Dynamics　model　and　anti-disturbance　L2　gain　robust　backstepping　control　for　space　manipulators　with　fully　flexible　links　were　discussed.　A　dynamic　model　of　the　system　was　successively　derived　by　combining　with　Lagrange　equations,　the　system　linear　momentum　and　assumed　mode　method.　Based　on　singular　perturbation　method,　the　system　was　decomposed　into　a　slow　subsystem　which　was　described　joint　rigid　trajectory　tracking,　and　a　fast　subsystem　which　was　described　the　vibrations　of　flexible　links.　A　robust　backstepping　controller　which　made　the　external　bounded　disturbances　had　the　performance　of　the　L2　gain　of　the　output　system　is　less　than　the　given　value.　And　the　controller　also　might　suppress　external　bounded　interferences.　Vibrations　of　the　flexible　links　were　suppressed　by　optimal　control　theory　of　linear　systems　for　the　fast　subsystem.　Numerical　simulations　show　the　feasibility　and　effectiveness　of　the　hybrid　control.　©　2017,　China　Mechanical　Engineering　Magazine　Office.　All　right　reserved.