AbstractStarting from the Boltzmann equation the moment equations up to the third order for a non‐quasineutral plasma are derived. It is shown that for a non‐quasineutral plasma, in the distinction from the second order set of moment equations, the systems of the first order and of the third order can be closed in a physically reasonable manner by a relatively simple method when near the walls the ion gas has a high drift velocity caused by an electric field. From this follows that in non‐quasineutral plasmas the ion pressure must be neglected in the first order set of equations consisting of the equations of continuity and of momentum transfer. Terms of the first order in the ion pressure related to the electron pressure are taken into consideration for the third order system. In this way one obtains a unified set of differential equations to treat both the quasineutral plasma core and the space charge sheath at the walls jointly taking into account a non‐vanishing ion temperature. This set of equations is applied to the positive column in the free‐fa