This　paper　analyzes　the　damping　dissipation　of　damped　outrigger　tall　buildings　with　inerter　and　negative　stiffness　considering　soil-structure-interaction　(SSI).　A　unified　characteristic　equation　is　established　concerning　different　soil　conditions　and　outrigger　systems.　By　solving　the　unified　characteristic　equation,　the　multi-mode　damping　effect　are　parametrically　investigated　to　evaluate　the　influence　of　SSI　on　tall　buildings　installing　conventional　outrigger　(CO),　conventional　damped　outrigger　(CDO),　negative　stiffness　damped　outrigger　(NSDO),　and　inerter　damped　outrigger　(IDO).　Then,　the　vibration　performances　of　damped　outrigger　systems　considering　SSI　are　evaluated　under　both　wind　and　earthquake　loadings.　Two　key　points　are　highlighted:　(i)　the　interaction　between　the　soil　rocking　behavior　and　the　outrigger　rotation　in　tall　buildings;　(ii)　the　influence　of　frequency　variation　caused　by　SSI　on　the　damping　effect　of　IDO　and　NSDO　with　frequency-dependent/independent　features.　Analyzing　results　indicate　that　a　stronger　CO　would　increase　the　damping　effect　of　the　foundation　soil　as　long　as　the　CO　is　not　installed　at　lower　stories.　The　SSI　effect　will　render　CDO　itself　undergo　more　dissipation　for　the　first　mode　but　limit　CDO＇s　damping　effect　on　higher　modes.　IDO　can　be　effective　for　the　target　mode,　but　is　very　sensitive　to　SSI　effect　due　to　its　frequency-dependent　feature;　a　re-optimization　of　IDO　to　proper　vibration　mode　is　always　needed　in　resisting　wind　and　earthquake.　In　contrast,　NSDO＇s　damping　effect　is　less　sensitive　to　the　SSI　effect　and　can　be　effective　to　multiple　modes　due　to　its　frequency-independent　feature.　For　example,　the　majority　of　the　input　energy　from　winds　(over　90%)　and　earthquake　(over　70　%)　will　be　dissipated　by　NSDO,　and　such　high　values　change　little　under　SSI　conditions,　validating　NSDO　can　provide　effective　and　robust　control　to　multiple　hazards.　©　Elsevier　Ltd