A combined energy dissipation system is developed in this paper. In this system lead robber dampers and their parallel connection with oil dampers are used in the braces of a structural frame. A dynanric analysis method of the system, including the modelling of the lead robber damper and the oil damper, is proposed. In the analysis method, the restoring force characteresfics of the lead rubber damper is simulated by the Boue-Wcn hysteretic model, and the behaviour of the oil damper is simulated by a velocity and displacement-related model in which the contributions of the oil damper to the damping force and stiffness of the system are considered. A series of shaking table tests of a three storey steel frame with the combined energy dissipation system are carried out Io evaluate the performance of the system and Io verify the analysis method. The test and analysis show that the performance of the combined energy dissipation system is quite satisfactory and there is a good agreement between the analysis and test results, which indicates that the analysis method proposed in this paper is valid and suoable for the dynamic analysis of the combined energy dissipation system.