A pair of measuring electrodes comprising a first and a second, preferably in each case sheet-like electrode comprises an insulation layer arranged between said electrodes. One or more nanopores, which extend through said insulation layer as far as said first electrode, the surface of which is at least partially uncovered by said nanopores, are provided in each second electrode. The invention also describes a biosensor comprising a pair of measuring electrodes of this type, an electrochemical cell comprising a biosensor of this type and a process for producing said pair of measuring electrodes.