Fuel cells incorporating a novel ion-conducting membrane are disclosed. The membrane comprises a plurality of acid-stable polymer molecules each having at least one ion-conducting component covalently bonded to at least one flexible connecting component. The membrane has ion-conducting components of the polymer molecules ordered such that a plurality of continuous ion-conducting channels penetrate the membrane from a first face to a second face and such that the ion-conducting channels are situated in an elastic matrix formed by the flexible connecting components. A preferred membrane is obtained by (1) sulfonating SEBS with sulfur trioxide under conditions that result in greater than 25 mol % sulfonation and (2) heating the polymer.