The　flexibility　of　space　robot　system　is　mainly　embodied　in　links　of　space　robot　and　their　connected　hinge　joints.　For　the　reason　of　complexity　of　space　robot　system　structure,　researchers　usually　pay　less　attention　on　the　system　which　both　has　flexible　joint　and　link.　So　it＇s　discussed　in　this　paper　for　dynamics　simulations,　algorithm　design　of　motion　control,　and　active　suppression　problem　of　joint　and　link　double　flexible　vibration　for　space　robot　system　with　flexible-joint　and　flexible-link　under　the　situation　of　parameter　uncertain.　With　the　conservation　relationship　of　linear　and　angular　momentum,　a　system　dynamics　model　is　established　by　Lagrange　equations,　linear　torsion　spring　and　hypothesis　modal　method.　To　solve　the　problem　that　the　application　of　traditional　singular　perturbation　approach　is　limited　by　joint　flexibility,　a　joint　flexibility　compensation　controller　is　introduced,　which　can　properly　enhance　the　equivalent　stiffness　of　joints.　Then,　based　on　singular　perturbation　theory,　the　whole　system　is　resolved　into　flexible　arm　subsystem　and　motor　moment　power　subsystem　on　the　basis　of　joint　flexible　compensation　controller　and　singular　perturbation　technology.　An　robust　control　scheme　is　proposed　for　flexible　arm　subsystem,　since　tracking　virtual　desired　trajectory,　so　rigid　trajectory　track　is　guaranteed　just　by　inputting　one　control,　and　at　the　same　time,　active　suppression　on　flexible　vibration　is　made.　And　for　motor　moment　power　subsystem,　a　moment　differential　feedback　controller　is　designed　to　inhibit　system　elastic　vibration　that　caused　by　joint　flexibility.　Computer　numerical　simulation　comparison　experiment　testifies　the　reliability　and　availability　of　this　scheme.