Anti-interference　motion　control　and　elastic　vibration　synchronous　suppression　of　base　and　joints　for　an　elastic-base　elastic-joint　space　robot　with　uncertainties　are　studied.　On　the　basis　of　equivalent　linear　spring　assumptions　about　the　elastic　base　and　joints,　the　dynamic　equations　of　the　space　robot　are　established,　then　both　singular　perturbation　slow　and　fast　subsystems　are　deduced　with　the　equivalent　stiffness　concept.　The　traditional　parameter　adaptive　control　law　is　improved　by　using　σ　modification,　and　is　then　combined　with　the　robust　anti-interference　control.　An　improved　singular　perturbation　adaptive　robust　anti-interference　control　scheme　is　proposed　for　the　slow　subsystem　to　track　the　rigid　motion　trajectories　of　the　base＇s　attitude　and　links＇　joints　subject　to　uncertain　parameters　and　bounded　external　disturbances.　A　high-gain　linear　state　observer　is　employed　to　measure　the　fast　higher-order　states　in　real　time,　and　an　improved　optimal　control　method　is　designed　for　the　fast　subsystem　to　synchronously　suppress　the　elastic　vibrations　of　the　base　and　joints.　Simulation　result　demonstrates　the　validity　of　the　presented　hybrid　control　scheme　in　anti-interference　motion　control　and　vibration　suppression　of　the　space　robot.　Copyright　©　2018　Acta　Automatica　Sinica.　All　rights　reserved.