For low-pressure gas discharges a theory is established taking into account excited atoms, in particular metastable atoms, and stepwise ionisation processes. A macroscopic boundary condition for the outward-directed drift velocity of the excited atoms is derived. Using this condition the concentration of metastable atoms can be calculated. At a low degree of ionisation and low gas density the drift considerably reduces the density of the metastables. Saturation of the concentration of the metastables occurs as the electron density is increased. For argon the spatial distributions of the particle densities and of the drift velocities of the metastable atoms and of the charge carriers are calculated. The influence of the metastable atoms and of the stepwise ionisation on the electron temperature is discussed.