This　paper　focuses　on　the　ductility　demand　of　self-centering　structures　with　flag-shaped　(FS)　hysteretic　behavior　under　near-fault　(NF)　pulse-like　ground　motions.　To　this　end,　the　general　features　of　spectral　regions　for　the　NF　pulse-like　ground　motion　are　first　described.　The　effects　of　structural　and　ground　motion　characteristics　on　the　ductility　demand　spectra　are　further　carried　out.　The　results　indicate　that　the　variation　trends　of　the　ductility　demand　spectra　of　the　FS　model　are　closely　related　to　the　spectral　regions　of　the　ground　motion.　Finally,　a　predictive　model　is　established　to　evaluate　the　ductility　demands　for　self-centering　structures　under　NF　pulse-like　ground　motions.