Heave Compensation (HC) greatly improves the operability of lifting operations at sea, performed from ships under influence of heave motion. Especially with long cables and heavy payloads, the payload starts moving with larger amplitudes than the ship itself when no HC control is involved. HC aims to decouple the ships vertical motion due to the waves (the heave) with the cable, such that the cable and payload are as unaffected as possible by the heave motion. Several implementations are possible for HC, but in this Thesis only Hybrid Heave Compensation is elaborated. In order to decouple the cable from the ship's motion, the cable is actuated. In this Thesis a heave compensation cylinder is evaluated to control the cable length. This is a set of hydraulic cylinders between two sheaves, with the cable wound around them. Cable dynamics are very important when lifting a payload to deep sea. Cable lengths of up to 3000 m are considered in this Thesis. In contrast to most papers on HC, a lot of effort is put in the cable model, which has proven to be necessary. In most papers, the cable is simulated as a single mass-spring-damper, which has consequently only one resonant frequency. The cable model in this Thesis is based on PDE equations and includes the first twenty resonant modes of the cable and payload. Simulations point out that multiple modes are significantly present in the payload motion and forces in the cable, which indicate that these resonant modes cannot be neglected. The most basic control strategy in HC is feedforward on the heave measurement, which is taken as benchmark. A PID on velocity is added to the feedforward to assist in decoupling the ship from the cable, which is a common control strategy in HC. This controller however causes worse payload movement compared to the benchmark in simulations with long cable lengths. Another control strategy is feedback on the measured force at the top of the cable combined with the feedforward, which performs better than the benchmark. This controller however cannot cope with steady state errors, causing the heave compensation cylinder to drift to it's limits. A better option is to combine the velocity and force feedback in parallel, combined with the feedforward. Two options for balancing between force and velocity feedback are evaluated under different working conditions; the controllers are simulated under multiple cable lengths, payload masses, noise and control delays. It turns out that force feedback combined with a low bandwidth velocity feedback performs best at the different scenarios. This is in comparison to velocity feedback with additional damping from the force PID and the benchmark controller. The parallel PID with emphasis on force feedback performs especially well on damping resonant modes in the cable and payload and limiting force variations. Under the conditions as in this Thesis, the parallel PID controller with emphasis on force feedback is recommended for use in HC control.