The actuator device (1) comprises: - a stationary support structure (2, 3), - a movable member (5) displaceable relative to said structure (2, 3), and - a wire (SMW) of a shape-memory material, which extends in the structure (2, 3) between two anchoring elements (15, 16) and the movable member (5, 6) such that the wire (SMW) shortens when an electric current flows therethrough, causing a displacement of the movable member (5, 6) against the action of a contrast member (8). In the structure (2, 3) there are provided two deflection members (21, 22; 23, 24) disposed along the path of the shape-memory wire (SMW), each one between the movable member (5, 6) and the corresponding anchoring element (15, 16) of the wire (SMW), such as to cause a deflection of the wire (SMW) between each anchoring element (15, 16) and the movable member (5, 6).