Abstract: The stable nonsynchronous responses and the stability of motion of a rigid rotor supported on squeeze film damper bearings(SFDB)without a centralizing spring are studied by means of harmonic balance method.The motion of the system is approximately simulated by two coupled second order differential equations.The stable nonsynchronous response at the action point of nonlinear oil film force can be obtained from the periodic solution of the differential equations of motion.With the help of an equivalent linearized model of the oil film force,the equivalent dynamic characteristic coefficients corresponding to the determined motion of the original system are obtained.A new method to analyse the stability of the motion of the equivalent linearized system is put forward in detail according to the theory of small pertubation.It is quite interesting to point out that the derived criterion for the motion stability is simple in form and depends on the equivalent damping coefficients only.A system with 1/2 order subharmonic response is taken as an example to illustrate this method.The calculated results are compared with those of fourth order Runge Kutta method.It is shown that our method has the same accuracy of calculation,but gains an advantage in saving computing time.