The present paper set out a nonlinear boundary value problem involving the interaction of surface waves with large submerged structures in two dimensions. The problem is solved to second order by a time-stepping procedure on the basis of two alternative methods. Both of these involve the application of Green’s theorem, a Taylor series expansion of variables at the free surface and a perturbation series representation of the pertinent variables. Differences between the two solutions are associated with alternative integral equations applicable to second-order terms. The two second-order solutions are compared with each other and with previous theoretical and experimental results, and their applicability is assessed.