This paper presents an extension of the corresponding states principle to mixtures of low molecular weight, nonpolar gases at low temperatures. It corrects the corresponding states principle for quantum mechanical effects but neglects any deviation from Maxwell-Boltzmann statistics. A comparison is made between compressibility factors obtained from reduced second-virial coefficients and those obtained from pseudo-critical values. The use of reduced virial coefficients is limited by the fact that there are not enough experimental data to permit extensive correlations of third-virial coefficients. The pseudo-critical expressions derived for higher temperatures are accurate at cryogenic temperatures provided the reference substance chosen has a molecular weight close to that of the mixture as well as a similar molecular shape.