A stabilized, dynamically vulcanized thermoplastic elastomer composition comprising dispersed dynamically vulcanized particles of at least one first elastomer or rubber comprising halogenated isobutylene-containing elastomer and dispersed particles of at least one second elastomer or rubber comprising at least one functional group capable of reacting with and grafting to a polyamide, the particles of the at least one first and at least one second elastomers dispersed in a continuous thermoplastic polyamide or nylon resin matrix comprising at least one nylon homopolymer, nylon copolymer or mixture thereof, the composition or the at least one first elastomer further comprising at least one stabilizer against degradation induced by exposure to actinic, particularly ultraviolet, radiation. The compositions are preferably produced in a mixing extruder and are suitable for producing durable, flexible, thermoplastic elastomer fluid barrier films or layers useful in industrial articles such as vehicle tire innerliners and hoses.