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Due to aerodynamic instabilities induced by combination of rain and wind, civil engineering cables are submitted to cyclic loadings during their whole operating life. To prevent them from fatigue issues, internal and external dampers are increasingly used.Recently, innovative damping devices based on Shape Memory Alloys have demonstrated a true efficiency, thanks to their dissipation properties. Indeed, near-equiatomic Nickel-Titanium alloys (NiTi) present an interesting damping capacity due to a solid-solid displacive phase transformation of austenite into martensite. This transformation occurs under thermal and/or mechanical loadings.Two different damping devices embedding NiTi wires are presented in this paper. Both are evaluated ad hoc, using a full-scale vibration cable bench under several loading and environment configurations. The effectiveness of the damping device has been demonstrated. A direct link has been made between the system "cable + damper" vibration response and NiTi behaviour. First, results show that several damping regimes observed during mitigation of the cable vibration amplitude are due to NiTi microstructural changes and phase transformations. Secondly, this paper demonstrates that stiffness and vibration frequency changes are governed by the NiTi stress-strain curve secant stiffness modulus.