In this paper a course-keeping autopilot for a containership designed with fuzzy logic theory is presented. The autopilot control strategy is deduced heuristically by exploiting expert knowledge and is implemented by means of fuzzy logic. In order to facilitate analytical analysis of the closed loop system non-linear control theory is used to guide the choice of control structure. An interpretation in terms of Fourier analysis of the control strategy is given and used in order to improve the performance of the autopilot in different sailing conditions while preserving the grey nature of fuzzy systems. The final autopilot is proved to be locally stable in the Lyapunov sense while a set of simulation results on a non-linear model of a containership shows the viability of the proposed approach. Keywords: Ship motion control, Fuzzy control, Lyapunov stability.