The recent research on stability of gas bearing-rotor systems still mostly adopts the same method as in oil-lubricated bearing-rotor systems. The dynamic coefficients of gas bearings in the case that the perturbation frequencies are same as the rotating speed are used to carry out the stability analysis of rotor systems. This method does not contact the frequency characteristics of dynamic stiffness and damping coefficients of gas bearings with the dynamical behaviors of rotor systems. Furthermore, the effects of perturbation frequencies on the stability of systems are not taken into account. In this paper, the dynamic stiffness and damping coefficients of tilting-pad gas bearings are calculated by the partial derivative method. On the base of solution of dynamic coefficients, two computational models are produced for stability analysis on rotor systems supported by tilting-pad gas bearings according to whether the degrees of the freedom of pads tilting motions are included in the equations of motion or not. In the condition of considering the frequency effects of dynamic coefficients of tilting-pad gas bearings, the corresponding eigenvalues of the rigid and first five vibration modes of the system with the working speeds of 8-30 kr/min are computed through iteratively solving the equations of motion of rotor-system by using two computational models, respectively. According to the obtained eigenvalues, the stability of rotor system is analyzed. The results indicate that the eigenvalues and the stability of rotor system obtained by these two computational models are well agreement each other. They all can more accurately analyze the stability of rotor systems supported by tilting-pad gas bearings. This research has important meaning for perfecting the stability analysis method of rotor systems supported by gas bearings.