Fixed support structures for offshore wind turbines are commonly used for shallow water (till 45 meters). In many countries shallow-waters are rare. Floating support structures may be the solution for these areas. Many concepts have been developed but three concepts have been analyzed (spar, semi-submergible and the tension leg platform (TLP)) in the literature. This study focuses on the TLP, which has the lowest weight of these concepts but the dynamic system is complex and has significant more risk than the other support structures, for example the risk of resonance of structural elements. The structural integrity of the total structure is important for the tension leg platform wind turbine (TLPWT). This study investigates the modelling techniques of the flexible TLPWT, with the aim to model the dynamics of floating wind turbine correctly. An Aero-hydro-elastic-servo model is implemented in Matlab, which includes aerodynamics of the wind turbine, hydrodynamic loads on the floating structure and mooring system, the flexibility of the total structure and the control system of the wind turbine. This model solves the equation of motion with the Houbolt numerical time integration method. In addition, the validity of the model is confirmed by validation using an Orcaflex model. The model is used to analyze the effect of the gyroscopic moments and the non-harmonic periodic load oscillations on the motion responses. Steel structures are vulnerable to cyclic loading. Small cracks may initiate and grow in the structure, this is called fatigue. Fatigue is stress driven and resonance drives stresses. The fatigue performance can be improved by avoiding resonance of structural elements. A method has been developed to find a design with the natural frequencies outside the wind, wave and passing blade frequencies. The method consists of two algorithms, mode tracking algorithm and the selection algorithm. The method is used for a North-Sea site and the result of this an improved design, which has the natural frequencies outside the frequencies where wave and wind have energy. This design has better dynamic characteristics, which indicate better fatigue performance, in comparison of the reference TLPWT, which is predominantly designed to prevent slack tendons. The approach has shown to be successful but the method can only assist in the preliminary design phase of a TLPWT for any given site.