A method is provided for making a crosslinked polymer by direct fluorination of a non-perfluorinated polymer comprising first pendent groups which comprise sulfonyl halide groups or by direct fluorination of a polymer mixture of a first polymer which is a non-perfluorinated polymer and a second polymer which comprises first pendent groups which comprise sulfonyl halide groups. Such crosslinked polymers or polymer mixtures may be used to make polymer electrolyte membranes (PEM's) that may be used in electrolytic cells such as fuel cells and which should demonstrate increased durability in fuel cell use.