The invention is a monitoring system for a battery having a plurality of accumulators. The system comprises apparatus for measuring the voltage on the terminals of each accumulator; measuring the temperature of the battery; measuring the current flowing through the battery, calculating a voltage difference between a maximum voltage measured on the terminals of one of the accumulators and a minimum voltage measured on the terminals of one of the accumulators; comparing the voltage difference with at least one threshold value depending on the measured temperature and current, and reporting an error if the voltage difference is greater than or equal to the at least one threshold value.