Abstract: The present invention relates to a process for the early detection of a crack in a rotating shaft, particularly in a shaft of a turbo generator used in a power plant. Signals that represent flexural vibrations of the shaft are measured--as a function of the rotational angle, continuously or at time intervals by means of vibration sensors in at least two radial, preferably perpendicular, directions with respect to each other. These signals are transmitted to a signal processor which uses the signals to ascertain the harmonic vibration components with single and/or double and/or triple rotational frequencies and then the processor forms single and/or double and/or triple rotational-frequent vibration orbits by means of a vectorial combination of these vibration components.