AbstractThe sets of differential equations usually used for the description of the low pressure discharges are underconstrained if several species of atoms and of ions and stepwise processes are taken into consideration. Using the equations of continuity, of momentum transfer, and of energy transfer for each species it is shown that, besides known closing statements for these sets of differential equations, additional conditions are necessary. It is found that the following relatively simple condition is sufficient for positive ions. The radial pressure gradient has to be assumed to vanish at least with the third order as the distance from the axis approaches zero. Various simpler and also more accurate and cumbersome approximations describing non‐excited atoms, positive and negative ions are investigated. Under some conditions one can formulate additional boundary conditions at the wall instead of additional conditions on the axi