In　this　paper,　several　criteria　on　the　existence　of　periodic　solutions　for　a　tethered　satellite　system　(TSS)　in　an　elliptical　orbit,　as　well　as　the　uniqueness　of　periodic　solutions　for　the　TSS　in　a　circular　orbit　are　presented　on　the　basis　of　coincidence　degree　theory.　In　addition,　the　conditions　on　the　global　asymptotic　stability　of　the　equilibrium　states　for　the　TSS　are　also　addressed　in　accordance　with　the　Lyapunov　stability　theory　and　Barbashin-Krasovski　theory.　(C)　2012　Elsevier　Ltd.　All　rights　reserved.