Shape Memory Alloys (SMA) show particular properties associated to their martensitic transformation between metastable phases. Their use in dampers requires a deep knowledge of the SMA behavior and its coherence with the application requirements. In earthquakes engineering standard conditions require that, after several years or decades at rest, an excellent performance is necessary for one or two minutes, i.e., nearly 200 working oscillations. When the target is the damping of stayed cables in bridges under the wind or rain actions, a larger number of oscillations is expected per each working day. This contribution analyzes the fatigue behavior of a CuAlBe alloy (appropriate for earthquakes) and discusses the results of some available experiments on a NiTi alloy for their eventual application to stayed cables..