The　joint　motion　robust　control　and　optimal　flexible　vibration　control　of　a　free-floating　two-flexible-link　space　manipulator　based　on　linear　observers　was　discussed.　The　dynamic　model　of　a　free-floating　space　manipulator　with　two　flexible　links　was　established　by　the　momentum　conservation　and　the　Lagrange　equations.　Based　on　singular　perturbation　approach　and　choosing　appropriate　local　coordinate　frame,　a　slow　subsystem　and　a　flexible-link　fast　subsystem　were　obtained.　The　corresponding　controllers　were　proposed　for　the　two　subsystems,　which　was　the　linear　observer　based　robust　slow　subsystem　controller　and　the　linear　observer　based　flexible　link　fast　subsystem　optimal　controller.　Numerical　simulation　demonstrates　the　proposed　control　algorithm＇s　efficiency.　©　2016,　The　Editorial　Board　of　Journal　of　System　Simulation.　All　right　reserved.