Aviation has to reduce its emission. In the past the improvements of aero engine technology have been achieved by higher turbine inlet temperatures, higher overall pressure ratios, higher bypass ratios and more efficient components. However, these methods hold only limited potential for further improvements. Therefore, research into alternative cycle concepts started. No best solution for future aircraft engines has been identified yet and thus this research continues. As part of this research, the combined cycle engine has been proposed as a new solution. It has been realised that the thermal energy of the exhaust gases is the biggest energy loss in a turbofan engine. The combined cycle engine uses a combination of a conventional turbofan engine and an additional supercritical Brayton cycle to use this exhaust gas heat to produce additional thrust power. A heat exchanger uses the exhaust gases of the main engine as the heat source for the supercritical cycle. Initial investigations showed many difficulties in the application of this cycle and limited potential for fuel burn reduction. This study aims at investigating the behaviour of different combined cycle engine designs to find an optimal design and to be able to estimate the potential of the concept based on this optimal design. To predict the behaviour of the combined cycle engine, a simulation framework has been created and the results have been compared to similar investigations in literature. In addition to this, a gradient based optimization routine has been implemented to be able to optimize the system for the maximum range. With this methodology, the effect of the supercritical cycle operating conditions, the configuration of the main engine, the supercritical working fluid, the supercritical cycle configuration and the heat exchanger design have been investigated. It was found that the behaviour of the system is very non linear. The optimum performance becomes a trade off between the specific fuel consumption and the weight. The operating parameters of the supercritical cycle and the heat exchanger design have the biggest impact on the system performance. The heat exchanger technology plays an important role in enabling good heat exchanger designs in that it limits the minimum size and wall thickness of the heat exchanger tubes. The addition of an inter turbine burner to the main engine was found to be beneficial to the performance of the supercritical cycle and the combined cycle engine as a whole. While a turboshaft configuration of the main engine brings thermodynamic benefits for the combined cycle engine, it causes a higher weight of the heater. Therefore, a turbofan engine is the superior main engine for the combined cycle engine. The combination of a turbofan engine with an inter turbine burner and a simple recuperated supercritical carbon dioxide cycle has been identified as the best configuration of the combined cycle engine. In this configuration, the cooler is placed downstream of the fan of the main engine. The application of this cycle on a Boeing 777ER could increase the range of the aircraft by 0.46 %. With more advanced production techniques for the heat exchangers, a range increase of 2.15 % becomes possible. However, more in depth research has to be performed, to confirm these results.