Nonlinear coupled responses of a moored spar in random waves with and without colinear currents are investigated in both time and frequency domains. The first and second-order wave forces, added mass and radiation damping, and wave drift damping are calculated from a hydrodynamics software package called WINTCOL. The total wave force time series (or spectra) are then generated in the time (or frequency) domain based on a two-term Volterra series model. The mooring dynamics are solved using the software package WINPOST, which is based on a generalized-coordinate-based finite element method. The mooring lines are attached to the platform through linear and rotational springs and dampers so that various boundary conditions can be modeled using proper spring and damping values. In the time-domain analysis, the nonlinear drag forces on the hull and mooring lines are applied at the instantaneous position. In the frequency-domain analysis, nonlinear drag forces are stochastically linearized, and solutions are obtained by an iterative procedure. The time-domain results are systematically compared with the frequency-domain results.