A new approach to the study of the parametric rolling of ships in a following sea is presented. The new aspect is the consideration of the interference of surge with the roll dynamics. When the waves are long and steep, the oscillatory component of the surge velocity can become large when compared with the mean value. As the oscillatory surge grows in amplitude, it tends also to become asymmetric due to the existence of nonlinearity. The nature of asymmetric surging is such that a ship spends more time on the crests than on the troughs of the waves. This means, however, that the probability of capsize is increased because a ship's roll-restoring capability around the crest is at a minimum. We propose a new second-order differential equation of roll which incorporates automatically the surge effect through appropriate position-dependent coefficients. We explore numerically how this asymmetry in surge influences the build up of parametric rolling. The layout of the stability transition lines of the coupled system was found to be notably different from that of a Mathieu-type system. We pay attention also to the vicinity of surf-riding, where the capsize is more of a ‘pure-loss’ type.