The stability of a glow discharge in rare‐gas mixtures containing a small fraction of attaching species is examined, using the e‐beam‐sustained KrF laser discharge as a generic example. The stability limit is shown to lie near the peak of the voltage‐current characteristic, while the mode of instability is dependent on external circuit parameters. The calculated maximum discharge voltage is in good agreement with experimental observation over a wide range of e‐beam current densities.