As offshore wind turbines are moving further from the coast, floating wind turbines are being considered. These structures need to be able to endure high dynamic loads while remaining as still as possible in order to minimize internal stresses and maximize the efficiency of the turbine. To find ways to combat large responses, the effectiveness of tuned mass dampers (TMDs) and tuned liquid dampers (TLDs) has been widely researched. While both systems have been shown to be effective, these damping systems are being used separately. This thesis investigates the effectiveness of vertical TMDs combined with a TLD by analysing three barge-turbine structures. The first system is the undamped structure, which works as a control. The second system combines vertical TMDs with a TLD. These damping systems are not directly linked. The third system interdependently combines vertical TMDs with a TLD by stacking the damping systems. This makes the TMD displacement determine the shape of the TLD tank, which causes the system to be significantly nonlinear. The analysis of the three systems begins with the development of a program that creates the frequency response function for each of these systems. The basis for these programs is a linear modal analysis. The nonlinearity of the third system is accounted for by Newton iteration. The effectiveness of each damping system is determined by the performance index, which is based on the integral of the frequency response function. The damping parameters of the independent TMD and TLD are optimized. Due to computational difficulties no parameter optimization is performed for the interdependent damping system. In order to judge possible performance improvement for this system, a rough sensitivity study is performed on the damping parameters of this system. The results of the optimization and sensitivity study show that the independently damped system performs best of all three systems when using these particular parameters. The interdependently damped system has unknown damping potential. It is not possible to definitively conclude from this research whether the TMDs and TLD damp more effectively when they work either separately or interdependently. Both damped systems are able to perform better than the undamped system with the correct damping parameters. The developed programs give reasonable frequency response spectra for all three systems. From this it is concluded that the programs of the three systems work as intended, including the nonlinear part.