This diploma thesis presents the implementation of active damping for servohydraulic systems with the example application for a roadheader mining and tunneling machine. At first the basic physical principles of damping are introduced. Then an overview is given of the most important techniques applied in modern hydraulic systems. To establish an algorithm for damping a system, the theory of optimal control was chosen, which offers a very promising approach for the active damping of servohydraulic systems. Two particular methods of the optimal control theory - the Hamiltonian function method and Pontryagin's maximum principle - are explained and then applied using the example of an elementary spring-mass system. The results are compared with the commonly used solution of a speed-proportional friction damper. After this an active damping system based on these methods is developed for the hydraulic system of a roadheader mining and tunneling machine. Finally a discussion of the results is given.