Control　of　coordinated　motion　between　the　base　attitude　and　the　arm　joints　of　a　free-floating　dual-arm　space　robot　with　uncertain　parameters　is　discussed.　By　combining　the　relation　of　system　linear　momentum　conversation　with　the　Lagrangian　approach,　the　dynamic　equation　of　a　robot　is　established.　Based　on　the　above　results,　the　free-floating　dual-arm　space　robot　system　is　modeled　with　RBF　neural　networks,　the　GL　matrix　and　its　product　operator.　With　all　uncertain　inertial　system　parameters,　an　adaptive　RBF　neural　network　control　scheme　is　developed　for　coordinated　motion　between　the　base　attitude　and　the　arm　joints.　The　proposed　scheme　does　not　need　linear　parameterization　of　the　dynamic　equation　of　the　system　and　any　accurate　prior-knowledge　of　the　actual　inertial　parameters.　Also　it　does　not　need　to　train　the　neural　network　offline　so　that　it　would　present　real-time　and　online　applications.　A　planar　free-floating　dual-arm　space　robot　is　simulated　to　show　feasibility　of　the　proposed　scheme.