A shape memory actuator is described. The shape memory actuator has a supporting body, a driven element slidably mounted on the supporting body for movement between a stable rest position and a stable operative position, a driving element that drives the driven element, the movement of the driving element being determined by a SMA wire and by first resilient return means acting to return the driving element to the rest position upon deactivation of the SMA wire, second resilient return means acting on the driven element in opposition to the SMA wire, engaging means suitable to achieve at the operative position a reversible engagement between the driven element and the supporting body, either directly or indirectly, said engagement being able to resist the action of second resilient return means, and a control system for the engagement and disengagement of the engaging means.