  Locally finite omega languages were introduced by Ressayre in [Journal of
Symbolic Logic, Volume 53, No. 4, p.1009-1026]. They generalize omega languages
accepted by finite automata or defined by monadic second order sentences. We
study here closure properties of the family LOC_omega of locally finite omega
languages. In particular we show that the class LOC_omega is neither closed
under intersection nor under complementation, giving an answer to a question of
Ressayre.
