Time domain simulations of slow drift motion are compared with model experiments in wave basin. The simulations include various slow motion hydrodynamic forces such as drag coefficient depending on Kc number, time varying wave drift damping, added mass change due to waves etc. as well as second order wave excitation. Most of them are given by slow motion forced oscillation tests in regular waves. The simulation and the model experiments are carried out for two types of floating structures moored in bi-chromatic or irregular waves. They show excellent agreement with the experiments. It is clarified that importance of each slow motion hydrodynamic forces on the slow drift oscillation in irregular waves of a moored floating vessel depends on a type of vessel. Wave drift damping affects significantly the tuned motion amplitude of not only a barge but also a semi-submersible. Added mass change due to waves affects the tuned frequency only for a semi-submersible.