The stability assessment is an important task in the mechanical design of railway vehicles. For a detailed model of a railway passenger coach, the hunting behavior depending on the running speed, on wheel-rail contact conditions, and on different model configurations is analyzed using two different methods: The path-following method based on a direct computation of limit cycles enables an automatic computation. However, due to the direct computation, which exploits the periodicity of the solution, this method is restricted to strictly periodic behavior. In the brute-force method, an initial disturbance limited to a certain time interval is applied to the model. This method allows the analysis of the behavior independently from the type of the solution, but requires manual intervention. The comparison of the results obtained with both methods shows a good agreement and thereby the reliability of the results and the methods.