This two-part paper presents the integration of the free-vortex wake method (FVM) into an aeroelastic framework suitable to model the rotor-wake interactions engendered by floating offshore wind turbine (FOWT) rotors in operation. Part 1 of this paper introduces the numerical development and validation of an aeroelastic framework. Because no experimental aeroelastic benchmarks exist for FOWTs, a series of validation studies are conducted against the rotor aerodynamic and structural performance of the National Renewable Energy Laboratory (NREL) 5-MW reference wind turbine. Part 2 of this paper focuses on the modeling of different aeroelastic operational conditions of FOWTs. Numerical results of the current framework captures consistently the aerodynamic rotor performance, such as power, thrust, and torque of wave-induced pitching FOWTs. In addition, the presented aeroelastic framework captures additional information about the power, thrust, and torque fluctuations due to the out-of-phase blade passing frequency and corresponding blade deflections. The fidelity of the presented framework showcases, for the first time, an FVM-based aeroelastic method capable of carrying out investigations on rotor-wake interactions and relevant aeroelastic phenomena of FOWTs. (C) 2019 Elsevier Ltd. All rights reserved.