Abstract Offshore wind energy is expected to provide a significant contribution to the achievement of the European Renewable Energy targets. One of the main technological issues affecting floating offshore wind turbines concerns generated power fluctuations and structural fatigue caused by sea-wave/platform interactions. This paper presents a fully-coupled aero/hydro/servo-mechanic model for response and control of floating offshore wind turbines in waves, suitable for preliminary design. The wind-turbine is described by a multibody model consisting of rigid bodies (blades and tower) connected by hinges equipped with springs and dampers (for realistic low-frequency simulation). The aerodynamic loads are evaluated through a sectional aerodynamic approach coupled with a wake inflow model. A spar buoy floating structure supports the wind turbine. The hydrodynamic forces are evaluated through a linear frequency-domain potential solver, with the free surface deformation effects included through a reduced-order, state-space model. An optimal controller is identified and applied for rejection of annoying fluctuations of extracted power and structural loads. The developed comprehensive model has been successfully applied to a floating version of the NREL 5 MW wind turbine for stability analysis, as well as for the analysis of uncontrolled and controlled responses to regular and irregular short-crested sea waves. The proposed controller, based on the combined use of blade pitch and generator torque as control variables and the application of an observer for non-measurable aerodynamic and hydrodynamic states estimation, has been demonstrated to be effective in a wide frequency range for alleviation of both generated power fluctuations and vibratory loads.