Abstract: To investigate the localization problems of fc-tame coalgebras and fc-wild coalgebras,based on the concepts and properties of fc-tame coalgebras and fc-wild coalgebras,using the method of localization and applying the quotient functor and section functor,the authors studied the finitely copresented comodules,fc-tame coalgebras and fc-wild coalgebras and obtained the weak localization properties of finitely copresented comodules.In particular,the relations of fc-tame and fc-wild between coalgebras and localized coalgebras were given.