In a packet-switching and/or cell-switching communication network which comprises a plurality of switching nodes and in which the individual switching nodes in the communication network are each allocated a unique identification, eavesdropping measures are provided in order to eavesdrop on at least one data link that has been formed between two communication subscribers, in which case one of the two communication subscribers is identified by means of at least one eavesdropping measure as a communication subscriber to be eavesdropped on. The switching nodes which are intended for activation of eavesdropping measures are each allocated at least one activation database which has the identifications of the switching nodes which are enabled for activation of further eavesdropping measures. In this case, a further eavesdropping measure is activated in the switching node to be eavesdropped on only if the identification of the switching node to be eavesdropped on matches at least one identification which is contained in the activation database.