System for stabilizing an offshore horizontal axis wind turbine having a tower, the system comprising: at least one sensor for generating sensor signals representing detected movements of the tower; one or more gyroscopes, each gyroscope having three mutually perpendicular axes: a spinning axis, an input axis and an output axis, and a flywheel rotatable about the spinning axis; a first gyroscope actuator for each gyroscope, said first gyroscope actuator being arranged with its related gyroscope in such a way that this first gyroscope actuator can apply a torque about the input axis of the gyroscope; a second gyroscope actuator for at least one of the gyroscopes, said second gyroscope actuator being arranged with said gyroscope in such a way that this second gyroscope actuator can apply a torque about the output axis of the gyroscope; and a control unit for receiving the sensor signals representing detected movements of the tower, providing at least one of the first gyroscope actuators with suitable control signals for said first gyroscope actuator to apply a torque about the related gyroscope input axis, said torque about the input axis producing a torque about the output axis of the same gyroscope that at least partly dampens the detected movements of the tower, and providing the second gyroscope actuator with suitable control signals for said second gyroscope actuator to apply a torque about its related output axis, said torque about the output axis causing a torque about the input axis of the same gyroscope that at least partly dampens the detected movements of the tower; wherein the control unit is adapted to alternatively provide, depending on the detected movements of the tower, the suitable control signals to the first gyroscope actuator or to the second gyroscope actuator related to the same gyroscope. at least one sensor for generating sensor signals representing detected movements of the tower; one or more gyroscopes, each gyroscope having three mutually perpendicular axes: a spinning axis, an input axis and an output axis, and a flywheel rotatable about the spinning axis; a first gyroscope actuator for each gyroscope, said first gyroscope actuator being arranged with its related gyroscope in such a way that this first gyroscope actuator can apply a torque about the input axis of the gyroscope; a second gyroscope actuator for at least one of the gyroscopes, said second gyroscope actuator being arranged with said gyroscope in such a way that this second gyroscope actuator can apply a torque about the output axis of the gyroscope; and a control unit for receiving the sensor signals representing detected movements of the tower, providing at least one of the first gyroscope actuators with suitable control signals for said first gyroscope actuator to apply a torque about the related gyroscope input axis, said torque about the input axis producing a torque about the output axis of the same gyroscope that at least partly dampens the detected movements of the tower, and providing the second gyroscope actuator with suitable control signals for said second gyroscope actuator to apply a torque about its related output axis, said torque about the output axis causing a torque about the input axis of the same gyroscope that at least partly dampens the detected movements of the tower; wherein the control unit is adapted to alternatively provide, depending on the detected movements of the tower, the suitable control signals to the first gyroscope actuator or to the second gyroscope actuator related to the same gyroscope.