Dynamic stability problems of a two-degree-of-freedom system with bilinear hysteresis damping and subjected to a circulatory force are considered. Steady-state oscillations and critical loads for flutter of the system are investigated using energy considerations and the method of slowly varying parameters. Problems concerning stability limits (limiting values of the critical load) for vanishing hysteresis damping are examined and compared with those found by earlier investigators for vanishing viscous damping. It is shown that, in a circulatory system, small hysteresis damping may have a destabilizing effect similar to linear viscous damping, but the hysteretic model generally yields a satisfactory stability limit as the hysteresis damping effect approaches zero. The viscoelastic model generally leads to unsatisfactory stability limits as the viscous damping effect varies from small values to zero. Thus, the hysteretic model is shown to be more adequate than the viscoelastic model. The study also shows that for some different sets of initial perturbation there may exist two disparate states of steady-state oscillations of the system under the same loading.