The predictive capability of two-dimensional (2D) fully-nonlinear-potential-flow (FNPF) models of an experimental submerged moored sphere system subjected to waves is examined in this study. The experimental system considered includes both single-degree-of-freedom (SDOF) surge-only and two-degree-of-freedom (2DOF) surge-heave coupled motions, with main sources of nonlinearity from free surface boundary, large geometry, and coupled fluid-structure interaction. The FNPF models that track the nonlinear free-surface boundary exactly hence can accurately model highly nonlinear (nonbreaking) waves. To examine the predictive capability of the approximate 2D models and keep the computational effort manageable, the structural sphere is converted to an equivalent 2D cylinder. Fluid-structure interaction is coupled through an implicit boundary condition enforcing the instantaneous dynamic equilibrium between the fluid and the structure. The numerical models are first calibrated using free-vibration test results and then employed to investigate the wave-excited experimental responses via comparisons of time history and frequency response diagrams. Under monochromatic wave excitations, both SDOF and 2DOF models exhibit complex nonlinear experimental responses including coexistence, harmonics, subharmonics, and superharmonics. It is found that the numerical models can predict the general qualitative nonlinear behavior, harmonic and subharmonic responses as well as bifurcation structure. However, the predictive capability of the models deteriorates for superharmonic resonance possibly due to three-dimensional (3D) effects including diffraction and reflection. To accurately predict the nonlinear behavior of moored sphere motions in the highly sensitive response region, it is recommended that the more computationally intensive 3D numerical models be employed.