly fluorinated polymers having pendent sulfonic acid groups, by crosslinking through pendent groups which include a sulfonyl chloride group (--SO.sub.2Cl). The sulfonyl chloride group may be removed by application of electromagnetic radiation, typically in the ultraviolet band, or a radical initiator, leaving behind a radical which readily binds covalently to other polymer strands or to crosslinking agents to form crosslinks. Typically, the polymer is made by providing a polymer comprising pendent groups which include a group according to the formula --SO.sub.2F and converting at least a portion of the --SO.sub.2F groups to --SO.sub.2Cl. After crosslinking, the remaining --SO.sub.2F groups may be converted to sulfonic acid groups, yielding a crosslinked polymer electrolyte. Such crosslinked polymer electrolytes may be used to make polymer electrolyte membranes (PEM's) that may be used in electrolytic cells such as fuel cells.