Using　damping　devices　connected　among　three　adjacent　structures　to　implement　their　aseismic　control　was　proposed　here.　The　random　response　formula　was　derived　based　on　a　single-DOF　system　simplified　model　for　three　adjacent　structures.　Further,　a　multi-DOF　system　model＇s　stiffness　matrix　and　damping　one　construction　method　for　three　adjacent　structures　was　presented　and　the　multi-DOF　system＇s　random　response　formulas　were　deduced　based　on　the　complex　mode　superposition　method.　Finally,　the　aseismic　control　effects　of　various　combinations　of　the　single-DOF　system　simplified　model　for　three　adjacent　structures　were　analyzed,　respectively　and　those　of　the　multi-DOF　system　model　for　three　adjacent　structures　were　also　studied　in　detail.　The　simulation　results　showed　that　after　using　connected　damping　devices,　the　aseismic　control　effects　for　three　adjacent　structures　and　those　for　two　adjacent　structures　are　almost　the　same;　when　the　aseismic　control　is　invalid　due　to　two　adjacent　structures＇　symmetry,　the　aseismic　control　effects　for　three　adjacent　structures　are　still　better;　in　addition,　three　adjacent　structures　have　a　good　robustness　and　their　higher-order　response　peaks　are　suppressed　significantly　under　random　earthquake　excitation.　©　2017,　Editorial　Office　of　Journal　of　Vibration　and　Shock.　All　right　reserved.