In　this　paper,　we　study　analytically　and　numerically　the　singular　limits　of　the　nonlinear　Klein-Gordon-Schrodinger　(KGS)　equations　in　R(d)　(d　=　1,　2,　3)　both　with　and　without　a　damping　term　to　the　nonlinear　Schrodinger-Yukawa　(SY)　equations.　By　using　the　two-scale　matched　asymptotic　expansion,　formal　limits　of　the　solution　of　the　KGS　equations　to　the　solution　of　the　SY　equations　are　derived　with　an　additional　correction　in　the　initial　layer.　Then　for　general　initial　data,　weak　and　strong　convergence　results　are　established　for　the　formal　limits　to　provide　rigorous　mathematical　justification　for　the　matched　asymptotic　approximation　by　using　the　weak　compactness　argument　and　the　(　modulated)　energy　method,　respectively.　In　addition,　for　well-prepared　initial　data,　optimal　quadratic　and　linear　convergence　rates　are　obtained　for　the　KGS　equations　both　with　and　without　the　damping　term,　respectively,　and　for　ill-prepared　initial　data,　the　optimal　linear　convergence　rate　is　obtained.　Finally,　numerical　results　for　the　KGS　equations　are　presented　to　confirm　the　asymptotic　and　analytic　results.