The　dynamics　modeling,　motion　trajectory　tracking　control　and　elastic　vibration　suppressing　problems　of　freefloating　space　manipulator　system　with　flexible　joints,　uncertain　system　parameters　and　external　disturbances　are　studied.　The　system＇s　dynamic　equations　are　established　by　using　the　momentum　conservation,　angular　momentum　conservation　and　the　Lagrange　equation.　According　to　the　singular　perturbation　method,　the　system　is　decomposed　into　two　independent　subsystems:　a　slow　subsystem　(represents　the　system＇s　rigid　part)　and　a　fast　subsystem　(represents　the　system＇s　flexible　part).　For　the　slow　subsystem,　a　robust　backstepping　control　method　based　on　a　state　observer　is　designed　to　eliminate　the　＂rigid-flexible　rotation　angle　error＂,　compensate　the　uncertain　system　parameters　and　the　external　disturbances,　and　achieve　the　asymptotic　tracking　of　the　space　manipulator.　During　the　control　procedure,　there　is　no　need　to　measure　and　feedback　the　system＇s　velocity　signals　by　use　of　the　state　observer,　so　the　control　method　is　simpler　and　more　precise.　For　the　fast　subsystem,　a　velocity　difference　feedback　control　method　is　used　to　stabilize　the　elastic　vibrations　caused　by　the　flexible　joints,　and　guarantee　the　system＇s　stability.　The　simulation　results　prove　the　proposed　control　method＇s　efficiency.