The motion equations of a nonlinear vibrating system are given firstly. The nonlinear stiffness of springs is equivalently linearized as a function of the response of system by the asymptotic method. The synchronization criterion of dual homodromy rotors with eccentric masses is derived theoretically, as well as the stability criterion. It is shown that the phase difference is close to zero during a sub-resonant state, otherwise it approaches π. The nonlinear characteristics of system are discussed numerically. By the comparisons among theory, numeric and simulation, the validity of the theory method used is examined.