Floating offshore wind turbines offer a means to access wind resources in waters that are too deep for bottom-fixed offshore wind turbines. To operate a floating wind farm, it must be possible to perform maintenance on the turbines. A critical maintenance aspect is the exchange of a major component such as a blade. It involves a lift of a large component to and from the turbine, which is subject to dynamic excitations from environmental loads. Jack-up vessels are used for major component exchanges on bottom-fixed offshore wind turbines, but due to the increased water depth in floating wind farms these types of vessels cannot extend their legs to the seabed and operate. As an alternative, an onsite blade exchange using a turbine mounted crane is considered in this thesis. The lifting dynamics during the operation are studied, as a knowledge gap is identified in this area. A 15 MW floating wind turbine on a tension-leg platform (TLP) is considered as a case study. This type of floater is considered the most difficult to disconnect from its mooring and tow to a port for maintenance using a shore-based crane. The Offshore Self-Climbing Crane (OSCC) from Huisman Equipment is considered as maintenance equipment, which consists of a base docked on the TLP and a lattice structure coupled to the turbine tower, on which a crane is mounted. Due to the mass of the OSCC, the tension in the tendons of the TLP is reduced, which lowers its natural frequencies in surge, sway and yaw and shifts them closer to wind excitation frequencies. The roll and pitch natural frequencies of the TLP are lowered due to the top mass of the crane and the coupling between the bending modes of the lattice and the tower, shifting them closer to wave excitation frequencies. Snap loads in the tendons occur for sea states with wave peak periods near the roll and pitch natural periods at significant wave heights of 2.5 meters and above. Steps of the blade exchange operation are studied. The operability of the installation of the OSCC is found to be limited by vessel motions, while the TLP remains relatively still. Installation of the OSCC is found to be a bottleneck in the blade exchange due to low operability and a limited number of suitable installation vessels. Free-hanging blade installation is not deemed possible, due to low installation operability and the unconstrained yaw mode. The stiffness in yaw resulting from a line-up tool attached to the blade root or yoke is assessed. The low stiffness of the line-up tool at the yoke results in a large response due to crane tip displacements caused by wind-induced motions of the TLP. Placing a line-up tool at the root of the blade results in the highest operability of the blade lifts. Yoke motions during its attachment to the old blade become limiting instead. The design choices of the top crane mass, lattice stiffness and the type of line-up tool are related to the operability of the blade exchange.