Parametric rolling in head seas is a kind of nonlinear phenomenon that has attracted much attention recently. A third order nonlinear mathematical model that couples heave, roll and pitch motions has been proposed by the Authors. This new model has succeeded in reproducing strong parametric resonance conditions. However, there are some important nonlinear characteristics that have not been completely understood yet. This paper explores the influence of third order nonlinearities as well as the relevance of coupling between the vertical modes and the roll motion in the modeling of parametric resonance in head seas. New derived limits of stability are introduced and discussed. Some relevant dynamical aspects are clarified. The influence of initial conditions on the development of roll amplifications is investigated and the effect of coupled or uncoupled modeling of the roll motion is addressed. Analytical and numerical limits are discussed. © 2007 American Bureau of Shipping.