In　the　present　paper,　a　nonlinear　dynamic　model　of　free-floating　dual-arm　space　robot　systems　is　presented　based　on　the　Lagrange　method,　and　the　dynamic　model　of　an　object　is　presented　in　terms　of　the　Newton-Euler　method.　Based　on　the　results　and　closed　kinematic　chain　constraints,　the　dynamic　model　of　a　synthetical　system　is　obtained,　and　the　control　problems　for　the　object　to　track　the　desired　trajectory　in　the　workspace　and　adjustment　of　interactive　forces　due　to　the　interaction　between　the　object　and　the　end-effectors　are　discussed.　Because　of　the　high　structure　complexity　and　the　parameter　uncertainty　of　such　systems,　the　scheme　of　variable　structure　sliding-mode　compensation　control　with　better　robustness　to　uncertainty　and　disturbance　is　proposed　to　track　the　desired　trajectory　of　an　object,　and　the　corresponded　scheme　of　internal　force　control　is　proposed　synchronously.　Therefore,　the　object　position　and　internal　forces　can　be　regulated　simultaneously.　The　effect　of　the　controllers　is　testified　by　computer　simulation.