Structural flexibility is an inherent characteristic of a class of macro-micro manipulators consisting of a rigid micro manipulator mounted on a long-reach (flexible) macro manipulator. Vibrations caused by flexibility make it difficult to achieve accurate control of the end-point of the micro manipulator. In this paper, we develop a control strategy that can be applied to such a system. An experimental test-bed has been developed in which a 6 DOF PUMA 560 manipulator is mounted on a compliant platform. The control strategy consists of a rigid body inverse dynamics controller together with a neural network based strategy for damping out the oscillations due to the flexible base. Experimental results obtained from the test-bed are presented to show the effectiveness of the proposed control scheme.