Because　of　their　unique　properties　and　good　performance,　some　elastic　components,　such　as　the　harmonic　reducers　and　the　torque　sensors,　are　widely　used　in　the　joints　of　the　space　robots　and　manipulators,　in　order　to　obtain　high　reduction　ratio.　However　these　elastic　components　bring　joint　flexibility　into　the　system　at　the　same　time,　which　makes　its　stability　control　more　complex.　Based　on　this,　this　paper　discussed　radial　basis　function　neural　network　adaptive　control　and　elastic　vibration　suppression　for　flexible-joint　space　robots,　it　worked　under　the　unknown　parameter.　Firstly,　mathematical　models　which　been　suit　for　design　of　control　system　are　established　by　using　a　joint　flexibility　compensation　controller,　the　model　composed　of　the　slow-subsystem　robot　dynamics　model　and　and　the　fast-subsystem　dynamics　model　is　deduced　by　the　second　type　of　Lagrange　method.　Then,　for　the　dynamic　model　of　the　fast-subsystem　dynamics　model,　the　torque　differential　feedback　control　algorithm　is　adopted　to　the　premise　that　the　ultimate　doundedness　of　system,　for　the　slow-subsystem　robot　dynamics　model,　the　radial　basis　function　neural　network　adaptive　control　algorithm　is　designed　to　to　track　the　desired　trajectory　in　joint　space.　The　whole　control　system　is　superposed　by　the　slow-subsystem　and　the　fast-subsystem　control　algorithm.　The　system　simulation　comparison　test　proves　the　effectiveness　of　said　algorithm.　©　2018　IEEE.