Self-centering systems have attracted significant interest in earthquake-engineering research, due to their excellent performance under simulated seismic loading through their self-centering capabilities. A comprehensive parametric study is presented to compare the ductility demands on single-degree-of-freedom (SDOF) systems, when subjected to ground motions with a probability of exceedance of 10% in 50 years in California. The influences of different parameters were analyzed under SDOF structural responses in terms of displacement ductility and absolute acceleration. The responses of the flag-shaped hysteretic SDOF systems were also compared against the responses of similar bilinear elasto-plastic hysteretic SDOF systems. Two ensembles of far-field and near-fault historical earthquake records, corresponding to ordinary earthquakes, were used for the parametric study to compare the ductility demands. Although a flag-shaped hysteretic SDOF system of equal or lesser strength can often match or better the response of an elasto-plastic hysteretic SDOF system with almost no residual drift, the analysis shows that seismic design of self-centering systems should account for the difference between far-field and near-fault ground motion.