Abstract: Based on the Hamilton principle, the synchronization/stability characteristic analysis for multi-machine vibration system is theoretically put forward. Then, based on the Lagrange theory and earlier works concerning synchronous stability for 6-DOF multi-machine vibration system, a dynamic model of 12-DOF multi-machine vibration system is developed first and, on the Hamilton principle, it provides the characteristic conditions for synchronous operation and especially the synchronously stable operation. Such a synchronization/stability theory is available to apply widely to segmental vibration screens of multi-machine and multi-screen systems. The analysis result indicated that a segmental vibrating screen system with 3-DOF inertial reversing rotation is available to work synchronously and stably if satisfying certain conditions, thus providing theoretically a reference for the design of those systems.