The　robustness　of　a　schedule　is　an　important　problem　in　practice.　In　this　paper　it　is　studied　in　the　angle　that　the　optimal　schedules　do　not　change.　Firstly　the　neighbor　robustness　of　an　optimal　schedule　is　defined,　that　is　the　property　that　an　optimal　schedule　keeps　the　same　when　some　of　the　parameters　(considered　as　a　point　in　the　responding　hyperspace)　in　the　scheduling　problem　vary　in　one　of　its　neighbors.　Then　the　results　in　this　paper　are　proved.　The　results　are:　for　a　problem　with　continuous　objective　its　strictly　optimal　schedule　is　of　neighbor　robustness,　and　for　single　machine　total　weighted　completion　time　problem　its　optimal　schedule　is　of　neighbor　robustness　with　probability　of　1.　Some　discussion　and　examples　are　given.