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The potential offered by the thermo-mechanical properties of shape memory alloys (SMA) in structural engineering applications has been the topic of many research studies during the last two decades. The main issues concern the long-term predictability of the material behaviour and the fatigue lifetime of the macro structural elements (as different from the one of wire segments). The laboratory tests reported in this paper are carried out on bar specimens and they were planned in order to pursue two objectives. First, the creep phenomenon is investigated for two different alloys, a classical Ni-Ti alloy and a Cu-based alloy. The attention is then focused on the Cu-based alloy only and its fatigue characteristics at given temperatures are investigated. Stress and thermal cycles are alternated to detect any path dependency.