The　optimal　nonholonomic　motion　planning　of　free-floating　space　robot　system　with　dual-arms　is　discussed.　Base　on　the　linear　and　angular　momentum　conservations　of　the　system,　the　system　state　equations　for　control　design　are　established,　so　the　nonholonomic　motion　planning　objective　of　attitude　control　of　space　robot　system　is　translated　as　the　solution　for　a　canonical　nonlinear　control　problem.　The　proposed　optimal　control　scheme　of　the　system　is　studied,　and　an　adaptive　genetic　algorithm　for　computing　approximate　optimal　control　of　the　system　is　developed.　The　proposed　optimal　motion　planning　approach　possesses　the　advantages　which　can　obtain　the　desired　angles　of　the　base＇s　attitude　and　arms＇　joints　only　by　controlling　the　arms＇　joints　motion.　A　planar　free-floating　space　robot　system　with　dual-arms　is　simulated　to　verify　the　proposed　approach.