Floating platforms are being deployed and developed further for offshore wind power generation in deep water. Platforms undergo surge and pitch in waves, causing their supported wind turbine to oscillate back and forth. An important input to modelling the platform – and hence hub – motion are the forces, moments and energy dissipation provided by the turbine rotor. Blade-element momentum theory (BEMT) provides a numerically-efficient method of calculating these quantities in steady flow, but its application to an oscillating turbine is largely untested. To test how appropriate a quasi-steady BEMT methodology is for this application, BEMT (with a high-axial-induction-factor correction) is compared with CFD using an actuator-line representation of the NREL 5 MW design, typical of the type of turbine that might be deployed. For simplicity we assume constant rotor speed and pitch angle. The paper demonstrates that, for typical wave periods and onset wind, a quasi-steady BEMT model provides a good descriptionof loads on an oscillating turbine rotor and provides near-identical results to CFD for forces and power dissipation. However, a common time-dependent BEMT variant does not improve predictions in this application, but proves detrimental to power prediction. The paper also derives a simple formula, based on steady-flow load characteristics, to estimate dissipative damping by the rotor.