This thesis considers the design and evaluation of autopilots for Remotely Operated Underwater Vehicles (ROVs), unmanned submarines used in offshore oil, salvage and military applications. A very comprehensive hydrodynamic model of a ROV produced by the National Maritime Institute, Feltham, Middlesex, is subjected to an extensive verification study. It is concluded that conventional hydrodynamic modelling techniques are very expensive and uncertain and hence any ROV autopilot must be, in some manner, adaptive; that is, independent of 'a priori' knowledge of the vehicle. The theory, implementation and simulated performance of three different adaptive autopilots is presented, based on the NMI model. Two of these systems use multivariable recursive system identification techniques to estimate the performance of the vehicle on-line. These methods are also discussed as an alternative route to ROV models. A summary of the thesis is given along with recommendations for areas which require further study. An appendix is included which describes a series of tank trials at Admiralty Research Establishment (Haslar); one of the goals of these tests was to validate this simulation study.