In the dynamic analysis of a floating structure, coupled analysis refers to a procedure in which the vessel, moorings, and risers are modeled as a whole system, thus allowing for interactions between various system components. Because coupled analysis in the time domain is impractical owing to prohibitive computational costs, a highly efficient frequency domain approach was developed in a previous work, wherein the drag forces are linearized. The study showed that provided the geometric nonlinearity of the moorings/risers is insignificant, which often holds for ultradeepwater systems, the mean-squared responses yielded by the time and frequency domain methods are in close agreement. Practical design is concerned with the extreme response, for which the mean upcrossing rate is a key parameter. Crossing rate analysis based on statistical techniques is complicated as the total response occurs at two timescales, with the low frequency contribution being notably non-Gaussian. Many studies have been devoted to this problem, mainly relying on a technique originating from Kac and Siegert; however, these studies have mostly been confined to a single-degree-of-freedom system. The aim of this work is to apply statistical techniques in conjunction with frequency domain analysis to predict the extreme responses of the coupled system, in particular the modes with a prominent low frequency component. It is found that the crossing rates for surge, sway and yaw thus obtained agree well with those extracted from time domain simulation, whereas the result for roll is less favorable, and the reasons are discussed.