A method of monitoring the mechanical condition of a machine in which statistically significant measurements on a characteristic signal are made over a period of time which can include interruptions and variations in the operation of the machine giving rise to uncharacteristic signals and the processing of the signal during the statistically significant measurement automatically excludes those parts of the signal associated with interruptions and variations in the operation of the machine. The invention also includes apparatus for carrying out the above method including a preamplifier, adapted to provide output to a further amplifier, adapted to provided output to dynamic enveloping circuitry, adapted to provide an output to an analogue to digital converter, adapted to provide an output to a digital micro-electronic device.