The use of shape memory alloy (SMA) wires as passive elements for damping the vibrations of stayed cables requires that the essential conditions of SMA necessary for the application are well established. The specific conditions of the cable define the appropriate characteristics of the damper, such as the length and the number of the NiTi SMA wires. As the stayed cables in bridges remain under forces near 1 MN, the main study is focused on SMA wires of diameter 2.46 mm that produces forces of about 2 kN. With these forces the use of one or several wires only induces minor changes in the stress distribution within the structure. In this work, the requirements for the SMA wires including, for instance, the fracture level, the thermal actions and the convection, are evaluated. Furthermore, several examples of the application of SMA in laboratory facilities and the simulation of the SMA actions in realistic cables are included. The non-linearities of the SMA dampers are visualized by windowed Fourier transform and Morlet wavelets analysis of the oscillating behavior. There is a change of the cable natural frequency during the damping process, the frequency increases as amplitude decreases. From the experimental results obtained in ELSA, JRC, Ispra, Italy, IFSTTAR, Nantes, France, and in the Pavia University, Italy, the general rules for the preparation of the SMA dampers are also outlined.