Abstract. The VIRGO superattenuator (SA) is effective in depressing the seismic noise below the thermal noise level above 4 Hz. On the other hand, the residual mirror motion associated to the SA normal modes can saturate the dynamics of the interferometer locking system. This motion is reduced implementing a wideband (DC-5 Hz) multidimensional control (the so called inertial damping) which makes use of both accelerometers and position sensors and of a DSP system. Feedback forces are exerted by coil-magnet actuators on the top of the inverted pendulum. The inertial damping is successful in reducing the mirror motion within the requirements. The results are presented. I INTRODUCTIONThe test mass suspension of the VIRGO detector, the superattenuator (SA) [1], has been designed in order to suppress the seismic noise below the thermal noise level above 4 Hz. The expected residual motion of the mirror is ∼ 10 −18 m √ Hz @4 Hz. At lower frequencies, the residual motion of the mirror is much larger (∼ 0.1 mm RMS), due to the normal modes of the SA (the resonant frequencies of the system are in the range 0.04-2 Hz).To lock the VIRGO interferometer the RMS motion of the suspended mirrors must not exceed 10 −12 m (to avoid the saturation of the read-out electronics). VIRGO locking strategy is based on a hierarchical control: feedback forces can be exerted on 3 points of the SA (inverted pendulum (IP) [2], marionetta and mirror). The control on the 3 points is operated in different ranges of frequency and amplitude. The maximum mirror displacement that can be controlled from the marionetta without injecting noise in the detection band is ∼ 10 µm. Therefore, a damping of the SA normal modes is required for a correct operation of the locking system. An active control of the SA normal modes, using sensors and actuators on 1)