We　study　cotilting　comodules　and　f-cotilting　comodules　and　give　a　description　of　localization　of　f-cotilting　comodules　and　classical　tilting　comodules.　First,　we　introduce　T-cotilting　injective　comodules　and　their　dimensions　which　are　important　for　researching　cotilting　comodules.　Then　we　characterize　the　localization　in　f-cotilting　comodules,　finitely　copresented　comodules,　and　classical　tilting　comodules.　In　particular,　we　obtain　a　localizing　property　about　finitely　copresented　comodules.