The dynamics of the nonlinear motions of compliant offshore structures is analysed with regard to the bandwidth of the stochastic excitation. It appears that there is the possibility of large amplitude and sudden oscillations that can take place through jumps at bifurcations. Since these phenomena, in the interest to the design stage and for the Classification Societies are not properly accounted by current approaches, a deeper stochastic analysis in the narrow band excitation case is proposed.