Abstract : In the present paper, the theory of generation of ground vibrations by moving train is considered. The theory takes into account contribution of each sleeper of the track subjected to the action of all wheel axles. Mechanical properties of the track and parameters of train and soil (including static contact nonlinearity of track-soil system) are taken into account. It is shown that generated ground-vibration spectra depend strongly on the periodicity of track (distance between adjacent sleepers), parameters of the train (train speed, distances between wheel axles and carriages), and on the axle loads of the carriages. A special attention is paid to the ground vibrations generated by superfast trains. It is shown that tremendous increase of vibration level may occur if the train speed exceeds the velocity of Rayleigh surface wave in the ground. Such a situation is not a fantastic one and may really happen, e.g., in the case of TGV trains for which the speeds of 500 km/h have been recently achieved on the experimental track in France. Simple methods of suppression of ground vibrations "on the track" are suggested.