Abstract: In a method of mooring floating structures a chain receiving device is secured to an anchor and a forerunner chain is extended through the chain receiving device, after which the anchor is secured in engagement with the sea floor. A mooring line is extended between a floating structure and the forerunner chain. A tensioning device on an anchor handling vessel is employed to apply mooring tension to the forerunner chain thereby applying mooring tension to the mooring line secured between the forerunner chain and the floating structure. Mooring tension is maintained by the chain receiving device on the anchor.