Seismic behaviors of base-isolated structures are highly affected by the nonlinear characteristics of the isolated systems.Most of the currently available methods for the identification of nonlinear properties of isolator require either the measurements of all structural responses or the assumptions of the proper mathematic models for the rubber-bearings.In this paper,two algorithms are proposed to identify the nonlinear properties of rubber-bearings in base-isolated buildings using only partial measurements of structural dynamic responses.The first algorithm is applicable to the case that proper mathematical models are available for the base isolators.It is based on the extended Kalman filter for the parametric identification of nonlinear models of rubber-bearing isolators and buildings.For the general case where it is difficult to establish a proper mathematical model to describe the nonlinear behavior of a rubber-bearing isolator,another algorithm is proposed to identify the model-free nonlinear property of rubber-bearing isolated system.Nonlinear effect of rubber-bearing is treated as ’fictitious loading’ on the linear building under severe earthquake.The algorithm is based on the sequential Kalman estimator for the structural responses and the least-squares estimation of the ’fictitious loading’ to identify the nonlinear force of rubber-bearing isolator.Simulation results demonstrate that the proposed two algorithms are capable of identifying the nonlinear properties of rubber-bearing isolated systems with good accuracy. Seismic behaviors of base-isolated structures are highly affected by the nonlinear characteristics of the isolated systems. Host of the currently available methods for the identification of nonlinear properties of isolators require either the measurements of all structural responses or the assumptions of the proper mathematic models for the rubber-bearings.In this paper, two algorithms are proposed to identify the nonlinear properties of rubber-bearings in base-isolated buildings using only partial measurements of structural dynamic responses. the first algorithm is applicable to the case that proper mathematical models are available for the base isolators. It is based on the extended Kalman filter for the parametric identification of nonlinear models of rubber-bearing isolators and buildings. For the general case where it is difficult to establish a proper mathematical model to describe the nonlinear behavior of a rubber -bearing isolator, another algorithm is proposed to identify the model-f ree nonlinear property of rubber-bearing isolated system. Nonlinear effect of rubber-bearing is treated as ’fictitious loading’ on the linear building under severe earthquake. The algorithm is based on the sequential Kalman estimator for the structural responses and least-squares estimation of the ’fictitious loading’ to identify the nonlinear force of rubber-bearing isolator. Simulation results demonstrate that the proposed two algorithms are capable of identifying the nonlinear properties of rubber-bearing isolated systems with good accuracy.