Abstract: A mooring apparatus for a semi-submersible oil exploration and drilling rig includes eight drum anchor hoists and winches on which are carried eight wire rope mooring lines. Each of these lines extends up over one of eight head sheaves and vertically down the outside face of the oil rig through a fairleader rotatably mounted with respect to the rig at a bottom submerged portion thereof. A linear line pull machine is mounted to the rig in encompassing relation to each of the vertical runs of mooring line between the head sheave and the fairleader. These eight mooring line assemblies are distributed around the periphery of the rig. Two mooring lines extend at 90.degree. from each other at each corner of the rig.