In the paper the issues related to identification and control of the drive system with an elastic joint has been presented. The NKF is proposed to provide on-line identification of the mechanical parameters of the two-mass system. The time constants of the shaft and the load machine are estimated simultaneously with high accuracy on the basis of the electromagnetic torque and motor speed. These parameters are used to calculate the gain coefficients of the advanced control structure for the two-mass system. Then the control structure with additional feedbacks, which allows to damp the torsional vibrations of the two-mass system effectively, is introduced. In this case the LKF is applied as an estimator of the non-measurable state variables such as the shaft torque, load speed as well as the load torque. Parameters of the covariance matrices Q and R of both considered estimators are selected using the genetic algorithm with special cost functions. The application of the global optimization technique allows to reach the global solution according to the defined cost function. However, the application of the genetic algorithm is possible only as an off-line process due to a long calculation time. The presented methods are complex and useful of the industrial drive with mechanical elasticity. They allow to ensure the optimal dynamics of the used estimators as well as the whole control structure. The proposed identification and control methods have been examined under simulation and experimental tests. The slight difference between the simulation and experimental results comes from the fact that the additional elements neglected under simulation study such as friction, nonlinear characteristics of the drive exit in the experimental set-up.