The two-axes wrist assembly of the chain-drive system for an industrial robot has a base wrist unit (12) disposed on one side of the robot arm (11). A hollow shaft (13) is fixed at one end thereof to the base wrist unit and is supported at the same end on one side wall of the free end of the robot arm so as to be rotatable about a first axis (.beta.) intersecting the longitudinal axis of the robot arm at right angles. The other end of the hollow shaft is positioned opposite to the inner surface of the other side wall of the free end of the robot arm. A fore wrist unit (16) is supported on the base wrist so as to be rotatable about a second axis (.alpha.) intersecting the first axis at right angles. A through shaft (17) is provided rotatably within and coaxially with the hollow shaft. The fore wrist unit is interlocked with the hollow shaft by a pair of bevel gears (18, 19). A first sprocket (22) is provided on the other end of the hollow shaft coaxially with the same within the free end of the robot arm. A second sprocket (23) is disposed provided on and coaxially with the through shaft adjacent to the first sprocket within the free end of the robot arm. The first and second sprockets engage first an second chains (26, 27) for power transmission, respectively.