The　tracking　control　for　coordinated　motion　of　a　free-floating　dual-arm　space　robot　system　in　task　space　is　developed.　Aiming　at　the　case　that　external　disturbances　exist　and　system　inertial　parameters　are　unknown,　an　adaptive　tuning　control　scheme　based　on　a　fuzzy　basis　function　(FBF)　network　is　designed.　A　fuzzy　basis　function　network　is　used　to　build　the　unknown　dynamic　model　of　dual-arm　space　robot　and　a　robust　technique　is　applied　to　deal　with　uncertainties　associated　with　modeling　errors　and　external　disturbances.　The　control　scheme　needs　neither　to　linearly　parameterize　the　dynamic　equations　of　the　system,　nor　to　require　a　priori　knowledge　of　system　inertial　parameters.　Meanwhile,　all　weights　and　parameters　of　the　FBF　network　can　be　adaptively　tuned　online　with　a　learning　rule,　and　consequently　the　control　scheme　is　flexible.　Stability　analysis　guarantees　global　stability　and　tracking　performance.　A　simulation　example　illustrates　that　the　proposed　control　scheme　can　effectively　control　the　base＇s　attitude,　and　the　end-effector　of　the　dual-arm　space　robot　is　able　to　track　desired　trajectories　synchronously.