In the positive column of low‐pressure gas discharges, the electron energy distribution can be markedly non‐Maxwellian, in particular in the tail of the distribution at low degrees of ionization. A method is described which enables one to account for large deviations from a Maxwellian distribution when calculating collision rates, energy flow terms, excited‐state densities, and the radiation output. Illustrative examples are given for Cs&sngbnd;Ar, Ar, and Hg&sngbnd;Ar discharges. Possible extensions and applications of the method are briefly discussed. Analytical formulas are derived for (i) the Coulomb relaxation between the electrons and (ii) the cross sections for ionization from excited states.