High-precision measurements of the quantized Hall resistance and the theories for the quantum Hall effect (QHE) suggest that the quantized value depends exclusively on fundamental constants and can be used as “mises en practique” for a realization of the electrical resistance in a new International System of Units (new SI). Such a new SI will be based on fixed values for fundamental physical constants or properties of atoms. Together with a similar application of the Josephson effect all electrical units could be realized with a much higher precision than in the present SI system. In addition high-precision realizations of the units ampere, farad, henry, coulomb, and watt with connections to the kilogram via the watt balance will be possible. In such a new SI system the conventional values of the von Klitzing constant and the Josephson constant which are used to maintain a worldwide uniformity of electrical units outside the official SI units become obsolete and the permittivity μ₀ of vacuum has to be determined experimentally.