Abstract: A floating semi-submersible platform is heave stabilized by velocity damping of platform motion. Vertical velocity of the platform is sensed and a force is applied to the platform as a function of and in opposition to the sensed heave velocity. The system may be passive, as by provision of velocity damping in tethering cables. It may be actively hydrostatic by employing variable ballast tanks and water pumps or air pressure for displacement of water, or it may be actively hydrodynamic by employing propellers or rotor blades for thrust generation. By applying a heave opposing force that is proportional to heave velocity, the platform response to waves at the platform resonant period is greatly reduced with exertion of relatively small magnitude opposing forces, whereby the platform may be designed with a considerably smaller resonant period for a given set of expected conditions.