Apparatus for remote monitoring of partial discharge events in electrical apparatus 1 includes one or more sensors 5 for detecting partial discharge pulses in one or more conductors 2 conveying electrical power to the apparatus. A programmed computer 5 analyses measured pulses and discriminates between those originating from the apparatus being monitored and elsewhere. Discrimination is achieved by analysing pulse shape, and by comparing pulses to partial discharge events measured locally to the sensors. The apparatus enables partial discharge events in electrical apparatus to be monitored without having to install sensors at the equipment itself.