Abstract: An offshore floating tower comprises two coaxial cylindrical enclosures (2 and 11) interconnected by continuous radial bulkheads (10) forming in the upper portion a ring of damping chambers (12) and in the lower portion a ring of buoyancy tanks (4) around a bell-shaped chamber (5) which is partially filled with air to produce pneumatic damping of vertical movement of the tower. The upper portion of the tower is separated from the lower portion by a horizontal slab (3). The upper portion of the internal enclosure is perforated in the vicinity of the horizontal slab.