This paper presents a robust speed controller for 2-mass resonance systems. Torsional vibration can be occurred in such system that a driving motor and a driven load are connected with a flexible long shaft. Torsional torque generating the vibration is compensated with disturbance observer or neural network estimator, which estimates the torsional torque and inertia value by using actual motor torque and speed. The simulation results of the proposed control method based on the neural network estimator are presented to show its effectiveness, especially against the system parameter variations.