The conventional form of solving the equations of motion governing the seismic response of building structures with nonlinear base isolation consists of using monolithic step by step integrationmethods. As an alternative, the application of a block iterative scheme is examined in this paper. After describing the particularities of the equations of motion of the structure with base isolation, different block iterative schemes are described. Their effectiveness is discussed and compared with that of monolithic step by step integration methods. Adequate examples are used with the aim of performing numerical comparisons.