- The response of a nonlinear marine riser model to both parametric and external excitation is examined using Markov methods. Moment-closure techniques are used to predict the response of the riser in a random seaway. An approximate nonlinear polynomial representation of the hydrodynamic damping term is developed in order to implement Gaussian and non-Gaussian momentclosure schemes. These methods are applied to solve the case of pure parametric excitation and the results are compared with those obtained using stochastic averaging. It is shown that as the parametric excitation level is varied, the response predictions from different techniques exhibit the same linear trends. However, the non-Gaussian closure scheme provides improved response estimates that are closer to stochastic averaging results. Moment-closure techniques are then extended to consider a riser under combined parametric and external excitation. For a fixed level of parametric excitation, the response statistics are found to vary nonlinearly with external excitation levels. The Gaussian closure scheme is found to overpredict structural response for the case of pure parametric excitation and to underpredict structural response for the case of pure external excitation. ASCE.