The　flexibility　of　space　robot　system　mainly　embodies　in　its　arm　bars　and　hinge　joints　connecting　the　arm　bars.　The　dynamics　simulation　of　an　space　robot　system　with　flexible　joints　and　flexible　arms　were　carried　out,　the　motion　control　algorithm　was　designed　and　the　active　hierarchical　vibration　inhibition　of　flexible　arms　and　joints　was　investigated　under　the　situation　of　all　the　parameters　uncertain.　According　to　the　principle　of　conservation　of　momentum　and　moment　of　momentum,　and　based　on　Lagrange　equations,　the　dynamic　model　of　the　system　was　deduced　under　the　supposition　of　linear　torsion　spring　and　by　using　the　hypothesis　modal　method.　On　this　basis,　considering　the　actual　situation　that　each　hinge　joint　has　strong　flexibility　in　space　robot,　a　flexible　joint　compensation　controller　was　introduced　and　making　use　of　the　singular　perturbation　technology,　the　whole　system　was　decomposed　into　a　motor　moment　power　subsystem　and　a　flexible　arm　subsystem　with　independent　time　scale.　For　the　motor　moment　power　subsystem,　a　moment　differential　feedback　controller　was　designed　to　inhibit　the　elastic　vibration　caused　by　joint　flexibility.　For　the　flexible　arm　subsystem,　an　adaptive　fuzzy　global　sliding　mode　control　scheme　was　proposed　based　on　the　concept　of　virtual　force.　By　using　the　concept　of　virtual　force,　the　control　target　of　not　only　tracking　the　expected　trajectory,　but　also　inhibiting　the　vibration　of　flexible　arm　was　achieved　by　only　designing　a　control　input.　The　results　of　numerical　simulations　testify　the　reliability　and　availability　of　the　scheme　proposed.　©　2016,　Editorial　Office　of　Journal　of　Vibration　and　Shock.　All　right　reserved.