We present a new numerical method for studying the evolution of free and bound waves on the nonlinear ocean surface. The technique, based on a representation due to Watson and West (1975), uses a slope expansion of the velocity potential at the free surface and not an expansion about a reference surface. The numerical scheme is applied to a number of wave and wave train configurations including longwave--shortwave interactions and the three-dimensional instability of waves with finite slope. The results are consistent with those obtained in other studies. One strength of the technique is that it can be applied to a variety of wave train and spectral configurations without modifying the code. ¿ American Geophysical Union 1987