A transition to clean hydrogen energy will not be possible until the issues related to its production, transportation, storage, etc., are adequately resolved. Currently, however, it is possible to use methane-hydrogen mixtures. Natural gas can be transported using a pipeline system with the required pressure being maintained by gas compression stations. This method, however, is affected by some problems too. Compressors emergency stops can be induced by vibrations because in some cases, mechanical methods are not able to reduce the vibration amplitude. As an example, it is known that a gas-dynamic flow effect in labyrinth seals can lead to increased vibrations. This paper presents the numerical simulation of rotor oscillations taking into account a gas-dynamic load. The influence of a transported mixture on the oscillatory process is investigated. Mixtures consisting of methane and hydrogen in various proportions and an air mixture are considered. The results are discussed for various operating pressures and include the rotor motion trajectories and oscillation frequency spectra obtained numerically. It is shown that the gas mixture composition has a significant effect on the oscillations and their occurrence. Hydrogen as a working fluid reduces the vibration amplitude. Operating a compressor with hydrogen leads to a decrease in the resonant frequency, bringing it closer to the operating one. However, the operating pressure at which maximum oscillations are observed depends slightly on the gas mixture composition.