The analysis of necessary conditions for autobalancing stability of rotor, which performs spatial oscillations, was carried out in this paper taking into account the influence of unbalance and autobalancer masses. It was found that the using of traditional models, where unbalance and autobalancer masses are assumed small, could lead to significant errors in the dynamics analysis of spatially moving rotor. The influence of this factor leads to the doubling of the critical rotational speeds spectrum. Moreover, the system motion between the split critical frequencies is unstable. There may be one or two onset areas of autobalancing mode motion depending on the dynamic rotor type, its location relative to the supports, the unbalance mass and other system parameters. It was found that rotors, that are long type or close to the spherical type, are the most sensitive to this factor. On the other hand, rotors of the short type are weakly sensitive. It is shown that the most preferred case is when the unbalance and autobalancer location plane passes through the common mass center of the composite rotor. The quantitative criterion is formulated for the necessity of taking into account (or not taking into account) the influence of this factor when analyzing the system dynamics