This article presents an investigation of a newly discovered motion instability phenomenon for floating wind turbines, first observed in numerical aero-hydro-servo-elastic simulations. The source of instability is identified as antisymmetric aerodynamic stiffness coupling terms in roll and yaw caused by the turbine thrust force. Analytical expressions for the roll–yaw and yaw–roll stiffness coupling terms are derived, using the actuator disk analogy of the rotor plane. It is demonstrated that a two degrees-of-freedom linear equation of motion without explicit external forcing qualitatively captures the instability. Based on this model, an analytical stability criteria is derived. An intuitive physical explanation of the phenomena is provided, considering the energy flow of the system. An important finding is that dissipative forces, in the form of aerodynamic and hydrodynamic damping, are needed to fully explain the observed instability. It is demonstrated, counterintuitively, that increased damping in yaw reduces the stability margin. This is explained by the fact that dissipative forces result in a phase difference between the harmonic roll and yaw motion in the coupled roll–yaw modes.