The motion response prediction of offshore structures may be carried out using time domain or frequency domain models or model tests. The frequency domain analysis uses the simplified, linearised form of the motion equations and it is very economical. The time domain analysis, unlike frequency domain models, is adequate to deal with non-linearities such as viscous damping and mooring forces, but it requires sophisticated solution techniques and it is expensive to employ. For moored semisubmersibles time domain techniques must be employed since there are strong nonlinearities in the system due to mooring line stiffness and damping and viscous drag forces. In the first part of this paper a time domain model to predict the dynamic response of a semi-submersibles are developed and the effect of thrusters and mooring line damping are incorporated into the time domain model. In the second part time domain simulations are carried out to find the total extreme motions and mooring forces.