The　trajectory　tracking　and　flexible　vibration　suppression　of　a　free-floating　double-flexible-arm　space　robot　system　with　joint　torque　output　dead-zone　and　external　disturbance　are　discussed.　Firstly,　the　two　flexible　arms　are　regarded　as　Euler-Bernoulli　beams,　and　the　dynamic　model　of　the　system　is　derived　from　the　second　equations　of　Lagrange,　the　principle　of　momentum　conservation　and　the　assumed　mode　method.　Secondly,　the　system　is　decomposed　into　a　slow-subsystem　that　represents　rigid　motion　and　a　fast-subsystem　that　describes　two　arms　flexible　vibration.　For　the　slow-subsystem,　an　adaptive　dynamic　surface　controller　is　designed.　The　application　of　dynamic　surface　is　adopted　to　avoid　the　computational　expansion.　The　fuzzy　logic　function　is　utilize　to　approximate　the　kinetic　uncertainties　including　the　dead-zone　error　and　external　disturbance.　For　the　fast-subsystem,　the　linear　quadratic　optimal　control　is　used　to　suppress　the　vibration　of　the　two　flexible　arms.　Finally,　computer　simulations　verify　the　effectiveness　of　this　control　approach.　Copyright　©　2018　by　the　International　Astronautical　Federation　(IAF).　All　rights　reserved.