The　residual　deformation　is　one　crucial　factor　determining　the　structural　safety　and　the　structural　repair　cost　after　earthquakes.　Hence,　the　quantitative　estimation　of　residual　displacements　is　necessary　for　modern　performance-based　design　and　assessment　procedures.　This　study　evaluates　the　residual　displacement　responses　of　single　degree　of　freedom　(SDOF)　systems　with　Bouc-Wen　model　under　near-fault　pulse-like　ground　motions　through　nonlinear　dynamic　analyses.　To　this　end,　four　quantitative　indexes　for　the　residual　displacement　responses　are　first　defined　and　calculated.　The　dispersion　of　the　four　quantitative　indexes　is　then　analyzed,　and　the　correlations　between　the　residual　displacement　and　the　yield　displacement,　maximum　inelastic　displacement　or　elastic　displacement　are　also　investigated.　The　analysis　results　indicate　that　using　the　maximum　inelastic　displacement　can　better　estimate　the　residual　displacement　of　structures　under　near-fault　pulse-like　ground　motions.　Furthermore,　the　influences　of　the　structural　properties　and　ground　motion　characteristics　on　the　ratio　of　the　residual　displacement　to　the　maximum　inelastic　displacement　(C-r　)　are　analyzed　statistically.　Finally,　a　simplified　equation　for　predicting　this　ratio　is　regressed　to　estimate　residual　displacements　of　structures　under　near-fault　pulse-like　ground　motions.