Experimental study of damping in civil engineering structures was done using smart materials (NiTi SMA). The study is focused on the stayed cables for bridges. The cable oscillations are induced by wind, rain or traffic. The SMA and their solid-solid phase transformation permits effective damping via the hysteresis cycle and the conversion of mechanical work in heat. The analysis of SMA behavior needs to be strictly coherent with the requirements associated to the application. In particular, the high requirement on working cycles induced by a strong storm of 3 or 4 days, the temperature – stress dependence of the phase transformation (via Clausius-Clapeyron equation), the self-heating effects, the SMA creep and the eventual effects of aging (temperature and time) on the transformation temperatures (i.e., atomic order and/or other effects) were studied. The SMA was applied to mitigate the oscillations induced in realistic cables in ELSA (45 m length) with positive results, and in the LCPC facility (50 m length), always with equivalent simulation tests. The experimental examples suggest that the SMA permit an effective reduction of the oscillation amplitudes better than a half. The work is realized in the frame of SMARTeR, one S3T-ESF project their goal is the damping in stayed cables of bridges. For instance, the Iroise bridge in the highway between Brest and Plougastel, France, or eventually in the St. Nazaire bridge in the “Loire Atlantique” near Nantes or other bridges (i.e. the “Viaducs du Boulonnais” in the A16 highway, France).