A method of monitoring a set of meters that are connected to a common remote processor device, the method comprising both first steps performed in each meter for: acquiring primary measurements of a magnitude representative of the occurrence of an anomaly; selecting pertinent measurements from the primary measurements, the pertinent measurements satisfying a pertinence criterion; regularly transmitting the pertinent measurements to the remote processor device; and second steps performed in the remote processor device, for: comparing, for each meter, the pertinent measurements with a detection threshold common to all of the meters of the set of meters in order to attempt detecting an anomaly associated with said meter; and adjusting the detection threshold dynamically as a function of the percentage of meters detected as being associated with an anomaly.