A method is developed for predicting vibration-response characteristics of systems whose configuration changes during operation. A cartesian robot, an example of such a position-dependent system, served as a test case and was studied in detail. The chosen system model was formulated using the technique of Component Mode Synthesis (CMS). The model assumes that the system is slowly varying, and connects the carriages to each other and to the robot structure at the slowly varying connection points. Specific problems addressed in this paper include modeling of continually varying points of connection between components and selection of boundary conditions to represent overconstrained component boundaries. A method for curve-fitting modal data is also presented.