In this paper, a new robust control system with the adaptive sliding neuro-fuzzy speed controller for the drive system with the flexible joint is proposed. A model reference adaptive control structure (MRAC) is used in this drive system. The torsional vibrations are successfully suppressed in the control structure with only one basic feedback from the motor speed. The damping ability of the proposed system has been confirmed for a wide range of the system parameters and compared with the other control concepts, like the adaptive PI-type neuro-fuzzy controller and the classical cascade PI structure.