A　robust　joint　motion　control　and　vibration　optimal　control　is　addressed　for　a　free-floating　two-flexible-link　space　manipulator　with　unknown　but　bounded　external　disturbances　and　parameters.　The　dynamic　model　of　a　free-floating　space　manipulator　with　two　flexible　links　is　established　by　the　momentum　conservation　and　the　Lagrange　equations.　Based　on　singular　perturbation　approach　and　choosing　appropriate　local　coordinate　frame,　the　interactions　of　rigid　and　flexible　motion　and　the　interactions　of　flexible　motion　of　the　two　flexible　links　are　decoupled,　and　a　slow　subsystem　and　a　flexible-link　fast　subsystem　are　obtained.　Then　the　corresponding　controllers　are　proposed　for　the　two　subsystems,　which　are　the　augmented　slow　subsystem　controller　and　the　flexible　link　fast　subsystem　optimal　controller.　And　a　composite　controller　is　combined　with　the　two　subsystem　controllers　to　control　the　joint　motion　and　the　flexible　links　vibrations　simultaneously.　Numerical　simulation　demonstrates　the　proposed　control　algorithm＇s　efficiency.　The　virtue　of　this　control　scheme　is　that　the　linear　position,　linear　velocity,　linear　acceleration　of　the　base　needn＇t　be　measured　directly.　©　2016,　Editorial　Office　of　Chinese　Journal　of　Computational　Mechanics.　All　right　reserved.