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The present work addresses functional fatigue of binary NiTi and ternary NiTiCu (with 5, 7.5, and 10 at. pct Cu) shape memory (SM) spring actuators. We study how the alloy composition and processing affect the actuator stability during thermomechanical cycling. Spring lengths and temperatures were monitored and it was found that functional fatigue results in an accumulation of irreversible strain (in austenite and martensite) and in increasing martensite start temperatures. We present phenomenological equations that quantify both phenomena. We show that cyclic actuator stability can be improved by using precycling, subjecting the material to cold work, and adding copper. Adding copper is more attractive than cold work, because it improves cyclic stability without sacrificing the exploitable actuator stroke. Copper reduces the width of the thermal hysteresis and improves geometrical and thermal actuator stability, because it results in a better crystallographic compatibility between the parent and the product phase. There is a good correlation between the width of the thermal hysteresis and the intensity of irrecoverable deformation associated with thermomechanical cycling. We interpret this finding on the basis of a scenario in which dislocations are created during the phase transformations that remain in the microstructure during subsequent cycling. These dislocations facilitate the formation of martensite (increasing martensite start (M_S) temperatures) and account for the accumulation of irreversible strain in martensite and austenite.