PCT No. PCT/NO96/00279 Sec. 371 Date Dec. 16, 1998 Sec. 102(e) Date Dec. 16, 1998 PCT Filed Nov. 26, 1996 PCT Pub. No. WO97/20729 PCT Pub. Date Jun. 12, 1997A dampening device for dampening the vertical wave-induced motion component of a floating structure. The dampener projects in the form of a skirt down below the bottom of the floating structure (11) and consists of a plurality of channels (47) which extend substantially horizontally and converge from an inlet opening (27, 28, 36, 37, 38) to an outlet opening (16, 46) leading away from the floating structure (11). When the structure (11) moves downwards water is forced from the underside through the channels (47) and creates a jet effect which acts with dampening effect on the vertical motion of the structure. The dampening device may also be made in the form of an outwardly projecting skirt on the floating structure and consist of a plurality of channels (17), where a number of first passages (27, 28) extend in a substantially vertical direction and merge into a number of second passages (29) which extend in an at least substantially horizontal direction, and thereby force the water from a substantially vertical direction of motion, through the first passages (27, 28), into a horizontal direction of motion through the second passages (29) during a part of the passage through the dampener (12). A combination of the two dampeners, in that the dampener (12) is located immediately above the dampener (13) is also possible.