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Vicso-elastic dampers are increasingly used to reduce earthquake-induced vibration of building structures, including wood house structures which show slip hysteresis under earthquake loading. In this paper, simplified theories are proposed for seismic response evaluation and preliminary design of slip-hysteretic structures combined with visco-elastic dampers. They are based on the single-degree-of-freedom (SDOF) idealization of multistory structure, and produce the control performance curve expressing the peak responses as a function of stiffness of all components, based on spectral characteristics of the earthquake. Against the target peak response, a rule to convert the SDOF design to multistory design, with consideration to distribute damper stiffness over the height of structure, is also presented. Accuracy of the approach is demonstrated by time history simulations over a wide range of parameters.