This　paper　is　concerned　with　the　periodic　problem　to　the　two-fluid　non-isentropic　Euler–Maxwell　(N-E-M)　equations.　The　equations　arises　in　the　modeling　of　magnetic　plasma,　in　which　appear　two　physical　parameters,　the　mass　of　an　electron　me　and　the　mass　of　an　ion　mi.　With　the　help　of　methods　of　asymptotic　expansions,　we　prove　the　local-in-time　convergence　of　smooth　solutions　to　this　problem　by　setting　me=　1　and　letting　mi→　+　∞.　Moreover,　when　the　initial　data　are　near　constant　equilibrium　states,　by　means　of　uniform　energy　estimates　and　compactness　arguments,　we　rigorously　prove　the　infinity-ion-mass　convergence　of　the　system　for　all　time.　The　limit　system　is　the　one-fluid　N-E-M　system.　©　2021,　The　Author(s),　under　exclusive　licence　to　Springer　Nature　Switzerland　AG　part　of　Springer　Nature.