In　this　article,　we　apply　the　localization　techniques　to　right　(*)-serial　coalgebras　and　obtain　some　interesting　results.　In　particular,　we　give　a　characterization　of　right　(*)-serial　coalgebras　by　means　of　its　＇local　structure＇,　which　is　the　localized　right　(*)-serial　coalgebras,　and　we　get　a　main　result-the　periodicity　theorem.