The control of coupled torsional and bending vibrations of drillstrings is studied. In the model used the WOB and the TOB are assumed to be functions of the bit rotation. The speed of the rotary table is assumed to be measured and used in feedback control of torsional vibrations. The rotary table speed control usually eliminates stick-slip vibrations, but under certain conditions it may also lead to resonance with respect to bending vibrations. Therefore, the effectiveness of any control strategy can only be assessed by a coupled model, in which both torsional and bending vibrations are being reduced.