A method for automatically assessing, with an alternating voltage, the aging of the earth-insulators of rotating machines running on a medium high voltage. The method can be used both when the machine is in operation and when it is switched off and comprises: measuring the amplitude and phase of the linear fundamental sinusoidal component of the current flowing through the insulator, in relation to the applied voltage; measuring the frequencies and amplitudes which characterize the pulse component of said current caused by the partial discharges, and demodulating the pulses according to their frequency components; and measuring the frequency and amplitude of the non-linear component of the current flowing through said insulator.A device for implementing the method on a machine in operation and a device for implementing the method on a machine not in operation are also provided.