This　paper　is　concerned　with　the　compressible　Euler-Maxwell　equations　arising　from　plasmas.　By　using　the　techniques　of　symmetrizer　and　energy　method,　the　well-posedness　of　solutions　to　periodic　problems　with　prepared　initial　values　was　investigated.　It　shows　that　the　periodic　problems　have　globally　smooth　solutions　near　a　non-constant　steady　state　with　an　asymptotic　stability　property.　©　2016,　Beijing　University　of　Technology.　All　right　reserved.