Recently,　the　authors　explored　the　effectiveness　of　using　an　inerter-based　device　to　mitigate　pounding　induced　damage　between　two　adjacent　bridge　structures,　and　the　advantages　of　this　system　were　illustrated　by　comparing　its　performances　with　the　conventional　viscous　dampers.　However,　the　seismic　excitations　at　the　supports　of　the　adjacent　bridge　structures　were　assumed　to　be　the　same　in　that　study,　i.e.　only　uniform　ground　motion　was　considered.　In　reality,　ground　motions　at　different　locations　of　a　structure　are　inevitably　different,　and　spatially　varying　ground　motions　(SVGMs)　can　influence　the　structural　seismic　responses　significantly.　Extensive　research　works　have　been　carried　out　to　investigate　the　influence　of　SVGMs　on　the　seismic　responses　of　engineering　structures.　However,　no　open　literature　reported　the　results　when　an　inerter-based　device　is　involved.　In　this　study,　the　motion　equations　of　two　adjacent　bridges　coupled　by　a　tuned　inerter　damper　(TID)　are　firstly　derived,　and　the　seismic　responses　of　the　adjacent　bridges　with　and　without　control　are　calculated.　In　particular,　the　parameters　that　significantly　influence　SVGMs,　i.e.　wave　passage　effect　and　coherency　loss　effect,　are　discussed.