In this research study, a new set of restoring force equations are proposed for seismic isolated structures subjected to far fault ground motions (FFGM) and near fault ground motions (NFGM). For this purpose, 110 FFGM and 49 NFGM are selected. Then, nonlinear time history analyses (NLTHA) of SDOF seismic isolated structures are performed using the selected ground motions to obtain their residual and maximum displacements. The analyses are repeated for an extensive range of parameters including peak ground acceleration, A(p), characteristic strength, Q(d) and post elastic period, T-d, of the isolation system. Next, the variations of the residual and maximum displacements are plotted as functions of the various combinations of the parameters considered in the analyses. Then, nonlinear regression analyses are performed to formulate the residual and maximum displacements as functions of the parameters considered in the analyses. The developed equations are then used to formulate the upper limits of T-d (restoring force equations) to ensure reasonable levels of residual and maximum isolator displacements. The developed restoring force equations are then compared with those of AASHTO and Eurocode-8 (EC-8) using the pool of residual and maximum displacement data obtained from NLTHA. It is observed that using the restoring force equations of AASHTO and EC-8 to check the design of seismic-isolated structures may, in some cases, produce unreasonably large levels of residual and maximum displacements. However, when the restoring force requirements proposed in this research study are applied, the residual and maximum displacements are observed to be within reasonable ranges.