The design of a floating wind turbine (FWT) should satisfy the serviceability limit state (SLS) requirement for an efficient and safe operation throughout the entire work life. The SLS requirements are introduced by the owner/developer of the wind turbine facility to achieve production of power or an efficient operation of the facility or a first step towards ensuring safety. Currently, there are limited information about SLS requirements in design standards. This study deals with an assessment of current methods, criteria and procedure for the SLS design check with an emphasis on tilt/pitch and nacelle accelerations in view of power production and its fluctuations. Moreover, other criteria, on the borderline between serviceability and safety criteria, e.g. relating to clearance, are briefly discussed. The criteria relating to power production are illustrated in a case study with a 10-MW semi-submersible FWT considered for an offshore site in the Northern North Sea. Static and dynamic analysis in terms of serviceability are presented, discussed and applied in the case study. A good understanding of wind turbine dynamic performance associated with serviceability is essential to facilitate design decision-making. The relative contribution of wind and wave loads to the different SLS criteria is investigated. Finally, the main conclusions are summarized. I lieu of the current state of the art regarding SLS requirements for FWTs, we hope that this study provides a basis for improving design standards and guiding research and engineering practice for the semi-submersible floater design of FWTs.