© 2016 Elsevier Ltd. The complexity of the dynamic response of offshore marine structures requires advanced simulations tools for the accurate assessment of the seakeeping behaviour of these devices. The aim of this work is to present a new time-domain model for solving the dynamics of moored floating marine devices, specifically offshore wind turbines, subjected to non-linear environmental loads. The paper first introduces the formulation of the second-order wave radiation-diffraction solver, designed for calculating the wave-floater interaction. Then, the solver of the mooring dynamics, based on a non-linear Finite Element Method (FEM) approach, is presented. Next, the procedure developed for coupling the floater dynamics model with the mooring model is described. Some validation examples of the developed models, and comparisons among different mooring approaches, are presented. Finally, a study of the OC3 floating wind turbine concept is performed to analyze the influence of the mooring model in the dynamics of the platform and the tension in the mooring lines. The work comes to the conclusion that the coupling of a dynamic mooring model along with a second-order wave radiation-diffraction solver can offer realistic predictions of the floating wind turbine performance.