In　this　paper,　we　investigate　the　convergence　of　the　time-dependent　and　non-isentropic　Euler-Maxwell　equations　to　incompressible　Euler　equations　in　a　torus　via　the　combined　quasi-neutral　and　non-relativistic　limit.　For　well　prepared　initial　data,　the　convergences　of　solutions　of　the　former　to　the　solutions　of　the　latter　are　justified　rigorously　by　an　analysis　of　asymptotic　expansions　and　energy　method.　(C)　2010　Elsevier　Ltd.　All　rights　reserved.