Tethered　satellite　systems　(TSSs)　are　becoming　more　widely　used　in　space　exploration　and　exploitation.　In　this　analytical　investigation,　the　criteria　on　the　existence　and　uniqueness　of　periodic　solutions　for　the　TSSs　are　presented　based　on　Mawhin＇s　continuation　theorem.　In　addition,　the　conditions　on　the　global　asymptotic　stability　for　the　equilibrium　states　of　the　TSSs　are　also　addressed　in　accordance　with　the　Lyapunov　stability　theorem.