With recent advances in offshore floating wind and wave energy technology, questions have emerged as to whether the two technologies can be combined to reduce their overall levelised cost of energy. In this paper, the potential for combining a floating offshore wind turbine to a point absorbing wave energy converter is investigated. The focus of the investigation is how much power might be produced by a combined floating wind and wave energy converter system, and the resultant changes in motion of the floating wind platform. A model for the combined wave and wind system is developed which uses the standardised NREL OC3 5 MW spar type wind turbine and a cylindrical buoyant actuator (BA), which is attached to the spar via a generic wave power take-off system (modelled as a spring-damper system). Modelling is conducted in the frequency domain and the tests span a wide range of parameters, such as wave conditions, BA sizes, and power take-off coupling arrangements. It is found that the optimal (with respect to power production) BA size is a draft and radius of approximately 14 m. It is found that this BA can theoretically produce power in the range of 0.3 to 0.5 MW for waves with a significant wave height of 2 m, and has the potential to produce power greater or near to 1 MW for waves with a significant wave height of at least 3 m. However, it is also found that, in terms of the relative capture width, significantly smaller BAs are optimal, and that these smaller BA sizes less significantly alter the motion of the floating wind platform.