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Today, rotors of high-speed turbochargers are commonly supported by floating ring bearings due to their low costs and reduced power losses. A well known effect of such rotor bearing-systems is the occurrence of self-excited vibrations. In order to study the different nonlinear vibration effects with the methods of numerical continuation, a perfectly balanced flexible turbocharger rotor is considered which is supported by two identical floating ring bearings. Here, the bearing forces are modeled by applying the short bearing theory for both fluid films. After deriving the equations of motion of the turbocharger rotor, bifurcation analyses are carried out with both rigid and flexible model. Thereby, the main focus of the investigation is on the limit-cycle oscillation of higher amplitudes, which may cause rotor damage.In the lower speed range of operation the equilibrium position of the turbocharger rotor becomes unstable by a Hopf bifurcation emerging limit-cycle oscillations. By increasing the rotor speed the limit-cycle may lose its stability by a torus bifurcations leading into an area of quasi-periodic vibrations of the system. Further torus bifurcations, which emanate stable limit-cycles again, and various jump phenomena are also observed. For higher speed ranges a saddle-node bifurcation may occur from which stable limit-cycle oscillations of high amplitudes arise. The rotor speed, where this saddle-node bifurcation takes place, may be defined as a nonlinear critical speed of the turbocharger system supported by floating ring bearings. In the range of the nonlinear critical speed the bifurcation behavior of the turbocharger in floating ring bearings is quite complicated, since a further stable solution coexists beside the critical limit-cycle oscillation. [ABSTRACT FROM AUTHOR]