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During offshore installations in harsh sea conditions, the involved crane system must satisfy rigorous requirements in terms of safety and efficiency. The forces resulting from the vertical motion of the vessel have an extensive effect on the overall crane structure and its lifetime. Moreover, vessel motion handicaps the operator during fine positioning of the payload. Hence, an active compensation system for the vertical vessel motion is proposed. An important point to consider for such systems is the time delay between the sensors and actuators, which diminishes performance. To compensate the dead times in the system, a prediction algorithm for the vertical motion of the vessel is proposed in the first part. In the second part, an inversion-based control strategy for the hydraulic-driven winch is formulated that considers the dynamic behavior of the drive system. A feedforward controller compensates the vertical-motion disturbance using the predicted motion. The proposed controller together with the prediction algorithm decouple the motion of the rope-suspended payload from the vessel's motion. The active compensation approach is evaluated with simulation and measurement results.