This paper describes a combined numerical and geometric approach to study the dynamic behavior of a moored semi-submersible based on solutions of the nonlinear differential equation used to model the system. Complex features including competing steady states, subharmonic resonances and chaos are shown to be typical responses in regular seas. A qualitative overview is used to classify the computer data generated from direct time simulation with the aim of illustrating the inadequacies and limitations of a linear or a purely analytical approach.