In　this　paper,　a　kind　of　nonlinear　dynamic　model　of　dual-arm　free-floating　space　robot　systems　is　presented　based　on　Lagrange　method.　Based　on　the　result,　the　control　problem　for　space　manipulator　to　track　the　desired　trajectory　in　joint　workspace　is　discussed.　Because　of　the　high　structure　complexity　and　the　parameter　uncertainty　of　space　manipulator　systems,　the　scheme　of　variable　structure　sliding-mode　control　with　better　robustness　to　uncertainty　and　disturbance　is　proposed.　Fuzzy　controllers　are　designed　at　the　aim　of　chattering　reduction　and　rapid　response.　The　fuzzy　controllers　can　tune　the　sliding　control　law　automatically　according　to　the　relationship　between　system　state　and　switching　manifold.　The　effect　of　the　controller　is　testified　by　computer　simulation.