Poly(aryl alkylene) polymers or poly(aryl-crown ether-alkylene) polymers with pendant cationic groups are provided which have an alkaline-stable cation, such as imidazolium, introduced into a rigid aromatic polymer backbone free of ether bonds. Hydroxide exchange membranes or hydroxide exchange ionomers formed from these polymers exhibit superior chemical stability, hydroxide conductivity, decreased water uptake, good solubility in selected solvents, and improved mechanical properties in an ambient dry state as compared to conventional hydroxide exchange membranes or ionomers. Hydroxide exchange membrane fuel cells and hydroxide exchange membrane electrolyzers comprising the poly(aryl alkylene) polymers or poly(aryl-crown ether-alkylene) polymers with pendant cationic groups exhibit enhanced performance and durability at relatively high temperatures.