The responses of a spar constrained by slack mooring lines to steep ocean waves and tensions in the mooring lines are simulated using two different numerical schemes: a quasi-static approach (SMACOS) and a coupled dynamic approach (COUPLE). The two approaches are the same in computing wave loads on the structure. Their difference is in modeling dynamic forces of mooring lines; that is the dynamic forces are included in the computation of COUPLE but neglected in SMACOS. The numerical simulation is examined against the laboratory measurements of the JIP Spar in a water depth of 318 m. The dynamic coupling effects between the JIP Spar and its mooring lines in different water depths (318, 618 and 1018 m) are investigated by the comparison of numerical simulations obtained using the quasi-static and coupled dynamic approaches. It is found that the damping of mooring lines reduces the slow-drift surge and pitch of the Spar, especially in deep water. The reduction in the amplitude of slow-drift surge can reach about 10% in a water depth of 1018 m. The tension in mooring lines may greatly increase in the wave frequency range when dynamic forces in mooring lines are considered. The mooring-line tension in the wave frequency range predicted by the coupled dynamic approach can be eight times as great as the corresponding prediction by the quasistatic approach in a water depth of 1018 m. This finding may have important implications for the estimation of the fatigue strength and life span of the mooring lines deployed in deep water oceans.