The problem of controlling the end-point position of a redundant coarse-fine manipulator is investigated. Such a system typically consists of a coarse robot for approximate positioning and, fastened to the end of it, a fast and accurate fine-motion robotic device. For small motions for which a linearized model of the coarse-fine dynamics is assumed, it is shown that, under mild assumptions, a good disturbance rejection over a wide frequency range of the fine manipulator is sufficient to insure stability and good performance of the coarse-fine redundant manipulator. The fine robot controller can be designed by H/sup infinity / norm minimization, while the coarse robot controller need not be changed. >