The　response-spectrum　mode　superposition　method　is　widely　used　for　seismic　response　analyses　of　linear　systems.　In　using　this　method,　the　complete　quadratic　combination　(CQC)　is　adopted　for　classically　damped　linear　systems　and　the　complex　complete　quadratic　combination　(CCQC)　formula　is　adopted　for　non-classically　damped　linear　systems.　However,　in　both　cases,　the　calculation　of　seismic　response　analyses　is　very　time　consuming.　In　this　paper,　the　variation　of　the　modal　correlation　coefficients　of　displacement,　velocity　and　displacement-velocity　with　frequency　and　damping　ratios　of　two　modes　of　interest　are　studied,　Moreover,　the　calculation　errors　generated　by　using　CQC　and　square-root-of-the-sum-of-the-squares　(SRSS)　methods　(or　CCQC　and　CSRSS　methods)　for　different　damping　combinations　are　compared.　In　these　analyses,　some　boundary　lines　for　classically　and　non-classically　damped　systems　are　plotted　to　distinguish　the　allowed　minimum　frequency　ratio　at　given　geometric　mean　of　the　damping　ratios　of　both　modes　if　their　relativity　is　neglected.　Furthermore,　the　simplified　method,　which　is　a　special　mode　quadratic　combination　method　considering　only　relativity　of　adjacent　modes　in　CQC　method　and　named　simplified　CQC　or　partial　quadratic　combination　(PQC)　method　for　classically　damped　linear　system,　is　proposed　to　improve　computational　efficiency,　and　the　criterion　for　determination　of　how　many　correlated　modes　should　be　adopted　is　proposed.　Similarly,　the　simplified　CCQC　or　complex　partial　quadratic　combination　(CPQC)　method　for　the　non-classically　damped　linear　system　and　the　corresponding　criterion　are　also　deduced.　Finally,　a　numerical　example　is　given　to　illustrate　the　applicability,　computational　accuracy　and　efficiency　of　the　PQC　and　CPQC　methods.