A robot arm drive apparatus of an industrial robot comprising: an electric motor (2) having a drive shaft (7); a first robot member (5) having the electric motor mounted thereon: a second robot member rotatably supported on the first robot member; and reduction gear means (3), for reducing rotation of the electric motor and then transmitting to the second robot member. The reduction gear means comprises a primary reduction gear (20) for reducing the rotation of the electric motor and a secondary, planetary reduction gear (21) for further reducing rotation of output of the primary reduction gear. The primary reduction gear has a reduction ratio so that the maximum number of rotations of the electric motor is reduced less than the characteristic torsion frequency of the drive system. The secondary reduction gear comprises an eccentric input shaft (30) connected with the primary reduction gear, an external gear (29a, 29b) which is rotatable eccentrically in response to rotation of the input shaft, an internal gear (28) held in mesh with and larger In number of teeth than the external gear by one, and carrier means (44) held in engagement with the external gear, said carrier means being connected to an output shaft (10) of the reduction gear means.