The　negative　stiffness　damper　(NSD)　has　shown　excellent　effectiveness　in　reducing　vibration.　However,　researches　focusing　on　the　analysis　and　optimization　of　the　adjacent　structures　with　negative　stiffness　damper　(ASNSD)　under　non-stationary　seismic　excitation　(NSSE)　and　varying　soil　conditions,　remain　scarce.　This　paper　proposes　a　soil-dependent　stochastic　optimization　procedure　(SDSOP)　to　investigate　the　optimal　parameters　of　ASNSD　under　NSSE　considering　firm,　medium　and　soft　soil　conditions.　The　novelty　of　this　procedure　is　it　integrates　stochastic　optimization　with　non-stationary　seismic　excitation　modeled　using　the　Clough-Penzien　spectrum　combined　with　time　modulation　function,　while　considering　different　soil　conditions.　Firstly,　the　state-space　representations　of　stochastic　seismic　excitation　and　ASNSD　are　combined　to　form　the　representations　of　the　augmented　structure-damper-earthquake　systems.　Subsequently,　the　optimal　designs　of　ASNSD　are　defined　via　the　solution　of　the　deferential　Lyapunov　equation.　Lastly,　the　obtained　optimal　parameters　of　ASNSD　are　further　examined　under　artificially　generated　seismic　excitation　real　earthquake　records　from　the　perspectives　of　dynamic　response.　The　results　demonstrate　the　effectiveness　of　the　proposed　SDSOP　and　highlight　the　advantages　of　ASNSD　for　all　soil　conditions.　Compared　to　firm　and　medium　soil　conditions,　the　requirements　for　negative　stiffness　and　damping　values　are　significantly　higher　in　soft　soil　conditions.　©　2025