Under influence of current and wind only, tankers moored to SPM Systems (Single Point Moorings) will under unstable conditions describe low-frequency horizontal motions inducing slowly varying forces in the mooring system. In this paper these low frequency large amplitude motions and resulting mooring forces are formulated in a mathematical model for computer simulation. This slowly oscillating system is a part of the total low frequency phenomena. For the total phenomena the slowly varying wave drift forces have to be induced. For the sea condition consisting of wind and current a set of Eulerian equations of motion has been drawn up, which describes the behaviour in three degrees of freedo-m of a ship (surge. sway and yaw), moored by means of a non-linear hawser type system. For the description of the motions, three coupled equations of motion are used. In one set of equations the impulse response function of Cummins has been used to determine the hydrodynamic reaction forces acting on the ship. In another set of equations of motion, use is made of constant coefficients for added mass and potential damping. In both sets of equations the forces due to wind and current are incorporated as non-linear. The equations take into account nonlinear mooring systems, while the exciting forces (current, wind, astern propulsion) may be arbitrary. Both sets of equations are solved in the time domain. The results concern the slowly oscillating motions and mooring forces of a hawser type SPM System in relatively deep water under various system parameters. Results of the computer simulations are compared with model tests.