Abstract Turbines, especially turbines supported in hydrodynamic bearings, often exhibit interesting oscillation effects, which result from the bearing nonlinearities. In the present work, an automotive turbocharger rotor is investigated. The rotor of the turbocharger examined here is supported in full-floating ring bearings, which give rise to complex system vibrations. Frequency spectra of run-up measurements, carried out on a hot-gas turbocharger test rig, are presented. The occurring nonlinear effects—self-excited vibrations, oil whirl/whip phenomena, subharmonics, superharmonics, combination frequencies and jump phenomena—are explained in detail with the help of a gyroscopic eigenvalue analysis and by run-up simulations with a multibody model of the rotor/bearing system. The influence of different operating conditions—oil supply pressure, oil supply temperature and rotor imbalance—on the rotor oscillations and the system bifurcations is studied.