The　dynamics　modeling,　motion　control　design　and　joint-link　double　flexible　vibration　active　suppression　of　free-floating　flexible-joint　flexible-link　space　robot　with　uncertain　parameters　and　external　disturbance　are　discussed.　The　system＇s　dynamic　equations　are　established　according　to　linear　momentum　conservation,　angular　momentum　conservation　and　Lagrange-Assumed　mode　method.　Based　on　singular　perturbation　method,　the　system　is　decomposed　into　a　slow　subsystem,　a　fast　subsystem　1　and　a　fast　subsystem　2.　For　the　slow　subsystem,　a　saturation　robust　fuzzy　sliding　controller　is　proposed　to　compensate　the　influences　of　the　uncertain　parameters,　rotation　angles＇　errors　and　the　external　disturbance,　and　thus　realize　the　asymptotic　tracking　of　the　system　desired　trajectory.　The　saturation　function　is　used　to　recede　the　chattering　of　the　sliding　control;　for　the　fast　subsystem　1,　a　velocity　difference　feedback　controller　is　used　to　suppress　the　flexible　vibration　caused　by　flexible-joint;　for　the　fast　subsystem　2,　linear　quadric　regulator　is　used　to　suppress　the　flexible　vibration　caused　by　flexible-link.　The　simulation　results　prove　the　controller＇s　efficiency.　©2015　Journal　of　Mechanical　Engineering.