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This paper first considers the underlying nuclear physics and then explores the potential application of that science to the propulsion of merchant ships. It then examines the options for the exploitation of nuclear technology and considers some of the engineering implications of deploying the technology. Consideration is then given to the application of nuclear propulsion to a series of ship types, including tankers, container ships and cruise vessels. In each case two sizes of ship are chosen, one of fairly conventional size and the other much larger.