A semianalytical method is developed for the stochastic analysis of a nonlinear moored ocean structure subjected to narrow band random waves. The method is then used to investigate the probability distribution of extreme values of the responses. To verify the accuracy and capability of the method in handling complex nonlinear behavior of the nonlinear moored ocean structure, experimental results are employed to calibrate numerical simulations and the resulting probability distributions obtained from the semianalytical method. A nonlinear-structure nonlinearly damped model is employed to model the moored structure considered and the system coefficients are identified through the reverse multiple-input/single-output technique. An examination of the comparisons indicates that the structural response extreme value probability distributions obtained from the semianalytical predictions are quite accurate.