A floating structure (1), such as a mooring buoy, moored to the seabed (2) via anchor lines (3,4) that comprise an anchor line section (9,10) which is stretchable in its length direction, such as a polyester line. A water-resistant element (7,8) is connected at or near the upper end of at least one of the stretchable anchor line sections (9,10) for resisting displacement in the length direction of the anchor lines (3,4). Preferably the water-resistance element (7,8) is connected to the floating structure (1) via a substantially non-stretchable anchor line section (5,6), such as chain section. The floating structure (1) can be moored in deep water, and reduces fatigue weakening of the floating structure (1) and of the anchor lines (3,4).