A spinning rotor, mounted on an elastic shaft and containing a symmetrically located cylindrical chamber partially filled with liquid, is assumed to undergo a small whirling motion. In the analysis, rotor unbalance, gravity, and gyroscopic terms are considered negligible, and the liquid motion is taken as being axially uniform. The added liquid produces a lowering of the usual synchronous critical speed. In addition, waves in the liquid layer couple with rotor whirl motion to produce a range of self-excited asynchronous whirl speeds above the critical, similar to those observed for nonsymmetrical solid rotors. Experiments completely corroborate the analytical results.