Abstract: An apparatus for measuring low currents with high dynamics, comprising in series: a multi-range preamplifier, a logarithmic amplifier, a thresholding circuit, an alarm circuit and a reading circuit, the preamplifier comprising in series: a first differential amplifier receiving at its inverting input the low current to be measured and a second amplifier, the first amplifier having a linear feedback chain of very high impedance and the second amplifier having a linear feedback chain of much lower impedence, a zero point adjustment and a circuit for testing the gain of the apparatus being also provided on the first amplifier.