This　paper　deals　with　a　complex　mode　superposition　method　for　the　seismic　responses　of　general　multiple　degrees　of　freedom　(MDOF)　discrete　system　with　complex　eigenvectors　and　eigenvalues.　A　delicate　general　solution,　completely　in　real　value　form,　for　calculating　seismic　time　history　response　of　the　MDOF　system　which　cannot　be　uncoupled　by　normal　modes,　is　deduced　based　on　the　algorithms　of　the　complex　superposition　method.　This　solution　comprises　of　two　parts　which　are　in　relation　to　the　Duhamel　integration　to　sine　and　cosine　function　respectively.　The　related　term　of　the　Duhamel　integration　to　sine　function　is　actually　the　displacement　response　of　the　oscillator　with　corresponding　modal　frequency　and　the　damping　ratio.　The　other　can　be　transferred　into　a　combination　of　the　displacement　and　velocity　responses　of　the　same　oscillator.　In　order　to　meet　the　practical　needs　of　seismic　design　based　on　code　design　spectra　for　various　kinds　of　structures　equipped　by　viscous　dampers,　the　complex　complete　quadratic　combination　(CCQC)　method　is　deduced　following　similar　procedures　such　as　the　well-known　CQC　method,　in　which　a　new　modal　velocity　correlation　coefficient,　together　with　a　new　modal　displacement-velocity　correlation　coefficient　are　involved　besides　the　modal　displacement　correlation　coefficient　in　normal　CQC　formula.　The　new　algorithm　of　CCQC　is　riot　only　as　concise　as　that　of　the　normal　CQC　but　also　has　explicit　physical　meaning.　The　results　obtained　from　complex　mode　superposition　approaches　are　discussed　and　verified　in　some　examples　through　step　by　step　integration　computation　under　a　prescribed　earthquake　motion　input.　From　these　examplary　analyses,　it　may　be　pointed　that　the　CCQC　algorithm　normally　yields　conservative　outcome　and　that　the　forced　mode　uncoupling　approach　has　good　approximation　even　the　discussed　examplary　structures　are　strongly　non-proportional.