Nonlinear　dynamic　equations　of　a　free-floating　space　robot　with　two　manipulators　and　a　flexible　end-manipulator　are　established　based　on　Lagrange　and　assumed　mode　methods.　Its　new　global　dynamic　model　in　terms　of　measured　joints　is　derived　by　coordinate　transformation,　and　the　decoupled　control　equations　for　joint　relative　angles　and　elastic　parts　of　the　flexible　manipulator　are　obtained　with　the　model-based　nonlinear　decoupling　feedback　control　method.　Trajectory　tracking　control　of　the　free　floating　space　robot　with　flexible　manipulators　is　discussed,　and　the　numerical　simulation　shows　that　the　proposed　model　transformation　and　control　method　is　efficient　in　trajectory　tracking　control　of　free　floating　space　robot　with　flexible　manipulators.