A device is provided for monitoring an electrical accumulation battery that includes a set of cells connected in series. The device includes means for measuring a current intensity delivered by the battery; means for measuring an electrical voltage between an upstream connection point and a downstream connection point of each cell of the battery; a recorder that records a zero-current electrical voltage between the upstream connection point and the downstream connection point of each cell of the battery; and an electrical resistance estimator configured to periodically estimate an electrical resistance of each cell in the battery, between the upstream connection point and the downstream connection point.