This article is a summary of a paper presented to the RINA Offshore Group in December 1985. The Authors, of John Brown Offshore Ltd, discuss mooring criteria, and the catenary mooring systems that have been evolved from them, for mobile offshore drilling units (MODUs) and, in particular, for floating production units (FPUs). The FPUs already in service have been converted from drilling units, with very little change in their moorings or in the mooring design philosophy, and a departure from accepted MODU mooring philosophy is needed to meet FPU requirements. The article is presented, in some detail, under the headings: Rules and Regulations; Mathematical Analysis of Catenary Moorings; Design Example; Mooring System Design for Floating Production; Risers; Vessel Excursions; Cable Type; Clump Systems; Optimisation; Extended >into survival conditions of a no-winch clump system<; Costs; Further Analysis. The clump systems referred to are new to the North Sea, but one has been successfully used in the Gulf of Mexico to moor Exxon's Lena guyed tower.