In　response　to　the　limitation　of　classical　Data　Envelopment　Analysis　(DEA)　models,　the　super　efficiency　DEA　models,　including　Andersen　and　Petersen　(Manag　Sci　39(10):　1261-1264,　1993)＇s　model　(hereafter　called　AP　model)　and　Li　et　al.　(Eur　J　Oper　Res　255(3):　884-892,　2016)＇s　cooperative-game-based　model　(hereafter　called　L-L　model),　have　been　proposed　to　rank　efficient　decision-making　units　(DMUs).　Although　both　models　have　been　widely　applied　in　practice,　there　is　a　paucity　of　research　examining　the　performance　of　the　two　models　in　ranking　efficient　DMUs.　Consequently,　it　is　unclear　how　close　the　rankings　obtained　by　the　two　models　are　to　the　＂true＂　ones.　Among　the　very　few　studies,　Banker　et　al.　(Ann　Oper　Res　250(1):　21-35,　2017)　pointed　out　that　the　ranking　performance　of　the　AP　model　is　unsatisfactory;　Li　et　al.　(Eur　J　Oper　Res　255(3):　884-892,　2016)　and　Hinojosa　et　al.　(Exp　Syst　Appl　80(9):　273-283,　2017)　demonstrated　the　L-L　model＇s　capability　of　ranking　efficient　DMUs　without　addressing　the　ranking　performance.　In　this　study,　we,　thus,　examine　the　ranking　performance　of　the　two　super-efficiency　models.　In　evaluating　their　performance,　we　carry　out　Monte　Carlo　simulations　based　on　the　well-known　Cobb-Douglas　production　function　and　adopt　Kendall　rank　correlation　coefficient.　Unlike　Banker　et　al.　(Ann　Oper　Res　250(1):　21-35,　2017),　we　use　the　rankings　obtained　based　on　the　two　models　and　the　＂true＂　ones　as　the　basis　of　performance　evaluation　in　our　simulations.　Moreover,　we　consider　several　types　of　returns　to　scale　(RS)　and　study　the　impact　of　changes　of　some　parameters　on　the　ranking　performance.　In　view　of　the　importance,　we　also　carry　out　additional　simulations　to　examine　the　influence　of　technical　inefficiency　on　the　two　models＇　ranking　performance.　Based　on　the　simulation　results,　we　conclude:　(1)　Under　different　RS,　the　ranking　performance　of　the　two　models　remains　the　same　when　changing　parameters,　e.g.,　the　distribution　of　input　variables;　(2)　Under　different　RS,　when　technical　inefficiency　(in　comparison　with　random　noise)　is　more　important,　the　two　models　have　satisfactory　performance　by　providing　rankings　that　are　close　to,　or　the　same　as,　the　＂true＂　ones;　(3)　The　L-L　model　has　better　performance　than　the　AP　model　and　is　more　robust.　This　is　especially　true　when　technical　inefficiency　is　less　important;　(4)　Under　different　RS,　when　technical　inefficiency　is　less　important,　both　models　have　unsatisfactory　ranking　performance;　and　(5)　The　relative　importance　of　technical　inefficiency　plays　an　prominent　role　in　ranking　efficient　DMUs.