In this thesis the extreme values of tension in the mooring lines on Hywind Demo is investigated. Hywind Demo is a floating wind turbine developed by Statoil ASA. The aim of the study is to evaluate the application of the environmental contour line method on the wind turbine. The environmental contour line method will be compared to a full long term analysis of the extreme response. It is expected that a full long term analysis will give a good estimates of the design loads and can be used to calibrate the contour line method. Since the long term analysis is very time demanding for complex non-linear systems it will be very beneficial if good estimates of design loads can be found with the environmental contour line method, which is a simplified less time demanding approach. Both methods requires a rather refined formulation of the environment in case of a joint probability model. An existing environmental model has been adapted to fit measurements from the Hywind Demo location. Numerous 3 hour time domain simulations has been executed as part of the long term analysis. From each time domain simulations extreme values of the response are collected and response surfaces are fitted for the extreme values and the Gumbel coefficients. Based on the response surfaces the design loads can be calculated based on a long term formulation and on the inverse first order reliability method. The environmental model is used to form contour surfaces corresponding to given return periods. By evaluation of the extreme values on the contour surface a design point can be defined for each case. The short term variation is examined in detail at the design point to identify a proper percentile level in the short term distribution corresponding to the design load. It is found that the long term formulation and the first order reliability method gives agreeing results. In addition it is found that the short term variation is small for the tension extrema in the mooring lines. This implies that the design load could be properly estimated by the median value in the short term extreme distribution at the design point. On the other hand by inspecting the mooring line tension's dependence on the wind parameter an inconsistency is found. Consequently important principles of the contour line method are violated. This inconsistency is blamed on the active control system regulating the rotor speed of the turbine. It is based on this concluded that the contour line method is unsuitable for application on Hywind Demo and that it should be used with care on other structures where control systems or for other reasons the load history is not strictly increasing.