While determining a leak resistance of a subscriber connection line provided, for example, with two wires in a communication network, a capacitor connected between two said wires is discharged prior to measuring leakage currents. For this purpose, prior to be connected to a high resistance of the other wire, the measurable wire and the other mentioned wire are supplied with a constantly falling and increasing voltage. For that, the final value of said tensions is determined in such a way that, when the connection to the high resistance of the other wire is produced, the voltage of said wire is equal to 0 volt. The leakage current is measured only when the discharge process is over, thereby making it possible to avoid an incorrect measurement caused by a current coming from the capacitor.