A frequently used technological solution of reducing the time varying forces transmitted between the rotor and its casing is represented by application of a flexible suspension with damping devices added to the constraint elements. To achieve their optimum performance their damping effect must be controllable. For this purpose a concept of a hybrid damping device working on the principle of squeezing the layers of normal and magnetorheological oils have been developed. Here in this article, there is investigated influence of the proposed damping element on stabilty of the rotor vibrations induced by its imbalance during the steady state operating regimes. The stability is assessed by the evolutive method which is based on evaluation of eigenvalues of the system linearized in a small neighbourhood of the rotor phase trajectory and calculation of the corresponding damping ratio or logarithmic decrement. and Obsahuje seznam literatury