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　trajectory　tracking　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.　Firstly,　the　dynamics　equation　of　system　is　deduced　by　modeling　multi-bodies　dynamics　method　and　combing　with　connatural　dynamics　characters　of　linear　momentum　and　angular　momentum　of　free-floating　space　robot.　And　on　basis　of　above,　as　each　joint　hinge　has　strong　flexibility　in　practical　use　of　space　robot,　a　joint　flexibility　compensation　controller　is　introduced　to　solve　such　problem　that　application　of　traditional　singular　perturbation　method　is　limited　by　joint　flexibility,　so　mathematical　model　that　be　suitable　for　the　design　of　control　systems　is　established.　Then　using　the　mathematical　model,　a　neural　network　adaptive　control　algorithm　that　based　on　the　idea　of　backstepping　in　the　slow　subsystem　is　designed　to　compensate　system　parameter　unknown　and　rotation　error　caused　by　flexible　joint,　thus　system　trajectory　tracking　performance　is　fulfilled.　For　the　fast　subsystem,　a　robust　optimal　control　algorithm　is　presented　to　suppress　the　system　double　elastic　vibration　that　caused　by　flexible　joint　and　flexible　link,　thus　the　stability　of　the　system　is　guaranteed.　Finally,　the　availability　of　said　designed　control　algorithm　is　testified　by　the　simulation　comparison　experiment.