In　this　paper,　based　on　Lyapunov　methods,　hierarchical　nonholonomic　path　planning　of　free-floating　dual-arm　space　robot　systems　with　joint　limits　is　discussed.　The　methods　utilize　fully　the　nonholonomic　mechanical　structure　of　space　robot　systems.　With　the　linear　and　angular　momentum　conversation　and　the　Jacobian　matrix,　the　system　state　equations　and　the　control　output　equations　for　control　design　are　established.　And　then　the　primary　Lyapunov　function　and　the　secondary　are　selected.　The　primary　function　insures　the　movement　of　the　end-effectors　from　the　start　point　to　the　desired　point.　The　secondary　ascertains　joint　limit　avoidance.　Combined　the　primary　Lyapunov　function　with　the　secondary,　the　end-effectors　implement　the　specific　movement　and　each　joint　realizes　joint　limit　avoidance.　A　planar　free-floating　dual-arm　space　robot　system　is　simulated　to　verify　the　proposed　methods.