The assumptions of straightforward moment models advanced to describe the equilibrium positive column in O2discharges are examined in a derivation from first principles. A particular such model employed by others is shown to lead, with the addition of consistent models for ionization, recombination, and mobility, to a nonlinear two‐point characteristic value problem. This problem is shown to have two distinct physically acceptable solutions at certain O2pressures. In one of these solutions, ratios of the number densities of the charged species are constants across the column, while the ratios vary with radial position in the other.