In this paper, the possibility offered by the Base Isolation System, designed according to the strategy of limitation seismic force, in order to ensure a significant level of robustness to the isolated superstructure, has been analyzed. In according to the strategy of limitation seismic force, a new seismic isolator called HDHSI (High Damping Hybrid Seismic Isolator) is proposed, obtained by the assembly in series of a LRB (Lead Rubber Bearing) and a FS (Friction Slider) with high friction coefficient. The HDHSI device is in contrast to the R-FBI (Resilient-Friction Base Isolation) isolator and is the optimization of the EDF (Electricité De France) system. A modeling with HDHSI devise has been presented by using nonlinear finite elements NLlink (Nonlinear link) and nonlinear dynamic analysis for a SDOF system with harmonic force, in order to characterize the cycle-hysteretic behavior of the device for different levels of shear deformation, are performed. Nonlinear dynamic analysis for a RC structure, base isolated by the proposed devices, are performed. As seismic actions, have been adopted the following registrations: an anomalous earthquakes for intensity and in particular El Centro earthquake (N00W component, 1940) with different amplification factors; an anomalous earthquake for frequency content and in particular Erzincan earthquake (N90W component, 1992).