Purpose <p>The purpose of this paper is the introduction of the operational rule of dual screw in hybrid coordinate and the development of the dual screw mathematical framework in which they may be used in the integarted dynamic modeling of rigid-flexible multibodies.</p> Methods <p>The hybrid coordinate dual screw in this paper is developed based on the dual number representation of a rigid body. We firstly provided a general six-dimensions screw form of vectors and matrices that can directly match the mechanical engineering parameters of a rigid body, to replace the currently three-dimensional dual form. On this basis, the representation and operation of six-dimensional dual screws are extended to n-dimensional space to describe vibration of a flexible body. Hybrid coordinate system is used to establishing a cross dimensional coupling function between n-dimensional vibration and six-dimensional attitude-orbit spiral motion. Specifically, two parameters, dual modes and dual coupling coefficients, are defined in hybrid coordinate dual screw.</p> Results <p>The general dynamic model for the rigid-flexible multibodies is developed based on the small deformation hypothesis, assumption of constant center of mass, and&#xa0;assumption of configuration stability.</p> Conclusion <p>The general dynamic model proposed in this paper can describe the motion envelope of rigid-flexible multibodies for close range relative missions with safety&#xa0;requirements, such as space debris capture, on-orbit services.</p>