System for the active and passive stabilization of a vessel (10), such as ships, boats, rigs, barges, platforms and cranes operating in a maritime environment, which vessel (10) is provided with tanks (Ha-d) to provide buoyancy and/or ballast, which tanks (11a-d) are provided with openings (12a-d) in the bottom, which openings (12a-d) are facing the medium in which the vessel (10) is floating. The tanks (11a-d) are independent of each other and the openings (12a-d) are so large that a sufficient volume of fluid can pass without cavitation or other resistance, and the system includes means (13a-d) for supplying fluid to the tanks (11a-d), controlled to counteract the effects of external forces on the movements of the vessel (11). The invention further includes methods for the passive and active stabilization of the vessel by use of the system.