A method for analyzing the dynamic behavior of a low‐pressure mercury rare‐gas positive column is presented. An eight‐state scheme analysis for mercury and argon mixture under a non‐Maxwell distribution of electron energy is established. The computing time is shortened by using the two‐temperature model for electron energy distribution which I have developed to give an analytical expression for the non‐Maxwellian distribution. Two‐temperature parametersTtandTbfor the tail and bulk temperature, respectively, are determined from a two‐term Legendre polynomial expansion of the Boltzmann equation. Then a useful empirical result is that the ratiorT=Tt/Tbis a function of a single variable of electron density times electric field strength. By storingrTcalculated as a function of this variable, the electron energy distribution, which should be calculated from the Boltzmann equation at each iteration step of solving the rate equations, is found simply by a table‐looking‐up procedure, whereby the computing time is shortened. The examination of the eight‐state scheme is done by comparing calculated and experimental results, discussing physical processes occurring among the eight states.