Abstract: Accurate prediction of wake flows is essential for wind turbine structure design and wind farm layout optimization. This paper investigates floating offshore wind turbines' wake flows induced by the surge, sway, and yaw of platforms by employing the linear stability theory and large-eddy simulations. Perturbations induced by different motions are represented by different circumferential wavenumbers in the stability analysis. The analysis shows that the wake flows are the most unstable when the dimensionless frequency ranges from 0.3 ≤ St ≤ 0.5 for surge motion and 0.2 ≤ St ≤ 0.4 for sway and yaw motions. No apparent amplification is found for low-frequency (St ≤ 0.1) and high-frequency (St ≥ 1.0) disturbances regardless of motion types. The large-eddy simulation confirms the results of the stability analysis. At St = 0.3, the surge motion leads to periodic contraction and expansion of the wake flow, while the other two motions result in lateral meandering that may induce large unsteady loads for downstream turbines. On the other hand, motions at St = 0.1 and St = 1.0 do not lead to apparent large-scale wake motions, yielding negligible unsteady loads for downstream turbines. Consequently, special attention is required to platform motions around St = 0.3 due to their potential hazards on downstream turbines.