If∑is a finite alphabet。w--language is the set which consists of some infi— nite strings over∑．e--regular language is the~o--language that be accepted by o--finte automata．The authors described a subclassω—language from set viewpoint．It cannot tradition that gives the subclass ω—regular language from generation or reeognizition．In this paper．the authors also show the subclass ω—regular language from set viewpoint．This subclass is more widely．