A gripper device (16; 30; 56; 90; 120) which is designed so as to be movable along a movement path, and which serves for grasping and holding a workpiece (70) and for moving the workpiece along the movement path, with at least one first contact section (18; 38; 66) which, to produce an operative pairing with the workpiece that effects the gripping or holding action, can be driven relative to a second contact section (20; 40; 68), which first contact section is assigned actuator means (22; 44; 54; 128), which are designed to exert a drive force in reaction to the application of a magnetic field, and which are composed of a magnetic shape-memory alloy material, wherein the actuator means for magnetic interaction are formed, for the application of a magnetic field, with magnetic field generating means that are static at one position of the movement path (52; 80; 86; 88), and/or with magnetic field generating means that are provided so as to be movable independently of the gripper device.