In a method and apparatus for early detection and prediction of damage to assemblies in machine plants, including mobile machine plants, structure-borne sound of the machine system is sensed by a sensor, output as an acceleration signal and analyzed in a digital signal processor. For this purpose, the acceleration signal is first transformed into the frequency domain by means of a fast-Fourier transformation, and the data obtained in this manner are then transformed back into the time domain by means of cepstrum analysis, so that resonance data relating to individual shock pulses (a cepstrum) is obtained in the time domain. This cepstrum is then compared with a reference cepstrum that is selected in accordance with load signals and rotational speed signals for the present operating state in a new machine plant in a storage device. When limiting values are exceeded, the diagnostic signal (in particular information relating to the assembly which is diagnosed as damaged and its predicted remaining service life) are displayed for the user and an emergency operating mode is initiated.