Horizontal motions of a tanker single point moored in current, wind, and waves were numerically investigated under four alternative configurations, namely, buoy mooring (SBM), articulated tower mooring (ATM), bow turret mooring (BTM), and internal turret mooring (ITM). The analysis was based on a previously validated, comprehensive mathematical model of the equations of motion in three degrees of freedom (surge, sway, and yaw) that considers five sets of forces: 1) nonlinear quasi-steady hydrodynamic response and control forces; 2) linear memory effects due to radiated waves; 3) nonlinear mooring restoring force characteristics; 4) empirical wind actions; and 5) first-order wave forces and wave drift forces. Locally linearized stability analyses showed that restoring characteristics have no influence on static bifurcations (typical for BTM and ITM) and only minor influence on dynamic bifurcations (typical for SBM and ATM). However, nonlinear time domain simulations revealed that they do affect the form of asymptotic motion trajectories as well as line tension amplitudes. It was found that turret position is a significant parameter and motion behavior is sensitive to the direction of wind and waves relative to current. Comparison of simulated time histories between autonomous and nonautonomous modes indicated that the traditional spectral analysis treating high-frequency and low-frequency responses separately may not be valid for locally unstable cases.