Dynamic analyses of structures with supplemental hydraulic dampers are considered in this paper. Supplemental dampers and bracings serve as Maxwell models while the structure is considered as Kelvin model. Governing equations of structures with Maxwell model is obtained by combining the equations of rate of forces in the Maxwell model with Kelvin model and transformed into state space equations. In this case, the rate of forces in the Maxwell model is derived from the constitutive equation. It is obtained that the sizes of matrices involved in governing equations of the proposed procedure are three-quarters of the one when additional degrees of freedom are considered at the damper locations. Numerical simulations to a thirtystorey building with supplemental dampers result in that the proposed method has a very good agreement with the one when additional degrees of freedom are considered at damper locations. Numerical simulations by varying damper location subject to various ground accelerations show that the nature of the response reduction depends on the location of supplemental dampers. © 2005 Civil-Comp Press.