This paper presents the results of analytical, numerical and experimental investigations of a single railway wheelset. Periodic parametric excitation is added to one of the simplest linear mechanical models. This extended model describes, for example, the geometric deviations often experienced on roller rigs. Above a certain critical speed, the stationary running of the wheelset loses its stability. To verify the analytical and numerical results for the critical speed, experiments were carried out on a simple roller rig having a large ratio of the radii of the roller and the railway wheel.