It is posed that angular air-hammer self-excited vibration and half frequency wobble self-excited vibration are two reasons for resulting angular wobble self-excited vibration for gas film face seals. In the stability analysis of this vibration, the influence of different face configuration, stiffness of the springs supporting the floated ring and damping of the secondary seal is resented. On the basis of small linearized distributed perturbation parameter method, the perturbed Reynolds equations of gas film and perturbed motion equations are simultaneously solved and the limits of stability are obtained by a numerical iteration. The adaptable finite element method is used for calculating the dynamic coefficients of gas film for three degrees of freedom-perturbed motions.