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The second-order high frequency (HF) radar cross section (RCS) of the ocean surface, normalized to the area of the scattering patch, is derived for the case in which the radar transmitting and receiving antennas are mounted on a swaying platform or barge. The second-order result includes both electromagnetic and hydrodynamic contributions. The derivation for the hydrodynamic patch scatter component, for time pulsed radars, is based on the first-order RCS found in the counterpart of this paper by replacing the first-order ocean wave spectrum with the second-order ocean wave spectrum. The electromagnetic patch scatter development begins with a general expression for the bistatically received second-order electric field in which platform sway is introduced. Based on an assumption that the ocean surface can be described as a Fourier series whose coefficients are random variables, the second-order monostatic RCS is developed. The resulting second-order cross section is found to consist of Bessel functions and no singularity exists in the newly derived electromagnetic coupling coefficient. Simulation results for the new RCS are also provided to indicate the effects of barge motion under a variety of sea states.