A hybrid seismic control system for building structures is considered, which combines a class of passive nonlinear base isolator with an active control system. The active control forces are applied to the structural base with the objective of reducing its absolute displacements. An adaptive control law is formulated to compute the control forces to assure a form of stable behavior of the system under seismic excitation and in the presence of uncertainties in the characteristics of the building and the base isolator. Numerical simulations are performed to assess the effectiveness of the hybrid control system. The global behavior of the structurebase-isolator system is such that the absolute base displacement is significantly reduced, the price paid being a slight increase of the response of the structure.