The nonlinearity in the wind loading expression for a complaint offshore structure, e.g., a tension leg platform (TLP), results in response statistics that deviate from the Gaussian distribution. This paper focuses on the statistical analysis of the response of these structures to random wind loads. The analysis presented here involves a nonlinear system with memory. As an improvement over the commonly used linearization approach, an equivalent statistical quadratization method is presented. The higher-order response cumulants are based on Volterra series. A direct integration scheme and Kac-Siegert technique is utilized to evaluate the response cumulants. Based on the first four cumulants, the response probability density function, crossing rates, and peak value distribution are derived. The results provide a good comparison with simulation. A nonlinear wind gust loading factor based on the derived extreme value distribution of nonlinear wind effects is formulated.