Abstract: A method and system are provided for diagnosing the health-condition of engines, in particular internal combustion reciprocating engines, in which the harmonic terms of the Fourier series representation of the engine vibration are correlated with the mechanical state of the engine. In particular, the characteristics of the harmonic components of the Fourier representation are monitored at one or more predetermined frequencies according to at least one first predetermined criterion, and the characteristics of these harmonic components are analysed according to at least one second predetermined criterion to determine the operational state of the engine correlated to the second criterion.