Abstract. One of the classical applications of the SMA is based on the used of the hysteresis cycle associated to the martensitic transformation (classically, described as a first order phase transition) for damping devices. For each application a detailed knowledge of the conditions to be accomplished by the material is absolutely necessary. For the stayed cables in bridges of the Iroise bridge, the oscillation frequencies are 1 and 3 Hz; and the peak to peak oscillation amplitude is close to 10 cm and, also, the SMA works in close contact with the external ambient temperature. In fact, the bridge is a 2*2 lanes free highway situated between Brest and Plougastel (France). The main requirement is related to several days of intense winds or rain associated to strong storms. The conditions imposed to the samples suggest appropriate behavior for, at least, 500000 cycles of working. The experimental analysis, centered in NiTi, is focused in 1) the fatigue life of the samples, 2) the evaluation of the Clausius-Clapeyron coefficient, 3) assuring that the degradation of the material properties remains below a safety limit in the expected time scale of application, 4) modeling the cable behavior to show the positive damping capacity of SMA and 5) studying the applications in semi-realistic scale in the ELSA-JRC (a civil engineering facility in Ispra, Italy) demonstrating the positive effect of the SMA.