In the study of ship dynamics the assumption is often made that excitation andresponse are related linearly. This has not been very helpful in the efforts to understand the fundamental aspects of ship motions in extreme environments because the assumption of linearity is often inappropriate there. In recent years, however, thetide seems to have changed as the ideas of nonlinear systems have started to enjoy increased popularity among the scientists of the field. The new potential generated has raised hopes for developing deeper knowledge and explanations about various phenomena of instability whose existence has been known for a long time. Perhaps the best-known success story of the application of the nonlinear methodology in ship dynamics concerns the rolling behaviour of ships in waves: significant new insights have been developed about the mechanism of ship capsize, the most fearful of all types of ship instability. Yet, the influence of nonlinearity on the dynamic response of a ship is not confined only in the roll direction.