When the flow over a submerged, round, upright cylinder, situated in a large ocean, is forced by a train of plane waves, linear theory (Yamamuro, 1981) shows that the response can be abnormally large for certain forcing frequencies. The aim of this paper is to present a weakly nonlinear theory, where wave interactions, arising from the quadratic terms in the free-surface boundary conditions, can yield abnormally large responses. A specific interaction will be considered between a flow at a subharmonic frequency and a flow at the driving frequency. The reason for considering such an interaction derived from a consideration of some experimental results of Barnard, Pritchard and Provis (1981). (Author).