We　develop　an　initial-boundary　value　problem　derived　from　the　Maxwell＇s　system　with　a　nonlinear　feedback-type　boundary　mechanism　in　metamaterials,　which　both　involves　polarization,　magnetization　ef-fect　and　time-localized　delay　effect　in　a　bounded　domain.　Based　on　the　nonlinear　semigroup　theory　and　the　properties　of　viscoelasticity　theory,　we　show　the　well-posedness　of　solution　in　an　appropriate　Hilbert　space.　Under　some　suitable　assumptions　and　geometric　conditions,　we　prove　the　exponential　stability　of　the　Maxwell＇s　system.(c)　2023　Elsevier　Inc.　All　rights　reserved.