An overview of problems associated to strong rolling motions in head seas is presented. In particular the importance of coupling heave and pitch to roll motion is discussed. In this context the appearance of a nonlinear detuning factor induced by the vertical modes is addressed. It is stressed that this is a typical nonlinear characteristic of strong parametric rolling. Distinct tools of analytical and numerical limits are also discussed. In an effort to clarify some aspects, a comparison is made of the limits of stability of a fishing vessel and a container ship. The differences are highlighted and some conclusions are drawn. © 2011 Taylor & Francis Group, London.