Tuned　inerter　damper　(TID)　has　been　demonstrated　as　an　effective　device　for　vibration　control　of　adjacent　structures.　However,　previous　studies　normally　assumed　inerter　as　a　linear　device,　and　applied　it　to　control　the　vibrations　of　linear　structures.　In　other　words,　both　the　inerter　and　structural　nonlinearities　were　ignored,　which　may　result　in　an　unreasonable　assessment　on　the　seismic　responses　of　adjacent　structures.　To　investigate　the　influences　of　nonlinearities　on　the　seismic　responses　of　adjacent　bridges,　OpenSees　software　is　adopted　in　the　present　study　due　to　its　capability　and　convenience　in　considering　structural/material　nonlinearity.　A　new　subroutine　is　developed　in　OpenSees　software　to　consider　TID　nonlinearity,　and　its　accuracy　is　validated　by　the　analytical　and　experimental　results.　To　examine　the　TID　control　effectiveness,　finite　element　(FE)　models　of　adjacent　bridges　considering　structural　nonlinearity　are　established　and　nonlinear　time　history　analyses　are　performed　to　investigate　the　seismic　performances　of　adjacent　bridges　with　and　without　TID.　The　results　show　that　TID　is　a　favourable　control　device　for　seismic　response　control　of　adjacent　bridges,　which　can　mitigate　the　displacements　of　bridge　decks,　drift　ratios　of　bridge　piers　and　delay　plastic　hinge　developments　in　the　bridge　piers.　Although　inerter　nonlinearity　can　potentially　enhance　TID　effectiveness　in　controlling　relative　displacement　response,　structural　nonlinearity　tends　to　reduce　the　TID　performances.　Furthermore,　both　the　inerter　and　structural　nonlinearities　have　the　potential　to　intensify　pounding　forces.　It　is　suggested　that　nonlinearities　should　be　considered　in　the　seismic　response　analyses　of　inerter-enhanced　adjacent　bridges.　©　2024　Elsevier　Ltd