A set of governing equations for dynamic transverse motions of a cable with small sag is firstly obtained where effects of finite motions of the cable and small support motions are included. Cable motions are separated into two parts; quasi-static motions and modal motions. The quasi-static motions are the displacements of the cable which moves as an elastic tendon due to the support movements. The modal motions are expressed as a combination of the linear undamped modes of a cable with fixed ends. By Lagrange's equations of motion, the governing equations of the non-linear cable motions are obtained, where quadratic as well as cubic non-linear couplings appear. The cable model developed is next applied to a cable-structure system. A global/local mode approach is employed; the total motions are expressed in terms of global and local motions. The local motions are the modal motions of the cable, while the global motions are 3-D motions of the structure which include quasi-static motions of the cables only. The global are expressed as a combination of the eigenmodes computed by 3-D FEM in which cables are treated as tendons. By using Lagrange's formulation, algebraic governing equations are finally obtained in which global-local interaction appears as linear and quadratic couplings. The model for the system is modified to include the actuator motions at the cable supports; the actuator motions are in the cable axis direction. The study shows many possibilities for the control of global and/or local modes.