Spar floating platforms have been largely used for deep water drilling, oil and natural gas production and storage of these fluids. In extreme weather conditions such structures may exhibit a highly nonlinear dynamic behavior. In this paper a 2-DOF model is used to study the heave and pitch coupled response in free and forced vibration. Special attention is given to the determination of the nonlinear vibration modes (NNMs). Non-similar and similar NNMs are obtained analytically by direct application of asymptotic methods and the results show important NNM features such as instability and multiplicity of modes. The NNMs are used to generate reduced order models that consist of 1-DOF nonlinear oscillators. It facilitates the parametric analysis and the derivation of important features of the system such as the frequency-amplitude relation associated to each nonlinear mode and resonance curves. The stability is analyzed by the Floquet theory. Bifurcation diagrams and Mathieu charts are used to identify the unstable regions in the force parameter space. The analytical results show good agreement with the numerical solution obtained by direct integration of the equation of motion.

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