This paper outlines the dynamic behavior of externally excited rotor/stator systems with occasional, partial rubbing conditions. The observed phenomena have one major source of a strong nonlinearity: transition from no contact to contact state between mechanical elements, one of which is rotating, resulting in variable stiffness and damping, impacting, and intermittent involvement of friction. A new model for such a transition (impact) is developed. In case of the contact between rotating and stationary elements, it correlates the local radial and tangential (“super ball”) effects with global behavior of the system. The results of numerical simulations of a simple rotor/stator system based on that model are presented in the form of bifurcation diagrams, rotor lateral vibration time-base waves, and orbits. The vibrational behavior of the system considered is characterized by orderly harmonic and subharmonic responses, as well as by chaotic vibrations. A new result is obtained in case of heavy rub of an anisotropically supported rotor. The system exhibits an additional subharmonic regime of vibration due to the stiffness asymmetry. The correspondence between numerical simulation of that effect and previously obtained experimental data supports the adequacy of the new model of impact.