The objectives of the present paper are to develop a powerful numerical method for computing the second-order sum- and difference-frequency responses on a conical floating structure and to clarify the nonlinear effects on the reponses induced by the effects of the cross angles of body and water surface. In the present paper, the second-order sum- and difference-frequency wave forces are obtained from the radiated wave potential of the sum- or difference-frequency and the first-order velocity potentials by using the extended Haskind formula. The effects of the cross angles of body and water surface is considered in the computation. The numerical results for the second-order sum- and difference-frequency responses are compared with the experimental results. The usefulness of the present method and the nonlinear effects are dscussed.