This paper examines the stability of the steady-state periodic response of a gear pair system supported by squeeze-film dampers. The steady-state response of the system is obtained by using the hybrid technique of Harmonic Balance Method and Time Collocation. The Fioquet-Liapunov theory is used to perform the stability analysis of the first variation equations with periodic coefficients, which is generated by the perturbation technique. The stability charts on gear mesh stiffness, spin ratio, disk unbalance, gravity, and squeeze-film damper are used to perform parameter studies. The numerical results show that the unstable region always occurs when the spin ratio is near the second coupled mode of the gear pair system. Furthermore, the mesh stiffness has a significant influence on the coupled critical speeds. Therefore, it plays an important role in determining the spin ratio stability range.