A method for reducing resonant vibrations and dynamic loads of cranes, whose horizontal and vertical motion of the pay load are controlled by a boom winch controlling the luffing motion of a pivoting boom and a hoist winch controlling the vertical distance between a boom tip and the load. Where the method includes determining the resonance frequencies of the coupled crane boom and load system, either experimentally or theoretically at least from data on inertia of the boom and stiffness of at least a boom rope, a hoist rope, a pedestal and an A-frame. The method further includes automatically generating a damping motion in at least one of said winches, that counteracts dynamic oscillations in the crane, and adding this damping motion to the motion determined by a crane operator.