When a rotor, excited by unbalance, is operating eccentrically within a clearance and in local contact with the stator it behaves as a bilinear oscillator with a natural periodic motion that resembles bouncing. When excited by unbalance at a subcritical rotative speed which is exactly or nearly 1/Nsuper times its natural frequency, the nonlinear system will respond by bouncing at or nearly at its natural frequency, or superharmonically at a frequency exactly Nsuper times the operating speed or forcing frequency. As in supercritical subharmonic response, there is a zone with characteristics of chaotic behavior in the transition zone between any order of superharmonic response and the next highest order of superharmonic response. There is also an intricate pattern of progressive bifurcations of the orbit on entry into this characteristically chaotic region and a reverse progression on exit from this region. The response is a mirror image or reciprocal set of the more thoughly studied supercritical subharmonic response of the same bilinear oscillator system which, when excited by unbalance at a supercritical rotative speed which is exactly or nearly a whole number Nsub times its natural frequency, the nonlinear system will respond by bouncing at exactly or nearly its natural frequency at a frequency exactly 1/Nsub times the operating speed or forcing frequency. Such supercritical subharmonic response is also characterized by the appearance of characteristically chaotic behavior in the transition zone between successive orders of subharmonic response and by patterns of progressive bifurcations of the orbit on entry into and exit from each region of characteristically chaotic response. Various aspects of subcritical superharmonic response are studied in a numerical model of the nonlinear system, and are compared to data taken on the core spool of an aircraft engine gas turbine. The engine data show many of the unique characteristics of response, wave form, and spectral content predicted by the numerical model of the bilinear oscillator when operating at subcritical rotative speed.