Abstract: The parametric and primary resonances of stay cables excited by the vibration of deck of curved cable-stayed bridge are investigated. The mechanical model of a curved cable-stayed beam is firstly established for research on nonlinear dynamic characters of erection and working stages of the curved cable-stayed bridge. Taking into account the effect of nonlinearity caused by the initial sag, the nonlinear dynamical equation of the curved cable-stayed beam is then obtained. The elastic bearing is applied to deal with the joints between the cable and curved beam. The method of multiple scales is applied to the differential governing equations to analyze the parametric and primary resonances of stay cables. The stability of the steady solutions is also studied. Finally, numerical simulation is used to investigate the parametric and primary resonances of stay cables. The time histories of stay cables under different damps and initial conditions are obtained. The results of numerical simulation show that a small scale vibration of the curved beam may stimulate the cable to undergo large scale movements when the frequency and amplitude of the curved beam within certain scale, it threatens the stability and security in the process of construction and working stage of curved cable-stayed bridges.