It is very important to estimate exactly low-frequency motions in designing mooring systems of floating offshore structures. This paper presents effects of multi-directinal waves upon the low frequency motions and a new calcuation process to obtain the slowly varying forces and motions in multi-directional waves. In the approximate calculation scheme using the far field method, some important components of quadratic transfer function of wave exciting forces are ignored. Thus we directly integrate the 2nd order hydrodynamic pressures on the floating body in order to estimate accurately the 2nd order wave exciting forces in multi-directional waves. With the expression of directional waves clarified in our recent researches, the two rerm Volterra series for the impulse response function is extended to multi-directional waves. Low frequency motions due to slowly varying forces are calculated using our new simulation program in the time domain. We investigate the effects of multi-directional waves on characteristics of surge and sway motions of a semisubmersible.