Method for monitoring partial discharges in an electric power transmission system comprising the steps of: - detecting electric pulses emitted from a component of the electric power transmission system; - performing on the detected electrical pulses a battery of a plurality of tests adapted to provide each a result indicative of presence or absence of possible partial discharge activity, said plurality of tests each comprising a set of operations of acquisition and evaluations of the detected electrical pulses, said acquisition and evaluation operations being executed under conditions defined by: ▪ at least 2 test parameters selected from: trigger level, electric pulse amplification gain level, minimum electric pulse amplitude threshold A min, minimum electric pulse phase parameter threshold P min, maximum electric pulse phase parameter threshold P max, test time length T, minimum number of partial discharge pulses threshold M, and ▪ a numerical value of said at least 2 test parameters, the plurality of tests being executed in succession one after the other according to a predefined time sequence and being equal to each other in that they comprise the identical set of operations of acquisition and evaluation, except for the numerical value taken by at least one of said at least 2 test parameters; - repeating said battery of tests during a preset period of time; - analyzing the results obtained by the batteries of tests executed in said preset period of time; and - generating an alarm depending on the outcome of said analysis, in the presence of a variation of the results of the batteries executed during said period of time. - detecting electric pulses emitted from a component of the electric power transmission system; - performing on the detected electrical pulses a battery of a plurality of tests adapted to provide each a result indicative of presence or absence of possible partial discharge activity, said plurality of tests each comprising a set of operations of acquisition and evaluations of the detected electrical pulses, said acquisition and evaluation operations being executed under conditions defined by: ▪ at least 2 test parameters selected from: trigger level, electric pulse amplification gain level, minimum electric pulse amplitude threshold A min, minimum electric pulse phase parameter threshold P min, maximum electric pulse phase parameter threshold P max, test time length T, minimum number of partial discharge pulses threshold M, and ▪ a numerical value of said at least 2 test parameters, the plurality of tests being executed in succession one after the other according to a predefined time sequence and being equal to each other in that they comprise the identical set of operations of acquisition and evaluation, except for the numerical value taken by at least one of said at least 2 test parameters; ▪ at least 2 test parameters selected from: trigger level, electric pulse amplification gain level, minimum electric pulse amplitude threshold A min, minimum electric pulse phase parameter threshold P min, maximum electric pulse phase parameter threshold P max, test time length T, minimum number of partial discharge pulses threshold M, and ▪ a numerical value of said at least 2 test parameters, - repeating said battery of tests during a preset period of time; - analyzing the results obtained by the batteries of tests executed in said preset period of time; and - generating an alarm depending on the outcome of said analysis, in the presence of a variation of the results of the batteries executed during said period of time.