Results of theoretical investigations of the stability characteristics of externally pressurized air journal bearing, of which bearing is synchronously vibrate with respect to rotor, are presented. Linearized perturbation method is used to get the dynamic coefficients of air bearing, and the Routh-Hurwitz criterion is used to obtain stability map. The stability characteristics operating at zero steady-state eccentricity is investigated of various phase difference of bearing to rotor. It is shown that stability of air bearing is greatly influenced by synchronous motion of bearing, there exists optimum phase difference which gives maximum stability threshold.