An analytical theory of two classes of vehicle modes for a multibody, deformable space station is presented: 1) hinges-free modes and 2) hinges-locked modes. Both modes are defined for the space station completely free in space; the former modes refer to free hinges, and the latter to locked hinges. Associated eigenvalue problems and orthogonality properties are developed and used to arrive at concise linear motion equations. The conciseness transpires because, with these vehicle modes, the translational and rotational deformations of an inboard body at a hinge have a simple modal expansion. Modal momental coefficients associated with both classes of modes are formulated. They play a pivotal role in discretization of partial differential equations governing the dynamics. The analysis is general: elastic deformation is three dimensional, structures have arbitrary geometry and obey Hooke's law of elasticity, and hinges are universal joints. The modal coefficients and dynamics of the space station are illustrated, and the pitfalls in using hinges-locked vehicle modes to predict hinges-free response are identified. A continuum formulation of dynamics of the space station with a mobile manipulator is also furnished.