The second-order forces acting on a fixed or free-floating two-dimensional body at a free surface are calculated on the basis of the perturbation theory. The first and second-order boundary value problems are solved by the Boundary Element Method (BEM) which includes both boundaries of the body and the free surfaces. The pressure distribution including the quadratic terms of the Bernoulli equation is evaluated from the solution. The hydrodynamic forces acting on the body are obtained by the integration along the instantaneous wetted contour of the body. Finally, motions of the body in waves are determined by the solution of the equation of the motion up to the second order. Experiments are carried out for the diffraction problems of a fixed or free-floating Lewis-form cylinder in steep regular waves. Those results are discussed in comparison with the numerical calculations. The steady heeling angles of the free-floating cylinder in waves are observed in the experiments as are predicted by the calculation.