Cationic polymer membranes that conduct free anions comprise all enabling area of research for alkaline membrane fuel cells and other solid-state electrochemical devices that operate at high pH The synthesis of anion exchange membranes based oil a poly(phenylene) backbone prepared by a Diels-Alder reaction is demonstrated The poly(phenylene)s have benzylic methyl groups that are converted to bromomethyl groups by a radical reaction. Cationic polymers result from conversion of the bromomethyl groups to ionic moieties by quaternization with trimethylamine in the solid state. The conversion to benzyltrimethylammonium groups is incomplete as evidenced by the differences between the IEC values measured by titration and the theoretical IECs based on H-1 NMR measurements The anion exchange membranes formed from these polymers have hydroxide ion conductivities as high as 50 mS/cm in liquid water, and they are stable under highly basic conditions at elevated temperatures.