The nonlinear response of an ocean system subjected to random excitations can exhibit very complex dynamic behaviors including jump phenomena and coexistence of attractors. In this study, the stochastic system response behavior of a simple (Duffing) oscillator under narrow-band random excitations is first examined in the subharmonic resonance region. A semi-analytical procedure based on the nonlinear response characteristics of the corresponding deterministic system is developed to derive the response transition probabilities within individual attraction domains and among finite attraction domains under the assumptions of stationarity and Markov process. Overall response amplitude probability distributions are obtained by applying the Bayes formula to the two different types of response transition probability distributions. To validate the prediction capability of the semi-analytical method, numerical simulation of the responses of the Duffing system are generated and statistical characteristics of the response behavior are compared with prediction results. It is shown that the semi-analytical procedure provides more accurate predictions than other approximate methods available in the literature. A parametric study on the effects of variations in excitation intensity and degree of narrow-bandedness is conducted. Results confirmed that the nonlinear response characteristics including jump phenomenon and co-existence of attraction domains are preserved under narrow-band random excitations. The semi-analytical prediction method developed above is then applied to analyze the stochastic response behavior of a nonlinear mooring system subjected to random ocean waves. For modeling of the structural system, a nonlinear�� structure, nonlinearly-damped (NSND) model is employed and a reverse multiple�� input/single-output technique is applied to identify the system coefficients. To verify the accuracy and capability of the semi-analytical method in predicting the complex behaviors of the nonlinear mooring system, analytical predictions are compared with experimental results and numerical simulations. System response amplitude probability distributions predicted by the semi-analytical procedure are shown to be in good agreement with experimental and simulation results. / Graduation date: 2001