The monitoring device of an electric power supply is supplied by this electric power supply. It comprises a battery (3) forming a secondary power supply and which is triggered in case of outage of the primary power supply. A management circuit monitors the voltage at the terminals of the battery. A comparator compares the measured voltage at the terminals of the battery with first and second threshold values. A management circuit commands flow of a discharge current at the terminals of the battery, by means of a switch and of a counter configured to count a quantity representative of the discharge current. The management circuit can inform the user that the battery is defective according to the value of the counter.