In this paper two different models for the damping moment to introduce in the roll motion differential equation are considered. They are linear+quadratic and respectively linear+cubic in the roll velocity and contain angle dependent terms. They constitute a generalization of all the models up to now presented in the literature. Approximate analytical solutions describing the roll decay and the forced roll motion are obtained by means of the Bogolyubov-Krylov asymptotic method. The analysis shows that the damping model more suitable cannot be decided based on roll decays only. It is necessary to examine the forced roll behaviour in synchronism and possibly in the other nonlinear resonance regions too. In this connection, a plane of experiments is presented.
