In　this　paper,　the　convergence　of　two-fluid　time-dependent　Euler-Maxwell　equations　to　two-fluid　compressible　Euler-Poisson　equations　in　a　torus　via　the　non-relativistic　limit　is　studied.　The　local　existence　of　smooth　solutions　to　both　systems　is　proved　by　using　energy　estimates　for　first　order　symmetrizable　hyperbolic　systems.　For　well　prepared　initial　data,　the　method　of　asymptotic　expansion　and　energy　methods　are　used　to　rigorously　justify　the　convergence　of　the　limit.　(C)　2009　WILEY-VCH　Verlag　GmbH　&　Co.　KGaA,　Weinheim