AbstractA class of hybrid control system which combines a passive nonlinear base isolator with an active controller is analyzed. The passive component of the system has a hysteretic behaviour. A single control force is applied on the structural base by means of a new adaptive control strategy, not requiring knowledge of the system parameters and the excitation and able to handle the typical nonlinearities associated with base isolators. A numerical study is performed to assess the improvement of the behaviour of buildings equipped with this control system.