This paper gives a complete kinetic theory of atomic discharges whatever their parameters. Very high-frequency discharges and high-pressure continuous discharges were studied in an earlier paper by the same authors [J. Plasma Phys. 54, 309 (1995)]; in the present paper we study low-pressure continuous discharges or high-frequency discharges whose parameters satisfy different conditions and therefore cannot be described by the earlier model. Analytical results are applied to a high-frequency argon discharge and to a low-pressure continuous argon discharge. The results are in good agreement with the numerical results of Ferreira and co-workers.