Base insolation systems partially uncoupled a structure from the seismic ground motion by means of specially designed, replaceable, devices inserted between the structure and its foundation. These devices are capable of absorbing part of the energy induced by earthquake [1-4] and drastically reduce the seismic action transmitted to the structure. A numerical simulation of their effect on the seismic response of structures requires algorithms capable of analyzing structures with both elastomeric (hysteric) bearing and sliding (frictional) bearings [5,6]. Different numerical schemes for solving the equations of motion have been proposed. The most often used numerical procedures are monolithic step-by-step integration schemes, that is, schemes that lead to algebraic systems of equations involving both the degrees of freedom corresponding to the structure and the foundation. On the other hand, there is the possibility of coupling these two sets of unknowns interactively, rather than by solving the full algebraic system. These iterative methods, when combined with the proper linearization of the nonlinear terms, yield block iterative schemes as those considered in this paper. Their capability for solving other problems, such as the dam-fluid interaction or the motion of thermally driven flows, is described in reference . In this paper, the application of schemes of this type in computing the seismic response of building structures with base isolation is considered, being this a problem of two systems coupled across their boundary conditions. The corresponding equations of motion are first written and details concerning the possibilities of numerical computation of the seismic response are given. Different manners of formulating block iterative schemes are described in a generic form and are then applied to the studied case. Their effectiveness in then explored on the basis of a complete numerical example.