This thesis deals with the physical understanding of the limit-cycleoscillations (LCO) of the AEROSTABIL wing model by means ofcomputational simulations. The LCOs have been measured by Dietzet al. (2003) in the Transonic Windtunnel G ̈ottingen in 2002/2003.Aeroelastic high-fidelity CFD-CSM methods have been developedand applied to simulate these transonic, clean wing LCOs.The aeroelastic methods include a versatile CFD-CSM couplingmethod, CFD mesh deformation with radial basis functions, steadyand unsteady fluid-structure interaction as well as unsteady forcedmotion methods for frequency domain analysis.To find a convincing AEROSTABIL LCO statement the avail-able experimental pressure and acceleration data have been usedto validate the computations. Static aeroelastic investigations arethe starting point: Here the AEROSTABIL model revealed strongprofile cambering. Only a detailed structural model allowed theaccurate prediction of these deformations and the measured staticpressures. An additional experiment including the AEROSTABILwing verified the profile deformations. The accuracy of the resultingstatic pressures is very important to allow the simulation of the un-steady LCO phenomena. Furthermore, the profile cambering mustbe incorporated into the unsteady investigations as well.Flow features at LCO conditions are very challenging for the ap-plied aerodynamic method. The double-shock system plus flow sep-aration could only be predicted with sufficient accuracy by certainturbulence models.The aerodynamically driven LCO could be explained by strongshock movement in the outer wing area. It is revealed that thiseffect leads to a nonlinearly reducing wing excitation with increasingmotion amplitude.Overall, an important scientific contribution of the studies is toshow the potential accuracy of state of the art aeroelastic methods.