Shape memory allow (SMA) components can affect vibrations of structures through two mechanisms. The stresses in a SMA element that experiences phase transformations, as a result of vibrations, have an effect on the frequency-amplitude characteristics. In addition, a dissipation of energy due to hysteresis in a SMA element can reduce the natural frequency and affect forced vibrations. The present paper illustrates the mathematical foundations of these concepts. The method of solution of the equation of motion of flexible superelastic SMA dampers is discussed. Potential benefits to vibrating structures associated with a hysteresis in superelastic SMA dampers are illustrated. As follows from the results shown in the paper, the effectiveness of superelastic dampers increases with temperature, as long as the latter remains within the range where the martensite formation is possible.