Abstract: Procedure for damping the swing of the load of a crane during the traversing motion of the trolley and/or bridge when the trolley bridge is controlled by a signal which controls the traversing motor. The length of the hoisting rope is determined and used for the calculation of the time of oscillation of the load swing, and when a new speed setting is given, a control signal compensating the swing prevailing at the moment and another control signal changing the speed are generated. From an equation for load swing, the momentary total oscillation generated by previous control actions is determined. The compensating control signal includes a first acceleration reference and a second acceleration reference, or alternatively, suitable unrealized parts of acceleration sequences. The speed change is achieved by giving new acceleration sequences which change the speed to a value corresponding to the new setting without generating oscillation.